TSTP Solution File: RNG001-3 by CARINE---0.734
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : RNG001-3 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Nov 28 04:26:30 EST 2010
% Result : Unsatisfiable 20.49s
% Output : Refutation 20.49s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Command entered:
% /home/graph/tptp/Systems/CARINE---0.734/carine /tmp/SystemOnTPTP13617/RNG/RNG001-3+noeq.car t=300 xo=off uct=32000
% CARINE version 0.734 (Dec 2003)
% Initializing tables ... done.
% Parsing ........ done.
% Calculating time slices ... done.
% Building Lookup Tables ... done.
% Looking for a proof at depth = 1 ...
% t = 0 secs [nr = 0] [nf = 0] [nu = 0] [ut = 4]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 12] [nf = 18] [nu = 0] [ut = 4]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 30001] [nf = 48] [nu = 27399] [ut = 101]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 98809] [nf = 78] [nu = 92383] [ut = 101]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 167617] [nf = 108] [nu = 157367] [ut = 101]
% Looking for a proof at depth = 6 ...
% t = 0 secs [nr = 236425] [nf = 138] [nu = 222351] [ut = 101]
% Looking for a proof at depth = 7 ...
% t = 0 secs [nr = 305233] [nf = 168] [nu = 287335] [ut = 101]
% Looking for a proof at depth = 8 ...
% t = 0 secs [nr = 374041] [nf = 198] [nu = 352319] [ut = 101]
% Looking for a proof at depth = 9 ...
% t = 1 secs [nr = 442849] [nf = 228] [nu = 417303] [ut = 101]
% Looking for a proof at depth = 10 ...
% t = 1 secs [nr = 511657] [nf = 258] [nu = 482287] [ut = 101]
% Looking for a proof at depth = 11 ...
% t = 1 secs [nr = 580465] [nf = 288] [nu = 547271] [ut = 101]
% Looking for a proof at depth = 12 ...
% t = 1 secs [nr = 649273] [nf = 318] [nu = 612255] [ut = 101]
% Looking for a proof at depth = 13 ...
% t = 1 secs [nr = 718081] [nf = 348] [nu = 677239] [ut = 101]
% Looking for a proof at depth = 14 ...
% t = 1 secs [nr = 786889] [nf = 378] [nu = 742223] [ut = 101]
% Looking for a proof at depth = 15 ...
% t = 1 secs [nr = 855697] [nf = 408] [nu = 807207] [ut = 101]
% Looking for a proof at depth = 16 ...
% t = 1 secs [nr = 924505] [nf = 438] [nu = 872191] [ut = 101]
% Looking for a proof at depth = 17 ...
% t = 1 secs [nr = 993313] [nf = 468] [nu = 937175] [ut = 101]
% Looking for a proof at depth = 18 ...
% t = 2 secs [nr = 1062121] [nf = 498] [nu = 1002159] [ut = 101]
% Looking for a proof at depth = 19 ...
% t = 2 secs [nr = 1130929] [nf = 528] [nu = 1067143] [ut = 101]
% Looking for a proof at depth = 20 ...
% t = 2 secs [nr = 1199737] [nf = 558] [nu = 1132127] [ut = 101]
% Looking for a proof at depth = 21 ...
% t = 2 secs [nr = 1268545] [nf = 588] [nu = 1197111] [ut = 101]
% Looking for a proof at depth = 22 ...
% t = 2 secs [nr = 1337353] [nf = 618] [nu = 1262095] [ut = 101]
% Looking for a proof at depth = 23 ...
% t = 2 secs [nr = 1406161] [nf = 648] [nu = 1327079] [ut = 101]
% Looking for a proof at depth = 24 ...
% t = 2 secs [nr = 1474969] [nf = 678] [nu = 1392063] [ut = 101]
% Looking for a proof at depth = 25 ...
% t = 2 secs [nr = 1543777] [nf = 708] [nu = 1457047] [ut = 101]
% Looking for a proof at depth = 26 ...
% t = 2 secs [nr = 1612585] [nf = 738] [nu = 1522031] [ut = 101]
% Looking for a proof at depth = 27 ...
% t = 3 secs [nr = 1681393] [nf = 768] [nu = 1587015] [ut = 101]
% Looking for a proof at depth = 28 ...
% t = 3 secs [nr = 1750201] [nf = 798] [nu = 1651999] [ut = 101]
% Looking for a proof at depth = 29 ...
% t = 3 secs [nr = 1819009] [nf = 828] [nu = 1716983] [ut = 101]
% Looking for a proof at depth = 30 ...
% t = 3 secs [nr = 1887817] [nf = 858] [nu = 1781967] [ut = 101]
% Restarting search with different parameters.
% Looking for a proof at depth = 1 ...
% t = 3 secs [nr = 1887817] [nf = 858] [nu = 1781967] [ut = 101]
% Looking for a proof at depth = 2 ...
% t = 3 secs [nr = 1887829] [nf = 876] [nu = 1781967] [ut = 101]
% Looking for a proof at depth = 3 ...
% t = 4 secs [nr = 2041652] [nf = 928] [nu = 1929788] [ut = 159]
% Looking for a proof at depth = 4 ...
% t = 7 secs [nr = 2676616] [nf = 990] [nu = 2445938] [ut = 277]
% Looking for a proof at depth = 5 ...
% t = 12 secs [nr = 3993455] [nf = 2941] [nu = 3598512] [ut = 277]
% Looking for a proof at depth = 6 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~product_3(a_0(),additive_identity_0(),additive_identity_0())
% B1: product_3(x0,x1,multiply_2(x0,x1))
% B2: sum_3(additive_identity_0(),x0,x0)
% B3: sum_3(additive_inverse_1(x0),x0,additive_identity_0())
% B4: ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5)
% B5: ~sum_3(x2,x3,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x0,x4,x5)
% B6: ~product_3(x0,x3,x4) | ~product_3(x0,x1,x2) | ~sum_3(x2,x4,x6) | ~sum_3(x1,x3,x5) | product_3(x0,x5,x6)
% B7: ~product_3(x0,x5,x6) | ~product_3(x0,x3,x4) | ~product_3(x0,x1,x2) | ~sum_3(x1,x3,x5) | sum_3(x2,x4,x6)
% Unit Clauses:
% --------------
% U1: < d0 v4 dv2 f1 c0 t5 td2 b > product_3(x0,x1,multiply_2(x0,x1))
% U2: < d0 v2 dv1 f0 c1 t3 td1 b > sum_3(additive_identity_0(),x0,x0)
% U3: < d0 v2 dv1 f1 c1 t4 td2 b > sum_3(additive_inverse_1(x0),x0,additive_identity_0())
% U6: < d3 v2 dv1 f2 c1 t5 td3 > sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0)
% U10: < d3 v2 dv1 f3 c1 t6 td4 > sum_3(additive_inverse_1(additive_inverse_1(additive_inverse_1(x0))),x0,additive_identity_0())
% U21: < d3 v2 dv1 f1 c1 t4 td2 > sum_3(x0,additive_inverse_1(x0),additive_identity_0())
% U29: < d3 v2 dv1 f2 c1 t5 td3 > sum_3(additive_identity_0(),x0,additive_inverse_1(additive_inverse_1(x0)))
% U31: < d3 v2 dv1 f2 c1 t5 td3 > sum_3(additive_identity_0(),additive_inverse_1(additive_inverse_1(x0)),x0)
% U62: < d3 v2 dv1 f0 c1 t3 td1 > sum_3(x0,additive_identity_0(),x0)
% U69: < d3 v2 dv1 f2 c1 t5 td3 > sum_3(x0,additive_identity_0(),additive_inverse_1(additive_inverse_1(x0)))
% U159: < d4 v0 dv0 f2 c5 t7 td2 > ~sum_3(multiply_2(a_0(),additive_identity_0()),multiply_2(a_0(),additive_identity_0()),additive_identity_0())
% U234: < d4 v3 dv1 f3 c3 t9 td2 > sum_3(multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0()))
% U277: < d6 v3 dv1 f5 c3 t11 td4 > sum_3(additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0()))
% U278: < d6 v3 dv1 f5 c3 t11 td4 > sum_3(multiply_2(x0,additive_identity_0()),additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),multiply_2(x0,additive_identity_0()))
% U286: < d6 v0 dv0 f3 c5 t8 td3 > ~sum_3(additive_identity_0(),additive_inverse_1(multiply_2(a_0(),additive_identity_0())),multiply_2(a_0(),additive_identity_0()))
% U319: < d6 v1 dv1 f3 c3 t7 td4 > sum_3(additive_identity_0(),additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),additive_identity_0())
% U356: < d6 v2 dv1 f3 c3 t8 td3 > sum_3(additive_identity_0(),additive_inverse_1(multiply_2(x0,additive_identity_0())),multiply_2(x0,additive_identity_0()))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% product_3(x0,x1,multiply_2(x0,x1)) ....... U1
% Derivation of unit clause U2:
% sum_3(additive_identity_0(),x0,x0) ....... U2
% Derivation of unit clause U3:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% Derivation of unit clause U6:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x2,x3,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x0,x4,x5) ....... B5
% ~sum_3(x0, x1, x2) | ~sum_3(x3, x0, additive_identity_0()) | sum_3(x3, x2, x1) ....... R1 [B2:L0, B5:L0]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% ~sum_3(x0, additive_inverse_1(x1), additive_identity_0()) | sum_3(x0, additive_identity_0(), x1) ....... R2 [R1:L0, U3:L0]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% sum_3(additive_inverse_1(additive_inverse_1(x0)), additive_identity_0(), x0) ....... R3 [R2:L0, U3:L0]
% Derivation of unit clause U10:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x2,x3,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x0,x4,x5) ....... B5
% ~sum_3(x0, x1, x2) | ~sum_3(x3, x0, additive_identity_0()) | sum_3(x3, x2, x1) ....... R1 [B2:L0, B5:L0]
% sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0) ....... U6
% ~sum_3(x0, additive_inverse_1(additive_inverse_1(x1)), additive_identity_0()) | sum_3(x0, x1, additive_identity_0()) ....... R2 [R1:L0, U6:L0]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% sum_3(additive_inverse_1(additive_inverse_1(additive_inverse_1(x0))), x0, additive_identity_0()) ....... R3 [R2:L0, U3:L0]
% Derivation of unit clause U21:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... B3
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_inverse_1(x2), x0, x3) | sum_3(x3, x1, additive_identity_0()) ....... R1 [B3:L0, B4:L0]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% ~sum_3(additive_inverse_1(x0), additive_identity_0(), x1) | sum_3(x1, x0, additive_identity_0()) ....... R2 [R1:L0, U2:L0]
% sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0) ....... U6
% sum_3(x0, additive_inverse_1(x0), additive_identity_0()) ....... R3 [R2:L0, U6:L0]
% Derivation of unit clause U29:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... B3
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, additive_identity_0(), x1) | ~sum_3(x0, additive_inverse_1(x2), x3) | sum_3(x3, x2, x1) ....... R1 [B3:L0, B4:L1]
% sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0) ....... U6
% ~sum_3(additive_inverse_1(additive_inverse_1(x0)), additive_inverse_1(x1), x2) | sum_3(x2, x1, x0) ....... R2 [R1:L0, U6:L0]
% sum_3(additive_inverse_1(additive_inverse_1(additive_inverse_1(x0))),x0,additive_identity_0()) ....... U10
% sum_3(additive_identity_0(), x0, additive_inverse_1(additive_inverse_1(x0))) ....... R3 [R2:L0, U10:L0]
% Derivation of unit clause U31:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... B3
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, additive_identity_0(), x1) | ~sum_3(x0, additive_inverse_1(x2), x3) | sum_3(x3, x2, x1) ....... R1 [B3:L0, B4:L1]
% sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0) ....... U6
% ~sum_3(additive_inverse_1(additive_inverse_1(x0)), additive_inverse_1(x1), x2) | sum_3(x2, x1, x0) ....... R2 [R1:L0, U6:L0]
% sum_3(x0,additive_inverse_1(x0),additive_identity_0()) ....... U21
% sum_3(additive_identity_0(), additive_inverse_1(additive_inverse_1(x0)), x0) ....... R3 [R2:L0, U21:L0]
% Derivation of unit clause U62:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... B3
% ~sum_3(x2,x3,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x0,x4,x5) ....... B5
% ~sum_3(x0, x1, x2) | ~sum_3(x3, additive_inverse_1(x1), x0) | sum_3(x3, additive_identity_0(), x2) ....... R1 [B3:L0, B5:L1]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% ~sum_3(x0, additive_inverse_1(x1), additive_identity_0()) | sum_3(x0, additive_identity_0(), x1) ....... R2 [R1:L0, U2:L0]
% sum_3(x0,additive_inverse_1(x0),additive_identity_0()) ....... U21
% sum_3(x0, additive_identity_0(), x0) ....... R3 [R2:L0, U21:L0]
% Derivation of unit clause U69:
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... B3
% ~sum_3(x2,x3,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x0,x4,x5) ....... B5
% ~sum_3(x0, x1, x2) | ~sum_3(x3, additive_inverse_1(x1), x0) | sum_3(x3, additive_identity_0(), x2) ....... R1 [B3:L0, B5:L1]
% sum_3(additive_identity_0(),x0,additive_inverse_1(additive_inverse_1(x0))) ....... U29
% ~sum_3(x0, additive_inverse_1(x1), additive_identity_0()) | sum_3(x0, additive_identity_0(), additive_inverse_1(additive_inverse_1(x1))) ....... R2 [R1:L0, U29:L0]
% sum_3(x0,additive_inverse_1(x0),additive_identity_0()) ....... U21
% sum_3(x0, additive_identity_0(), additive_inverse_1(additive_inverse_1(x0))) ....... R3 [R2:L0, U21:L0]
% Derivation of unit clause U159:
% ~product_3(a_0(),additive_identity_0(),additive_identity_0()) ....... B0
% ~product_3(x0,x3,x4) | ~product_3(x0,x1,x2) | ~sum_3(x2,x4,x6) | ~sum_3(x1,x3,x5) | product_3(x0,x5,x6) ....... B6
% ~product_3(a_0(), x0, x1) | ~product_3(a_0(), x2, x3) | ~sum_3(x3, x1, additive_identity_0()) | ~sum_3(x2, x0, additive_identity_0()) ....... R1 [B0:L0, B6:L4]
% ~product_3(a_0(), x0, x1) | ~sum_3(x1, x1, additive_identity_0()) | ~sum_3(x0, x0, additive_identity_0()) ....... R2 [R1:L1, R1:L0]
% product_3(x0,x1,multiply_2(x0,x1)) ....... U1
% ~sum_3(multiply_2(a_0(), x0), multiply_2(a_0(), x0), additive_identity_0()) | ~sum_3(x0, x0, additive_identity_0()) ....... R3 [R2:L0, U1:L0]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% ~sum_3(multiply_2(a_0(), additive_identity_0()), multiply_2(a_0(), additive_identity_0()), additive_identity_0()) ....... R4 [R3:L1, U2:L0]
% Derivation of unit clause U234:
% product_3(x0,x1,multiply_2(x0,x1)) ....... B1
% ~product_3(x0,x5,x6) | ~product_3(x0,x3,x4) | ~product_3(x0,x1,x2) | ~sum_3(x1,x3,x5) | sum_3(x2,x4,x6) ....... B7
% ~product_3(x0, x1, x2) | ~product_3(x0, x3, x4) | ~sum_3(x3, x1, x5) | sum_3(x4, x2, multiply_2(x0, x5)) ....... R1 [B1:L0, B7:L0]
% ~product_3(x0, x1, x2) | ~sum_3(x1, x1, x3) | sum_3(x2, x2, multiply_2(x0, x3)) ....... R2 [R1:L1, R1:L0]
% product_3(x0,x1,multiply_2(x0,x1)) ....... U1
% ~sum_3(x0, x0, x1) | sum_3(multiply_2(x2, x0), multiply_2(x2, x0), multiply_2(x2, x1)) ....... R3 [R2:L0, U1:L0]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% sum_3(multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0())) ....... R4 [R3:L0, U2:L0]
% Derivation of unit clause U277:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | sum_3(x3, x1, x2) ....... R1 [B2:L0, B4:L0]
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x4, x5, x1) | ~sum_3(x3, x4, x6) | sum_3(x6, x5, x2) ....... R2 [R1:L2, B4:L0]
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x1) | ~sum_3(x1, additive_identity_0(), x3) | sum_3(x3, x0, x2) ....... R3 [R2:L1, R2:L2]
% sum_3(multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0())) ....... U234
% ~sum_3(additive_identity_0(), multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0())) | ~sum_3(multiply_2(x0, additive_identity_0()), additive_identity_0(), x1) | sum_3(x1, multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0())) ....... R4 [R3:L0, U234:L0]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% ~sum_3(multiply_2(x0, additive_identity_0()), additive_identity_0(), x1) | sum_3(x1, multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0())) ....... R5 [R4:L0, U2:L0]
% sum_3(x0,additive_identity_0(),additive_inverse_1(additive_inverse_1(x0))) ....... U69
% sum_3(additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0())) ....... R6 [R5:L0, U69:L0]
% Derivation of unit clause U278:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | sum_3(x3, x1, x2) ....... R1 [B2:L0, B4:L0]
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x4, x5, x1) | ~sum_3(x3, x4, x6) | sum_3(x6, x5, x2) ....... R2 [R1:L2, B4:L0]
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x1) | ~sum_3(x1, additive_identity_0(), x3) | sum_3(x3, x0, x2) ....... R3 [R2:L1, R2:L2]
% sum_3(additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0())) ....... U277
% ~sum_3(additive_identity_0(), additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), multiply_2(x0, additive_identity_0())) | ~sum_3(multiply_2(x0, additive_identity_0()), additive_identity_0(), x1) | sum_3(x1, additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), multiply_2(x0, additive_identity_0())) ....... R4 [R3:L0, U277:L0]
% sum_3(additive_identity_0(),additive_inverse_1(additive_inverse_1(x0)),x0) ....... U31
% ~sum_3(multiply_2(x0, additive_identity_0()), additive_identity_0(), x1) | sum_3(x1, additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), multiply_2(x0, additive_identity_0())) ....... R5 [R4:L0, U31:L0]
% sum_3(x0,additive_identity_0(),x0) ....... U62
% sum_3(multiply_2(x0, additive_identity_0()), additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), multiply_2(x0, additive_identity_0())) ....... R6 [R5:L0, U62:L0]
% Derivation of unit clause U286:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | sum_3(x3, x1, x2) ....... R1 [B2:L0, B4:L0]
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x4, x5, x1) | ~sum_3(x3, x4, x6) | sum_3(x6, x5, x2) ....... R2 [R1:L2, B4:L0]
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x3, x3, x1) | sum_3(x1, x3, x2) ....... R3 [R2:L3, R2:L2]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% ~sum_3(additive_identity_0(), additive_inverse_1(x0), x1) | ~sum_3(x1, x1, x0) | sum_3(x0, x1, additive_identity_0()) ....... R4 [R3:L0, U3:L0]
% sum_3(multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0()),multiply_2(x0,additive_identity_0())) ....... U234
% ~sum_3(additive_identity_0(), additive_inverse_1(multiply_2(x0, additive_identity_0())), multiply_2(x0, additive_identity_0())) | sum_3(multiply_2(x0, additive_identity_0()), multiply_2(x0, additive_identity_0()), additive_identity_0()) ....... R5 [R4:L1, U234:L0]
% ~sum_3(multiply_2(a_0(),additive_identity_0()),multiply_2(a_0(),additive_identity_0()),additive_identity_0()) ....... U159
% ~sum_3(additive_identity_0(), additive_inverse_1(multiply_2(a_0(), additive_identity_0())), multiply_2(a_0(), additive_identity_0())) ....... R6 [R5:L1, U159:L0]
% Derivation of unit clause U319:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | sum_3(x3, x1, x2) ....... R1 [B2:L0, B4:L0]
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x4, x5, x1) | ~sum_3(x3, x4, x6) | sum_3(x6, x5, x2) ....... R2 [R1:L2, B4:L0]
% ~sum_3(additive_identity_0(), x0, x0) | ~sum_3(x1, x2, x1) | ~sum_3(x0, x1, x3) | sum_3(x3, x2, x3) ....... R3 [R2:L0, R2:L3]
% sum_3(additive_identity_0(),x0,x0) ....... U2
% ~sum_3(x0, x1, x0) | ~sum_3(x2, x0, x3) | sum_3(x3, x1, x3) ....... R4 [R3:L0, U2:L0]
% sum_3(multiply_2(x0,additive_identity_0()),additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),multiply_2(x0,additive_identity_0())) ....... U278
% ~sum_3(x0, multiply_2(x1, additive_identity_0()), x2) | sum_3(x2, additive_inverse_1(additive_inverse_1(multiply_2(x1, additive_identity_0()))), x2) ....... R5 [R4:L0, U278:L0]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% sum_3(additive_identity_0(), additive_inverse_1(additive_inverse_1(multiply_2(x0, additive_identity_0()))), additive_identity_0()) ....... R6 [R5:L0, U3:L0]
% Derivation of unit clause U356:
% sum_3(additive_identity_0(),x0,x0) ....... B2
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | sum_3(x3, x1, x2) ....... R1 [B2:L0, B4:L0]
% ~sum_3(x0,x4,x5) | ~sum_3(x1,x3,x4) | ~sum_3(x0,x1,x2) | sum_3(x2,x3,x5) ....... B4
% ~sum_3(x0, x1, x2) | ~sum_3(additive_identity_0(), x0, x3) | ~sum_3(x4, x5, x1) | ~sum_3(x3, x4, x6) | sum_3(x6, x5, x2) ....... R2 [R1:L2, B4:L0]
% ~sum_3(x0, x1, x2) | ~sum_3(x0, x3, x1) | ~sum_3(additive_identity_0(), x0, additive_identity_0()) | sum_3(additive_identity_0(), x3, x2) ....... R3 [R2:L1, R2:L3]
% sum_3(additive_inverse_1(additive_inverse_1(x0)),additive_identity_0(),x0) ....... U6
% ~sum_3(additive_inverse_1(additive_inverse_1(x0)), x1, additive_identity_0()) | ~sum_3(additive_identity_0(), additive_inverse_1(additive_inverse_1(x0)), additive_identity_0()) | sum_3(additive_identity_0(), x1, x0) ....... R4 [R3:L0, U6:L0]
% sum_3(additive_inverse_1(x0),x0,additive_identity_0()) ....... U3
% ~sum_3(additive_identity_0(), additive_inverse_1(additive_inverse_1(x0)), additive_identity_0()) | sum_3(additive_identity_0(), additive_inverse_1(x0), x0) ....... R5 [R4:L0, U3:L0]
% sum_3(additive_identity_0(),additive_inverse_1(additive_inverse_1(multiply_2(x0,additive_identity_0()))),additive_identity_0()) ....... U319
% sum_3(additive_identity_0(), additive_inverse_1(multiply_2(x0, additive_identity_0())), multiply_2(x0, additive_identity_0())) ....... R6 [R5:L0, U319:L0]
% Derivation of the empty clause:
% sum_3(additive_identity_0(),additive_inverse_1(multiply_2(x0,additive_identity_0())),multiply_2(x0,additive_identity_0())) ....... U356
% ~sum_3(additive_identity_0(),additive_inverse_1(multiply_2(a_0(),additive_identity_0())),multiply_2(a_0(),additive_identity_0())) ....... U286
% [] ....... R1 [U356:L0, U286:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 5429548
% resolvents: 5405006 factors: 24542
% Number of unit clauses generated: 4849327
% % unit clauses generated to total clauses generated: 89.31
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 4 [3] = 155
% [4] = 118 [6] = 80
% Total = 357
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 4849327 [2] = 517865 [3] = 31109 [4] = 24582 [5] = 6611 [6] = 54
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] product_3 (+)18 (-)28
% [1] sum_3 (+)245 (-)66
% ------------------
% Total: (+)263 (-)94
% Total number of unit clauses retained: 357
% Number of clauses skipped because of their length: 41791
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 5429607
% Number of unification failures: 57379650
% Number of unit to unit unification failures: 16663
% N literal unification failure due to lookup root_id table: 28856
% N base clause resolution failure due to lookup table: 140
% N UC-BCL resolution dropped due to lookup table: 0
% Max entries in substitution set: 19
% N unit clauses dropped because they exceeded max values: 1065034
% N unit clauses dropped because too much nesting: 248957
% N unit clauses not constrcuted because table was full: 0
% N unit clauses dropped because UCFA table was full: 0
% Max number of terms in a unit clause: 11
% Max term depth in a unit clause: 4
% Number of states in UCFA table: 826
% Total number of terms of all unit clauses in table: 2988
% Max allowed number of states in UCFA: 80000
% Ratio n states used/total allowed states: 0.01
% Ratio n states used/total unit clauses terms: 0.28
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 62809257
% ConstructUnitClause() = 1065387
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 1.37 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 271477
% | |
% --------------------------------------------------------
% Elapsed time: 20 secs
% CPU time: 20.48 secs
%
%------------------------------------------------------------------------------