Updates to arithmetic verification.

4 files changed, 452 insertions, 9 deletions

diff --git a/src/proof/acec/acecInt.h b/src/proof/acec/acecInt.h
index c0d899e1..0dc3f706 100644
--- a/src/proof/acec/acecInt.h
+++ b/src/proof/acec/acecInt.h
@@ -70,6 +70,8 @@ struct Acec_Box_t_
 /*=== acecCo.c ========================================================*/
 extern Vec_Int_t *   Gia_PolynCoreOrder( Gia_Man_t * pGia, Vec_Int_t * vAdds, Vec_Int_t * vAddCos, Vec_Int_t ** pvIns, Vec_Int_t ** pvOuts );
 extern Vec_Wec_t *   Gia_PolynCoreOrderArray( Gia_Man_t * pGia, Vec_Int_t * vAdds, Vec_Int_t * vRootBoxes );
+/*=== acecMult.c ========================================================*/
+extern Vec_Int_t *   Acec_MultDetectInputs( Gia_Man_t * p, Vec_Wec_t * vLeafLits, Vec_Wec_t * vRootLits );
 /*=== acecNorm.c ========================================================*/
 extern Gia_Man_t *   Acec_InsertBox( Acec_Box_t * pBox, int fAll );
 /*=== acecTree.c ========================================================*/
diff --git a/src/proof/acec/acecMult.c b/src/proof/acec/acecMult.c
new file mode 100644
index 00000000..397f6d57
--- /dev/null
+++ b/src/proof/acec/acecMult.c
@@ -0,0 +1,432 @@
+/**CFile****************************************************************
+
+  FileName    [acecMult.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [CEC for arithmetic circuits.]
+
+  Synopsis    [Multiplier.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - June 20, 2005.]
+
+  Revision    [$Id: acecMult.c,v 1.00 2005/06/20 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "acecInt.h"
+#include "misc/extra/extra.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+unsigned s_Classes4a[96] = {
+    0xD728, 0xB748, 0x9F60, 0xD278, 0xB478, 0x96F0, 0xC66C, 0x96CC, 0x9C6C, 0x96AA, 0xA66A, 0x9A6A,
+    0x28D7, 0x48B7, 0x609F, 0x2D87, 0x4B87, 0x690F, 0x3993, 0x6933, 0x6393, 0x6955, 0x5995, 0x6595,
+    0xEB14, 0xED12, 0xF906, 0xE1B4, 0xE1D2, 0xF096, 0xC99C, 0xCC96, 0xC9C6, 0xAA96, 0xA99A, 0xA9A6,
+    0x14EB, 0x12ED, 0x06F9, 0x1E4B, 0x1E2D, 0x0F69, 0x3663, 0x3369, 0x3639, 0x5569, 0x5665, 0x5659,
+    0x7D82, 0x7B84, 0x6F90, 0x78D2, 0x78B4, 0x69F0, 0x6CC6, 0x69CC, 0x6C9C, 0x69AA, 0x6AA6, 0x6A9A,
+    0x827D, 0x847B, 0x906F, 0x872D, 0x874B, 0x960F, 0x9339, 0x9633, 0x9363, 0x9655, 0x9559, 0x9565,
+    0xBE41, 0xDE21, 0xF609, 0xB4E1, 0xD2E1, 0xF069, 0x9CC9, 0xCC69, 0xC6C9, 0xAA69, 0x9AA9, 0xA6A9,
+    0x41BE, 0x21DE, 0x09F6, 0x4B1E, 0x2D1E, 0x0F96, 0x6336, 0x3396, 0x3936, 0x5596, 0x6556, 0x5956
+};
+
+unsigned s_Classes4b[384] = {
+    0x35C0, 0x53A0, 0x1DC0, 0x4788, 0x2788, 0x1BA0, 0x3C50, 0x5A30, 0x1CD0, 0x4878, 0x2878, 0x1AB0,
+    0x34C4, 0x606C, 0x3C44, 0x660C, 0x268C, 0x286C, 0x606A, 0x52A2, 0x486A, 0x468A, 0x660A, 0x5A22,
+    0x3AC0, 0x5CA0, 0x2EC0, 0x7488, 0x7288, 0x4EA0, 0x3CA0, 0x5AC0, 0x2CE0, 0x7848, 0x7828, 0x4AE0,
+    0x38C8, 0x6C60, 0x3C88, 0x66C0, 0x62C8, 0x6C28, 0x6A60, 0x58A8, 0x6A48, 0x64A8, 0x66A0, 0x5A88,
+    0xC530, 0xA350, 0xD10C, 0x8B44, 0x8D22, 0xB10A, 0xC350, 0xA530, 0xD01C, 0x84B4, 0x82D2, 0xB01A,
+    0xC434, 0x909C, 0xC344, 0x990C, 0x8C26, 0x82C6, 0x909A, 0xA252, 0x84A6, 0x8A46, 0x990A, 0xA522,
+    0xCA30, 0xAC50, 0xE20C, 0xB844, 0xD822, 0xE40A, 0xC3A0, 0xA5C0, 0xE02C, 0xB484, 0xD282, 0xE04A,
+    0xC838, 0x9C90, 0xC388, 0x99C0, 0xC862, 0xC682, 0x9A90, 0xA858, 0xA684, 0xA864, 0x99A0, 0xA588,
+    0x530C, 0x350A, 0x4730, 0x1D22, 0x1B44, 0x2750, 0x503C, 0x305A, 0x4370, 0x12D2, 0x14B4, 0x2570,
+    0x434C, 0x06C6, 0x443C, 0x0C66, 0x194C, 0x149C, 0x06A6, 0x252A, 0x129A, 0x192A, 0x0A66, 0x225A,
+    0xA30C, 0xC50A, 0x8B30, 0xD122, 0xB144, 0x8D50, 0xA03C, 0xC05A, 0x83B0, 0xD212, 0xB414, 0x85D0,
+    0x838C, 0xC606, 0x883C, 0xC066, 0x91C4, 0x9C14, 0xA606, 0x858A, 0x9A12, 0x91A2, 0xA066, 0x885A,
+    0x5C03, 0x3A05, 0x7403, 0x2E11, 0x4E11, 0x7205, 0x50C3, 0x30A5, 0x7043, 0x21E1, 0x41E1, 0x7025,
+    0x4C43, 0x09C9, 0x44C3, 0x0C99, 0x4C19, 0x41C9, 0x09A9, 0x2A25, 0x21A9, 0x2A19, 0x0A99, 0x22A5,
+    0xAC03, 0xCA05, 0xB803, 0xE211, 0xE411, 0xD805, 0xA0C3, 0xC0A5, 0xB083, 0xE121, 0xE141, 0xD085,
+    0x8C83, 0xC909, 0x88C3, 0xC099, 0xC491, 0xC941, 0xA909, 0x8A85, 0xA921, 0xA291, 0xA099, 0x88A5,
+    0xC035, 0xA053, 0xC01D, 0x8847, 0x8827, 0xA01B, 0xC305, 0xA503, 0xC10D, 0x8487, 0x8287, 0xA10B,
+    0xC131, 0x9093, 0xC311, 0x9903, 0x8923, 0x8293, 0x9095, 0xA151, 0x8495, 0x8945, 0x9905, 0xA511,
+    0xC03A, 0xA05C, 0xC02E, 0x8874, 0x8872, 0xA04E, 0xC30A, 0xA50C, 0xC20E, 0x8784, 0x8782, 0xA40E,
+    0xC232, 0x9390, 0xC322, 0x9930, 0x9832, 0x9382, 0x9590, 0xA454, 0x9584, 0x9854, 0x9950, 0xA544,
+    0x30C5, 0x50A3, 0x0CD1, 0x448B, 0x228D, 0x0AB1, 0x3C05, 0x5A03, 0x0DC1, 0x484B, 0x282D, 0x0BA1,
+    0x31C1, 0x6063, 0x3C11, 0x6603, 0x2389, 0x2839, 0x6065, 0x51A1, 0x4859, 0x4589, 0x6605, 0x5A11,
+    0x30CA, 0x50AC, 0x0CE2, 0x44B8, 0x22D8, 0x0AE4, 0x3C0A, 0x5A0C, 0x0EC2, 0x4B48, 0x2D28, 0x0EA4,
+    0x32C2, 0x6360, 0x3C22, 0x6630, 0x3298, 0x3928, 0x6560, 0x54A4, 0x5948, 0x5498, 0x6650, 0x5A44,
+    0x0C53, 0x0A35, 0x3047, 0x221D, 0x441B, 0x5027, 0x05C3, 0x03A5, 0x3407, 0x212D, 0x414B, 0x5207,
+    0x1C13, 0x0939, 0x11C3, 0x0399, 0x4613, 0x4163, 0x0959, 0x1A15, 0x2165, 0x2615, 0x0599, 0x11A5,
+    0x0CA3, 0x0AC5, 0x308B, 0x22D1, 0x44B1, 0x508D, 0x0AC3, 0x0CA5, 0x380B, 0x2D21, 0x4B41, 0x580D,
+    0x2C23, 0x3909, 0x22C3, 0x3099, 0x6431, 0x6341, 0x5909, 0x4A45, 0x6521, 0x6251, 0x5099, 0x44A5,
+    0x035C, 0x053A, 0x0374, 0x112E, 0x114E, 0x0572, 0x053C, 0x035A, 0x0734, 0x121E, 0x141E, 0x0752,
+    0x131C, 0x0636, 0x113C, 0x0366, 0x1346, 0x1436, 0x0656, 0x151A, 0x1256, 0x1526, 0x0566, 0x115A,
+    0x03AC, 0x05CA, 0x03B8, 0x11E2, 0x11E4, 0x05D8, 0x0A3C, 0x0C5A, 0x0B38, 0x1E12, 0x1E14, 0x0D58,
+    0x232C, 0x3606, 0x223C, 0x3066, 0x3164, 0x3614, 0x5606, 0x454A, 0x5612, 0x5162, 0x5066, 0x445A
+};
+
+unsigned s_Classes4c[768] = {
+    0x35C0, 0x53A0, 0x1DC0, 0x4788, 0x2788, 0x1BA0, 0x3C50, 0x5A30, 0x1CD0, 0x4878, 0x2878, 0x1AB0,
+    0x34C4, 0x606C, 0x3C44, 0x660C, 0x268C, 0x286C, 0x606A, 0x52A2, 0x486A, 0x468A, 0x660A, 0x5A22,
+    0xCA3F, 0xAC5F, 0xE23F, 0xB877, 0xD877, 0xE45F, 0xC3AF, 0xA5CF, 0xE32F, 0xB787, 0xD787, 0xE54F,
+    0xCB3B, 0x9F93, 0xC3BB, 0x99F3, 0xD973, 0xD793, 0x9F95, 0xAD5D, 0xB795, 0xB975, 0x99F5, 0xA5DD,
+    0x3AC0, 0x5CA0, 0x2EC0, 0x7488, 0x7288, 0x4EA0, 0x3CA0, 0x5AC0, 0x2CE0, 0x7848, 0x7828, 0x4AE0,
+    0x38C8, 0x6C60, 0x3C88, 0x66C0, 0x62C8, 0x6C28, 0x6A60, 0x58A8, 0x6A48, 0x64A8, 0x66A0, 0x5A88,
+    0xC53F, 0xA35F, 0xD13F, 0x8B77, 0x8D77, 0xB15F, 0xC35F, 0xA53F, 0xD31F, 0x87B7, 0x87D7, 0xB51F,
+    0xC737, 0x939F, 0xC377, 0x993F, 0x9D37, 0x93D7, 0x959F, 0xA757, 0x95B7, 0x9B57, 0x995F, 0xA577,
+    0xC530, 0xA350, 0xD10C, 0x8B44, 0x8D22, 0xB10A, 0xC350, 0xA530, 0xD01C, 0x84B4, 0x82D2, 0xB01A,
+    0xC434, 0x909C, 0xC344, 0x990C, 0x8C26, 0x82C6, 0x909A, 0xA252, 0x84A6, 0x8A46, 0x990A, 0xA522,
+    0x3ACF, 0x5CAF, 0x2EF3, 0x74BB, 0x72DD, 0x4EF5, 0x3CAF, 0x5ACF, 0x2FE3, 0x7B4B, 0x7D2D, 0x4FE5,
+    0x3BCB, 0x6F63, 0x3CBB, 0x66F3, 0x73D9, 0x7D39, 0x6F65, 0x5DAD, 0x7B59, 0x75B9, 0x66F5, 0x5ADD,
+    0xCA30, 0xAC50, 0xE20C, 0xB844, 0xD822, 0xE40A, 0xC3A0, 0xA5C0, 0xE02C, 0xB484, 0xD282, 0xE04A,
+    0xC838, 0x9C90, 0xC388, 0x99C0, 0xC862, 0xC682, 0x9A90, 0xA858, 0xA684, 0xA864, 0x99A0, 0xA588,
+    0x35CF, 0x53AF, 0x1DF3, 0x47BB, 0x27DD, 0x1BF5, 0x3C5F, 0x5A3F, 0x1FD3, 0x4B7B, 0x2D7D, 0x1FB5,
+    0x37C7, 0x636F, 0x3C77, 0x663F, 0x379D, 0x397D, 0x656F, 0x57A7, 0x597B, 0x579B, 0x665F, 0x5A77,
+    0x530C, 0x350A, 0x4730, 0x1D22, 0x1B44, 0x2750, 0x503C, 0x305A, 0x4370, 0x12D2, 0x14B4, 0x2570,
+    0x434C, 0x06C6, 0x443C, 0x0C66, 0x194C, 0x149C, 0x06A6, 0x252A, 0x129A, 0x192A, 0x0A66, 0x225A,
+    0xACF3, 0xCAF5, 0xB8CF, 0xE2DD, 0xE4BB, 0xD8AF, 0xAFC3, 0xCFA5, 0xBC8F, 0xED2D, 0xEB4B, 0xDA8F,
+    0xBCB3, 0xF939, 0xBBC3, 0xF399, 0xE6B3, 0xEB63, 0xF959, 0xDAD5, 0xED65, 0xE6D5, 0xF599, 0xDDA5,
+    0xA30C, 0xC50A, 0x8B30, 0xD122, 0xB144, 0x8D50, 0xA03C, 0xC05A, 0x83B0, 0xD212, 0xB414, 0x85D0,
+    0x838C, 0xC606, 0x883C, 0xC066, 0x91C4, 0x9C14, 0xA606, 0x858A, 0x9A12, 0x91A2, 0xA066, 0x885A,
+    0x5CF3, 0x3AF5, 0x74CF, 0x2EDD, 0x4EBB, 0x72AF, 0x5FC3, 0x3FA5, 0x7C4F, 0x2DED, 0x4BEB, 0x7A2F,
+    0x7C73, 0x39F9, 0x77C3, 0x3F99, 0x6E3B, 0x63EB, 0x59F9, 0x7A75, 0x65ED, 0x6E5D, 0x5F99, 0x77A5,
+    0x5C03, 0x3A05, 0x7403, 0x2E11, 0x4E11, 0x7205, 0x50C3, 0x30A5, 0x7043, 0x21E1, 0x41E1, 0x7025,
+    0x4C43, 0x09C9, 0x44C3, 0x0C99, 0x4C19, 0x41C9, 0x09A9, 0x2A25, 0x21A9, 0x2A19, 0x0A99, 0x22A5,
+    0xA3FC, 0xC5FA, 0x8BFC, 0xD1EE, 0xB1EE, 0x8DFA, 0xAF3C, 0xCF5A, 0x8FBC, 0xDE1E, 0xBE1E, 0x8FDA,
+    0xB3BC, 0xF636, 0xBB3C, 0xF366, 0xB3E6, 0xBE36, 0xF656, 0xD5DA, 0xDE56, 0xD5E6, 0xF566, 0xDD5A,
+    0xAC03, 0xCA05, 0xB803, 0xE211, 0xE411, 0xD805, 0xA0C3, 0xC0A5, 0xB083, 0xE121, 0xE141, 0xD085,
+    0x8C83, 0xC909, 0x88C3, 0xC099, 0xC491, 0xC941, 0xA909, 0x8A85, 0xA921, 0xA291, 0xA099, 0x88A5,
+    0x53FC, 0x35FA, 0x47FC, 0x1DEE, 0x1BEE, 0x27FA, 0x5F3C, 0x3F5A, 0x4F7C, 0x1EDE, 0x1EBE, 0x2F7A,
+    0x737C, 0x36F6, 0x773C, 0x3F66, 0x3B6E, 0x36BE, 0x56F6, 0x757A, 0x56DE, 0x5D6E, 0x5F66, 0x775A,
+    0xC035, 0xA053, 0xC01D, 0x8847, 0x8827, 0xA01B, 0xC305, 0xA503, 0xC10D, 0x8487, 0x8287, 0xA10B,
+    0xC131, 0x9093, 0xC311, 0x9903, 0x8923, 0x8293, 0x9095, 0xA151, 0x8495, 0x8945, 0x9905, 0xA511,
+    0x3FCA, 0x5FAC, 0x3FE2, 0x77B8, 0x77D8, 0x5FE4, 0x3CFA, 0x5AFC, 0x3EF2, 0x7B78, 0x7D78, 0x5EF4,
+    0x3ECE, 0x6F6C, 0x3CEE, 0x66FC, 0x76DC, 0x7D6C, 0x6F6A, 0x5EAE, 0x7B6A, 0x76BA, 0x66FA, 0x5AEE,
+    0xC03A, 0xA05C, 0xC02E, 0x8874, 0x8872, 0xA04E, 0xC30A, 0xA50C, 0xC20E, 0x8784, 0x8782, 0xA40E,
+    0xC232, 0x9390, 0xC322, 0x9930, 0x9832, 0x9382, 0x9590, 0xA454, 0x9584, 0x9854, 0x9950, 0xA544,
+    0x3FC5, 0x5FA3, 0x3FD1, 0x778B, 0x778D, 0x5FB1, 0x3CF5, 0x5AF3, 0x3DF1, 0x787B, 0x787D, 0x5BF1,
+    0x3DCD, 0x6C6F, 0x3CDD, 0x66CF, 0x67CD, 0x6C7D, 0x6A6F, 0x5BAB, 0x6A7B, 0x67AB, 0x66AF, 0x5ABB,
+    0x30C5, 0x50A3, 0x0CD1, 0x448B, 0x228D, 0x0AB1, 0x3C05, 0x5A03, 0x0DC1, 0x484B, 0x282D, 0x0BA1,
+    0x31C1, 0x6063, 0x3C11, 0x6603, 0x2389, 0x2839, 0x6065, 0x51A1, 0x4859, 0x4589, 0x6605, 0x5A11,
+    0xCF3A, 0xAF5C, 0xF32E, 0xBB74, 0xDD72, 0xF54E, 0xC3FA, 0xA5FC, 0xF23E, 0xB7B4, 0xD7D2, 0xF45E,
+    0xCE3E, 0x9F9C, 0xC3EE, 0x99FC, 0xDC76, 0xD7C6, 0x9F9A, 0xAE5E, 0xB7A6, 0xBA76, 0x99FA, 0xA5EE,
+    0x30CA, 0x50AC, 0x0CE2, 0x44B8, 0x22D8, 0x0AE4, 0x3C0A, 0x5A0C, 0x0EC2, 0x4B48, 0x2D28, 0x0EA4,
+    0x32C2, 0x6360, 0x3C22, 0x6630, 0x3298, 0x3928, 0x6560, 0x54A4, 0x5948, 0x5498, 0x6650, 0x5A44,
+    0xCF35, 0xAF53, 0xF31D, 0xBB47, 0xDD27, 0xF51B, 0xC3F5, 0xA5F3, 0xF13D, 0xB4B7, 0xD2D7, 0xF15B,
+    0xCD3D, 0x9C9F, 0xC3DD, 0x99CF, 0xCD67, 0xC6D7, 0x9A9F, 0xAB5B, 0xA6B7, 0xAB67, 0x99AF, 0xA5BB,
+    0x0C53, 0x0A35, 0x3047, 0x221D, 0x441B, 0x5027, 0x05C3, 0x03A5, 0x3407, 0x212D, 0x414B, 0x5207,
+    0x1C13, 0x0939, 0x11C3, 0x0399, 0x4613, 0x4163, 0x0959, 0x1A15, 0x2165, 0x2615, 0x0599, 0x11A5,
+    0xF3AC, 0xF5CA, 0xCFB8, 0xDDE2, 0xBBE4, 0xAFD8, 0xFA3C, 0xFC5A, 0xCBF8, 0xDED2, 0xBEB4, 0xADF8,
+    0xE3EC, 0xF6C6, 0xEE3C, 0xFC66, 0xB9EC, 0xBE9C, 0xF6A6, 0xE5EA, 0xDE9A, 0xD9EA, 0xFA66, 0xEE5A,
+    0x0CA3, 0x0AC5, 0x308B, 0x22D1, 0x44B1, 0x508D, 0x0AC3, 0x0CA5, 0x380B, 0x2D21, 0x4B41, 0x580D,
+    0x2C23, 0x3909, 0x22C3, 0x3099, 0x6431, 0x6341, 0x5909, 0x4A45, 0x6521, 0x6251, 0x5099, 0x44A5,
+    0xF35C, 0xF53A, 0xCF74, 0xDD2E, 0xBB4E, 0xAF72, 0xF53C, 0xF35A, 0xC7F4, 0xD2DE, 0xB4BE, 0xA7F2,
+    0xD3DC, 0xC6F6, 0xDD3C, 0xCF66, 0x9BCE, 0x9CBE, 0xA6F6, 0xB5BA, 0x9ADE, 0x9DAE, 0xAF66, 0xBB5A,
+    0x035C, 0x053A, 0x0374, 0x112E, 0x114E, 0x0572, 0x053C, 0x035A, 0x0734, 0x121E, 0x141E, 0x0752,
+    0x131C, 0x0636, 0x113C, 0x0366, 0x1346, 0x1436, 0x0656, 0x151A, 0x1256, 0x1526, 0x0566, 0x115A,
+    0xFCA3, 0xFAC5, 0xFC8B, 0xEED1, 0xEEB1, 0xFA8D, 0xFAC3, 0xFCA5, 0xF8CB, 0xEDE1, 0xEBE1, 0xF8AD,
+    0xECE3, 0xF9C9, 0xEEC3, 0xFC99, 0xECB9, 0xEBC9, 0xF9A9, 0xEAE5, 0xEDA9, 0xEAD9, 0xFA99, 0xEEA5,
+    0x03AC, 0x05CA, 0x03B8, 0x11E2, 0x11E4, 0x05D8, 0x0A3C, 0x0C5A, 0x0B38, 0x1E12, 0x1E14, 0x0D58,
+    0x232C, 0x3606, 0x223C, 0x3066, 0x3164, 0x3614, 0x5606, 0x454A, 0x5612, 0x5162, 0x5066, 0x445A,
+    0xFC53, 0xFA35, 0xFC47, 0xEE1D, 0xEE1B, 0xFA27, 0xF5C3, 0xF3A5, 0xF4C7, 0xE1ED, 0xE1EB, 0xF2A7,
+    0xDCD3, 0xC9F9, 0xDDC3, 0xCF99, 0xCE9B, 0xC9EB, 0xA9F9, 0xBAB5, 0xA9ED, 0xAE9D, 0xAF99, 0xBBA5
+};
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+
+/**Function*************************************************************
+
+  Synopsis    [Computes NPN-canonical form using brute-force methods.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned Extra_TruthCanonNPN2( unsigned uTruth, int nVars, Vec_Int_t * vRes )
+{
+    static int nVarsOld, nPerms;
+    static char ** pPerms = NULL;
+
+    unsigned uTruthMin, uTruthC, uPhase, uPerm;
+    int nMints, k, i;
+
+    if ( pPerms == NULL )
+    {
+        nPerms = Extra_Factorial( nVars );   
+        pPerms = Extra_Permutations( nVars );
+        nVarsOld = nVars;
+    }
+    else if ( nVarsOld != nVars )
+    {
+        ABC_FREE( pPerms );
+        nPerms = Extra_Factorial( nVars );   
+        pPerms = Extra_Permutations( nVars );
+        nVarsOld = nVars;
+    }
+
+    nMints    = (1 << nVars);
+    uTruthC   = (unsigned)( (~uTruth) & ((~((unsigned)0)) >> (32-nMints)) );
+    uTruthMin = 0xFFFFFFFF;
+    for ( i = 0; i < nMints; i++ )
+    {
+        uPhase = Extra_TruthPolarize( uTruth, i, nVars ); 
+        for ( k = 0; k < nPerms; k++ )
+        {
+            uPerm = Extra_TruthPermute( uPhase, pPerms[k], nVars, 0 );
+            Vec_IntPushUnique( vRes, uPerm );
+            if ( uTruthMin > uPerm )
+                uTruthMin = uPerm;
+        }
+        uPhase = Extra_TruthPolarize( uTruthC, i, nVars ); 
+        for ( k = 0; k < nPerms; k++ )
+        {
+            uPerm = Extra_TruthPermute( uPhase, pPerms[k], nVars, 0 );
+            Vec_IntPushUnique( vRes, uPerm );
+            if ( uTruthMin > uPerm )
+                uTruthMin = uPerm;
+        }
+    }
+    return uTruthMin;
+}
+
+void Acec_MultFuncTest5()
+{
+    Vec_Int_t * vRes = Vec_IntAlloc( 1000 );
+    int i, Entry;
+
+    unsigned Truth = 0xF335ACC0;
+    unsigned Canon = Extra_TruthCanonNPN2( Truth, 5, vRes );
+
+    Extra_PrintHex( stdout, (unsigned*)&Truth, 5 );  printf( "\n" );
+    Extra_PrintHex( stdout, (unsigned*)&Canon, 5 );  printf( "\n" );
+
+    printf( "Members = %d.\n", Vec_IntSize(vRes) );
+    Vec_IntForEachEntry( vRes, Entry, i )
+    {
+        Extra_PrintHex( stdout, (unsigned*)&Entry, 5 );  
+        printf( ", " );
+        if ( i % 8 == 7 )
+            printf( "\n" );
+    }
+
+    Vec_IntFree( vRes );
+}
+
+void Acec_MultFuncTest4()
+{
+    Vec_Int_t * vRes = Vec_IntAlloc( 1000 );
+    int i, Entry;
+
+    unsigned Truth = 0x35C0;
+    //unsigned Truth = 0xD728;
+    unsigned Canon = Extra_TruthCanonNPN2( Truth, 4, vRes );
+
+    Extra_PrintHex( stdout, (unsigned*)&Truth, 4 );  printf( "\n" );
+    Extra_PrintHex( stdout, (unsigned*)&Canon, 4 );  printf( "\n" );
+
+    printf( "Members = %d.\n", Vec_IntSize(vRes) );
+    Vec_IntForEachEntry( vRes, Entry, i )
+    {
+        Extra_PrintHex( stdout, (unsigned*)&Entry, 4 );  
+        printf( ", " );
+        if ( i % 12 == 11 )
+            printf( "\n" );
+    }
+
+    Vec_IntFree( vRes );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Acec_MultCollectInputs( Vec_Int_t * vPairs, Vec_Int_t * vRanks, int iObj )
+{
+    Vec_Int_t * vItems = Vec_IntAlloc( 100 );
+    int k, iObj1, iObj2;
+    // collect all those appearing with this one
+    Vec_IntForEachEntryDouble( vPairs, iObj1, iObj2, k )
+        if ( iObj == iObj1 )
+            Vec_IntPushUnique( vItems, iObj2 );
+        else if ( iObj == iObj2 )
+            Vec_IntPushUnique( vItems, iObj1 );
+    // sort items by rank cost
+    Vec_IntSelectSortCost( Vec_IntArray(vItems), Vec_IntSize(vItems), vRanks );
+    return vItems;
+}
+Vec_Int_t * Acec_MultDetectInputs1( Gia_Man_t * p, Vec_Wec_t * vLeafLits, Vec_Wec_t * vRootLits )
+{
+    Vec_Int_t * vInputs = Vec_IntAlloc( 100 );
+    Vec_Int_t * vCounts = Vec_IntStart( Gia_ManObjNum(p) );
+    Vec_Int_t * vRanks  = Vec_IntStart( Gia_ManObjNum(p) );
+    Vec_Int_t * vPairs  = Vec_IntAlloc( 100 );
+    Vec_Int_t * vItems  = Vec_IntAlloc( 100 );
+    Vec_Int_t * vItems0;
+    Vec_Int_t * vItems1;
+    Vec_Int_t * vLevel;
+    int i, k, iLit, iObj, Count;
+    // count how many times each input appears
+    Vec_WecForEachLevel( vLeafLits, vLevel, i )
+        Vec_IntForEachEntry( vLevel, iLit, k )
+        {
+            iObj = Abc_Lit2Var(iLit);
+            Vec_IntAddToEntry( vCounts, Gia_ObjFaninId0(Gia_ManObj(p, iObj), iObj), 1 );
+            Vec_IntAddToEntry( vCounts, Gia_ObjFaninId1(Gia_ManObj(p, iObj), iObj), 1 );
+/*
+            printf( "Rank %2d : Leaf = %4d : (%2d, %2d)\n", i, iObj, 
+                Gia_ObjFaninId0(Gia_ManObj(p, iObj), iObj), Gia_ObjFaninId1(Gia_ManObj(p, iObj), iObj) );
+            if ( k == Vec_IntSize(vLevel) - 1 )
+                printf( "\n" );
+*/
+        }
+    // count ranks for each one
+    Vec_WecForEachLevel( vLeafLits, vLevel, i )
+        Vec_IntForEachEntry( vLevel, iLit, k )
+        {
+            iObj = Abc_Lit2Var(iLit);
+            if ( Vec_IntEntry(vCounts, Gia_ObjFaninId0(Gia_ManObj(p, iObj), iObj)) < 2 )
+            {
+                printf( "Skipping %d.\n", iObj );
+                continue;
+            }
+            if ( Vec_IntEntry(vCounts, Gia_ObjFaninId1(Gia_ManObj(p, iObj), iObj)) < 2 )
+            {
+                printf( "Skipping %d.\n", iObj );
+                continue;
+            }
+            Vec_IntAddToEntry( vRanks, Gia_ObjFaninId0(Gia_ManObj(p, iObj), iObj), i );
+            Vec_IntAddToEntry( vRanks, Gia_ObjFaninId1(Gia_ManObj(p, iObj), iObj), i );
+
+            Vec_IntPushTwo( vPairs, Gia_ObjFaninId0(Gia_ManObj(p, iObj), iObj), Gia_ObjFaninId1(Gia_ManObj(p, iObj), iObj) );
+        }
+
+    // print statistics
+    Vec_IntForEachEntry( vCounts, Count, i )
+    {
+        if ( !Count )
+            continue;
+        if ( !Vec_IntEntry(vRanks, i) )
+            continue;
+        Vec_IntPush( vItems, i );
+        printf( "Obj = %3d  Occurs = %3d  Ranks = %3d\n", i, Count, Vec_IntEntry(vRanks, i) );
+    }
+    // sort items by rank cost
+    Vec_IntSelectSortCost( Vec_IntArray(vItems), Vec_IntSize(vItems), vRanks );
+    // collect all those appearing with the last one
+    vItems0 = Acec_MultCollectInputs( vPairs, vRanks, Vec_IntEntryLast(vItems) );
+    Vec_IntAppend( vInputs, vItems0 );
+    // collect all those appearing with the last one
+    vItems1 = Acec_MultCollectInputs( vPairs, vRanks, Vec_IntEntryLast(vItems0) );
+    Vec_IntAppend( vInputs, vItems1 );
+
+    Vec_IntPrint( vItems0 );
+    Vec_IntPrint( vItems1 );
+
+    Vec_IntFree( vCounts );
+    Vec_IntFree( vRanks );
+    Vec_IntFree( vPairs );
+    Vec_IntFree( vItems );
+    Vec_IntFree( vItems0 );
+    Vec_IntFree( vItems1 );
+    return vInputs;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Int_t * Acec_MultDetectInputs( Gia_Man_t * p, Vec_Wec_t * vLeafLits, Vec_Wec_t * vRootLits )
+{
+    Vec_Int_t * vInputs = Vec_IntAlloc( 100 );
+    Vec_Int_t * vSupp = Vec_IntAlloc( 100 );
+    Vec_Wrd_t * vTemp = Vec_WrdStart( Gia_ManObjNum(p) );
+    Vec_Int_t * vRanks  = Vec_IntStart( Gia_ManObjNum(p) );
+    Vec_Int_t * vCounts = Vec_IntStart( Gia_ManObjNum(p) );
+    Vec_Int_t * vLevel;
+    int i, k, iLit, iObj, j, Entry;
+
+    ABC_FREE( p->pRefs );
+    Gia_ManCreateRefs( p );
+    Gia_ManForEachCiId( p, iObj, i )
+        printf( "%d=%d ", iObj, Gia_ObjRefNumId(p, iObj) );
+    printf( "\n" );
+    Gia_ManForEachAndId( p, iObj )
+        if ( Gia_ObjRefNumId(p, iObj) >= 4 )
+            printf( "%d=%d ", iObj, Gia_ObjRefNumId(p, iObj) );
+    printf( "\n" );
+
+    Vec_WecForEachLevel( vLeafLits, vLevel, i )
+        Vec_IntForEachEntry( vLevel, iLit, k )
+        {
+            word Truth = Gia_ObjComputeTruth6Cis( p, iLit, vSupp, vTemp );
+            if ( Vec_IntSize(vSupp) >= 4 )
+            {
+                printf( "Leaf = %4d : ", Abc_Lit2Var(iLit) );
+                printf( "Rank = %2d  ", i );
+                printf( "Supp = %2d  ", Vec_IntSize(vSupp) );
+                Extra_PrintHex( stdout, (unsigned*)&Truth, Vec_IntSize(vSupp) );
+                if ( Vec_IntSize(vSupp) == 4 ) printf( "    " );
+                if ( Vec_IntSize(vSupp) == 3 ) printf( "      " );
+                if ( Vec_IntSize(vSupp) <= 2 ) printf( "       " );
+                printf( "  " );
+                Vec_IntPrint( vSupp );
+            }
+            // support rank counts
+            Vec_IntForEachEntry( vSupp, Entry, j )
+            {
+                Vec_IntAddToEntry( vRanks, Entry, i );
+                Vec_IntAddToEntry( vCounts, Entry, 1 );
+            }
+            if ( k == Vec_IntSize(vLevel)-1 )
+                printf( "\n" );
+        }
+
+    Vec_IntForEachEntry( vCounts, Entry, j )
+        if ( Entry )
+            printf( "%d=%d(%.2f) ", j, Entry, 1.0*Vec_IntEntry(vRanks, j)/Entry );
+    printf( "\n" );
+
+    Vec_IntFree( vSupp );
+    Vec_WrdFree( vTemp );
+    Vec_IntFree( vRanks );
+    Vec_IntFree( vCounts );
+    return vInputs;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+
diff --git a/src/proof/acec/acecTree.c b/src/proof/acec/acecTree.c
index 1c0af00a..53e1cb60 100644
--- a/src/proof/acec/acecTree.c
+++ b/src/proof/acec/acecTree.c
@@ -307,16 +307,16 @@ void Acec_TreeVerifyPhaseOne( Gia_Man_t * p, Vec_Int_t * vAdds, int iBox, Vec_Bi
     if ( fFadd ) // FADD
     {
         if ( TruthXor != 0x96 )
-            printf( "Fadd %d sum is wrong.\n", iBox );
+            printf( "Fadd %d sum %d is wrong.\n", iBox, Vec_IntEntry( vAdds, 6*iBox+3 ) );
         if ( TruthMaj != 0xE8 )
-            printf( "Fadd %d carry is wrong.\n", iBox );
+            printf( "Fadd %d carry %d is wrong.\n", iBox, Vec_IntEntry( vAdds, 6*iBox+4 ) );
     }
     else
     {
         if ( TruthXor != 0x66 )
-            printf( "Hadd %d sum is wrong.\n", iBox );
+            printf( "Hadd %d sum %d is wrong.\n", iBox, Vec_IntEntry( vAdds, 6*iBox+3 ) );
         if ( TruthMaj != 0x88 )
-            printf( "Hadd %d carry is wrong.\n", iBox );
+            printf( "Hadd %d carry %d is wrong.\n", iBox, Vec_IntEntry( vAdds, 6*iBox+4 ) );
     }
 }
 void Acec_TreeVerifyPhases( Gia_Man_t * p, Vec_Int_t * vAdds, Vec_Wec_t * vBoxes, Vec_Bit_t * vPhase )
@@ -356,7 +356,9 @@ void Acec_TreePhases_rec( Gia_Man_t * p, Vec_Int_t * vAdds, Vec_Int_t * vMap, in
     assert( Node != 0 );
     if ( Vec_BitEntry(vVisit, Node) )
     {
-        assert( Vec_BitEntry(vPhase, Node) == fPhase );
+        //assert( Vec_BitEntry(vPhase, Node) == fPhase );
+        if ( Vec_BitEntry(vPhase, Node) != fPhase )
+            printf( "Phase check failed for node %d.\n", Node );
         return;
     }
     Vec_BitWriteEntry( vVisit, Node, 1 );
@@ -386,7 +388,12 @@ void Acec_TreePhases_rec( Gia_Man_t * p, Vec_Int_t * vAdds, Vec_Int_t * vMap, in
         Acec_TreePhases_rec( p, vAdds, vMap, iObj, fPhaseThis, vPhase, vInvHadds, vVisit );
     }
     if ( Vec_BitEntry(vVisit, iXor) )
-        assert( Vec_BitEntry(vPhase, iXor) == fXorPhase );
+    {
+        //assert( Vec_BitEntry(vPhase, iXor) == fXorPhase );
+        if ( Vec_BitEntry(vPhase, iXor) != fXorPhase )
+            printf( "Phase check failed for XOR %d.\n", iXor );
+        return;
+    }
     if ( fXorPhase )
         Vec_BitWriteEntry( vPhase, iXor, fXorPhase );
 }
@@ -448,7 +455,7 @@ void Acec_PrintAdders( Vec_Wec_t * vBoxes, Vec_Int_t * vAdds )
     int i, k, iBox;
     Vec_WecForEachLevel( vBoxes, vLevel, i )
     {
-        printf( " %4d : {", i );
+        printf( " %4d : %2d  {", i, Vec_IntSize(vLevel) );
         Vec_IntForEachEntry( vLevel, iBox, k )
             printf( " %s%d=(%d,%d)", Vec_IntEntry(vAdds, 6*iBox+2) == 0 ? "*":"", iBox, 
                                      Vec_IntEntry(vAdds, 6*iBox+3), Vec_IntEntry(vAdds, 6*iBox+4) );
@@ -461,7 +468,7 @@ void Vec_WecPrintLits( Vec_Wec_t * p )
     int i, k, Entry;
     Vec_WecForEachLevel( p, vVec, i )
     {
-        printf( " %4d : {", i );
+        printf( " %4d : %2d  {", i, Vec_IntSize(vVec) );
         Vec_IntForEachEntry( vVec, Entry, k )
             printf( " %c%d", Abc_LitIsCompl(Entry) ? '-' : '+', Abc_Lit2Var(Entry) );
         printf( " }\n" );
@@ -473,7 +480,7 @@ void Acec_PrintRootLits( Vec_Wec_t * vRoots )
     int i, k, iObj;
     Vec_WecForEachLevel( vRoots, vLevel, i )
     {
-        printf( "Rank %d : ", i );
+        printf( "Rank %d : %2d  ", i, Vec_IntSize(vLevel) );
         Vec_IntForEachEntry( vLevel, iObj, k )
         {
             int fFadd = Abc_LitIsCompl(iObj);
@@ -573,6 +580,7 @@ Acec_Box_t * Acec_DeriveBox( Gia_Man_t * p, int fVerbose )
             Vec_WecSizeSize(pBox->vLeafLits), Vec_WecSizeSize(pBox->vRootLits)  );
     if ( pBox && fVerbose )
         Acec_PrintBox( pBox, vAdds );
+//    Acec_MultDetectInputs( p, pBox->vLeafLits, pBox->vRootLits );
     Vec_WecFreeP( &vTrees );
     Vec_IntFree( vAdds );
     return pBox;
diff --git a/src/proof/acec/module.make b/src/proof/acec/module.make
index 25fa2548..dbf86ac2 100644
--- a/src/proof/acec/module.make
+++ b/src/proof/acec/module.make
@@ -8,6 +8,7 @@ SRC +=    src/proof/acec/acecCl.c \
     src/proof/acec/acecPool.c \
     src/proof/acec/acecCover.c \
     src/proof/acec/acecFadds.c \
+    src/proof/acec/acecMult.c \
     src/proof/acec/acecNorm.c \
     src/proof/acec/acecOrder.c \
     src/proof/acec/acecPolyn.c \