TSTP Solution File: GRP686-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP686-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:48:59 EDT 2022
% Result : Unsatisfiable 14.61s 14.86s
% Output : Refutation 14.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 84 RR)
% Number of literals : 84 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP686-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP686-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP686-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP686-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP686-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP686-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
file('GRP686-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(mult(mult(a,mult(a,b)),c),mult(mult(a,a),mult(b,c))),
file('GRP686-1.p',unknown),
[] ).
cnf(28,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(34,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(53,plain,
equal(rd(mult(u,mult(v,mult(v,w))),w),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(55,plain,
equal(mult(u,mult(v,mult(v,ld(mult(u,mult(v,v)),w)))),w),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(61,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(62,plain,
equal(mult(rd(u,mult(v,v)),mult(v,mult(v,w))),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(66,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[6,61]),
[iquote('0:Rew:6.0,61.0')] ).
cnf(67,plain,
~ equal(mult(mult(a,mult(a,b)),c),mult(a,mult(a,mult(b,c)))),
inference(rew,[status(thm),theory(equality)],[66,8]),
[iquote('0:Rew:66.0,8.0')] ).
cnf(71,plain,
equal(rd(mult(u,mult(u,v)),v),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[66,4]),
[iquote('0:SpR:66.0,4.0')] ).
cnf(72,plain,
equal(ld(mult(u,u),mult(u,mult(u,v))),v),
inference(spr,[status(thm),theory(equality)],[66,2]),
[iquote('0:SpR:66.0,2.0')] ).
cnf(94,plain,
equal(rd(mult(u,v),ld(u,v)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[1,71]),
[iquote('0:SpR:1.0,71.0')] ).
cnf(112,plain,
equal(ld(mult(u,u),mult(u,v)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1,72]),
[iquote('0:SpR:1.0,72.0')] ).
cnf(172,plain,
equal(rd(u,ld(u,unit)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[5,94]),
[iquote('0:SpR:5.0,94.0')] ).
cnf(173,plain,
equal(rd(u,ld(v,ld(v,u))),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[1,94]),
[iquote('0:SpR:1.0,94.0')] ).
cnf(188,plain,
equal(rd(mult(u,mult(v,w)),ld(v,w)),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1,53]),
[iquote('0:SpR:1.0,53.0')] ).
cnf(215,plain,
equal(mult(rd(unit,u),rd(unit,u)),rd(rd(unit,u),u)),
inference(spr,[status(thm),theory(equality)],[28,172]),
[iquote('0:SpR:28.0,172.0')] ).
cnf(238,plain,
equal(ld(mult(u,u),v),ld(u,ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1,112]),
[iquote('0:SpR:1.0,112.0')] ).
cnf(456,plain,
equal(mult(u,mult(u,ld(mult(v,mult(u,u)),w))),ld(v,w)),
inference(spr,[status(thm),theory(equality)],[55,2]),
[iquote('0:SpR:55.0,2.0')] ).
cnf(510,plain,
equal(ld(rd(u,mult(v,v)),mult(u,w)),mult(v,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[62,2]),
[iquote('0:SpR:62.0,2.0')] ).
cnf(641,plain,
equal(rd(mult(u,v),ld(v,unit)),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[5,188]),
[iquote('0:SpR:5.0,188.0')] ).
cnf(747,plain,
equal(mult(u,mult(rd(unit,v),rd(unit,v))),rd(mult(u,rd(unit,v)),v)),
inference(spr,[status(thm),theory(equality)],[28,641]),
[iquote('0:SpR:28.0,641.0')] ).
cnf(751,plain,
equal(mult(u,mult(ld(u,v),ld(u,v))),rd(v,ld(ld(u,v),unit))),
inference(spr,[status(thm),theory(equality)],[1,641]),
[iquote('0:SpR:1.0,641.0')] ).
cnf(752,plain,
equal(mult(rd(u,v),mult(v,v)),rd(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[3,641]),
[iquote('0:SpR:3.0,641.0')] ).
cnf(762,plain,
equal(rd(mult(u,rd(unit,v)),v),mult(u,rd(rd(unit,v),v))),
inference(rew,[status(thm),theory(equality)],[215,747]),
[iquote('0:Rew:215.0,747.0')] ).
cnf(853,plain,
equal(mult(mult(u,u),mult(ld(u,unit),ld(u,unit))),rd(u,ld(ld(u,unit),unit))),
inference(spr,[status(thm),theory(equality)],[172,752]),
[iquote('0:SpR:172.0,752.0')] ).
cnf(864,plain,
equal(mult(u,mult(u,mult(ld(u,unit),ld(u,unit)))),rd(u,ld(ld(u,unit),unit))),
inference(rew,[status(thm),theory(equality)],[66,853]),
[iquote('0:Rew:66.0,853.0')] ).
cnf(865,plain,
equal(mult(u,rd(unit,ld(ld(u,unit),unit))),rd(u,ld(ld(u,unit),unit))),
inference(rew,[status(thm),theory(equality)],[751,864]),
[iquote('0:Rew:751.0,864.0')] ).
cnf(866,plain,
equal(rd(u,ld(ld(u,unit),unit)),unit),
inference(rew,[status(thm),theory(equality)],[1,865,34]),
[iquote('0:Rew:1.0,865.0,34.0,865.0')] ).
cnf(892,plain,
equal(mult(unit,ld(ld(u,unit),unit)),u),
inference(spr,[status(thm),theory(equality)],[866,3]),
[iquote('0:SpR:866.0,3.0')] ).
cnf(906,plain,
equal(ld(ld(u,unit),unit),u),
inference(rew,[status(thm),theory(equality)],[6,892]),
[iquote('0:Rew:6.0,892.0')] ).
cnf(1036,plain,
equal(mult(ld(u,unit),u),unit),
inference(spr,[status(thm),theory(equality)],[906,1]),
[iquote('0:SpR:906.0,1.0')] ).
cnf(1038,plain,
equal(mult(ld(u,unit),ld(u,unit)),rd(ld(u,unit),u)),
inference(spr,[status(thm),theory(equality)],[906,172]),
[iquote('0:SpR:906.0,172.0')] ).
cnf(1040,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[906,34]),
[iquote('0:SpR:906.0,34.0')] ).
cnf(1041,plain,
equal(rd(unit,ld(ld(u,unit),u)),mult(ld(u,unit),ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[906,173]),
[iquote('0:SpR:906.0,173.0')] ).
cnf(1057,plain,
equal(rd(mult(u,ld(v,unit)),v),mult(u,rd(ld(v,unit),v))),
inference(rew,[status(thm),theory(equality)],[1040,762]),
[iquote('0:Rew:1040.0,762.0')] ).
cnf(1070,plain,
equal(ld(ld(ld(u,unit),u),unit),rd(ld(u,unit),u)),
inference(rew,[status(thm),theory(equality)],[1040,1041,1038]),
[iquote('0:Rew:1040.0,1041.0,1038.0,1041.0')] ).
cnf(1080,plain,
equal(mult(ld(u,unit),mult(u,u)),rd(unit,ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[1036,641]),
[iquote('0:SpR:1036.0,641.0')] ).
cnf(1089,plain,
equal(rd(mult(u,unit),ld(ld(v,unit),v)),mult(u,mult(ld(v,unit),ld(v,unit)))),
inference(spr,[status(thm),theory(equality)],[1036,188]),
[iquote('0:SpR:1036.0,188.0')] ).
cnf(1098,plain,
equal(mult(ld(u,unit),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[34,1080]),
[iquote('0:Rew:34.0,1080.0')] ).
cnf(1110,plain,
equal(mult(u,mult(ld(v,unit),ld(v,unit))),rd(u,ld(ld(v,unit),v))),
inference(rew,[status(thm),theory(equality)],[5,1089]),
[iquote('0:Rew:5.0,1089.0')] ).
cnf(1111,plain,
equal(rd(u,ld(ld(v,unit),v)),mult(u,rd(ld(v,unit),v))),
inference(rew,[status(thm),theory(equality)],[1038,1110]),
[iquote('0:Rew:1038.0,1110.0')] ).
cnf(1140,plain,
equal(ld(ld(u,unit),u),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[1098,2]),
[iquote('0:SpR:1098.0,2.0')] ).
cnf(1166,plain,
equal(rd(ld(u,unit),u),ld(mult(u,u),unit)),
inference(rew,[status(thm),theory(equality)],[1140,1070]),
[iquote('0:Rew:1140.0,1070.0')] ).
cnf(1167,plain,
equal(mult(u,rd(ld(v,unit),v)),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1140,1111]),
[iquote('0:Rew:1140.0,1111.0')] ).
cnf(1169,plain,
equal(rd(ld(u,unit),u),ld(u,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[238,1166]),
[iquote('0:Rew:238.0,1166.0')] ).
cnf(1179,plain,
equal(rd(mult(u,ld(v,unit)),v),mult(u,ld(v,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[1169,1057]),
[iquote('0:Rew:1169.0,1057.0')] ).
cnf(1191,plain,
equal(mult(u,ld(v,ld(v,unit))),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1169,1167]),
[iquote('0:Rew:1169.0,1167.0')] ).
cnf(1193,plain,
equal(rd(mult(u,ld(v,unit)),v),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1191,1179]),
[iquote('0:Rew:1191.0,1179.0')] ).
cnf(1480,plain,
equal(mult(u,mult(u,ld(v,w))),ld(rd(v,mult(u,u)),w)),
inference(spr,[status(thm),theory(equality)],[3,456]),
[iquote('0:SpR:3.0,456.0')] ).
cnf(1486,plain,
equal(mult(u,mult(u,ld(u,v))),ld(ld(u,unit),v)),
inference(spr,[status(thm),theory(equality)],[1098,456]),
[iquote('0:SpR:1098.0,456.0')] ).
cnf(1499,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1,1486]),
[iquote('0:Rew:1.0,1486.0')] ).
cnf(1581,plain,
equal(rd(u,mult(v,u)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[1499,34]),
[iquote('0:SpR:1499.0,34.0')] ).
cnf(1589,plain,
equal(mult(rd(unit,u),v),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[28,1499]),
[iquote('0:SpR:28.0,1499.0')] ).
cnf(1597,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[1040,1589]),
[iquote('0:Rew:1040.0,1589.0')] ).
cnf(1672,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1,1581]),
[iquote('0:SpR:1.0,1581.0')] ).
cnf(1673,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,1581]),
[iquote('0:SpR:3.0,1581.0')] ).
cnf(1674,plain,
equal(rd(mult(u,u),rd(v,ld(u,unit))),ld(rd(v,u),unit)),
inference(spr,[status(thm),theory(equality)],[752,1581]),
[iquote('0:SpR:752.0,1581.0')] ).
cnf(1683,plain,
equal(rd(mult(u,u),rd(v,ld(u,unit))),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[1673,1674]),
[iquote('0:Rew:1673.0,1674.0')] ).
cnf(1693,plain,
equal(rd(ld(u,v),ld(v,unit)),mult(ld(u,unit),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1597,641]),
[iquote('0:SpR:1597.0,641.0')] ).
cnf(1731,plain,
equal(rd(ld(u,v),ld(v,unit)),ld(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1597,1693]),
[iquote('0:Rew:1597.0,1693.0')] ).
cnf(1854,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1673,1499]),
[iquote('0:SpR:1673.0,1499.0')] ).
cnf(1886,plain,
equal(ld(rd(u,v),mult(u,u)),rd(v,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[1854,752]),
[iquote('0:Rew:1854.0,752.0')] ).
cnf(2505,plain,
equal(rd(ld(u,ld(v,unit)),v),rd(ld(u,unit),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1597,1193]),
[iquote('0:SpR:1597.0,1193.0')] ).
cnf(3190,plain,
equal(rd(mult(u,u),ld(v,unit)),rd(u,ld(v,ld(u,unit)))),
inference(spr,[status(thm),theory(equality)],[1672,1683]),
[iquote('0:SpR:1672.0,1683.0')] ).
cnf(3267,plain,
equal(ld(u,mult(rd(unit,v),rd(unit,v))),rd(ld(u,rd(unit,v)),v)),
inference(spr,[status(thm),theory(equality)],[28,1731]),
[iquote('0:SpR:28.0,1731.0')] ).
cnf(3299,plain,
equal(rd(ld(u,ld(v,unit)),v),ld(u,ld(v,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[1597,3267,1040]),
[iquote('0:Rew:1597.0,3267.0,1040.0,3267.0')] ).
cnf(3300,plain,
equal(rd(ld(u,unit),mult(v,v)),ld(u,ld(v,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[2505,3299]),
[iquote('0:Rew:2505.0,3299.0')] ).
cnf(3304,plain,
equal(rd(ld(u,ld(v,unit)),v),ld(u,ld(v,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[3300,2505]),
[iquote('0:Rew:3300.0,2505.0')] ).
cnf(3383,plain,
equal(rd(mult(u,u),ld(v,unit)),mult(u,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1886,510]),
[iquote('0:SpR:1886.0,510.0')] ).
cnf(3424,plain,
equal(rd(u,ld(v,ld(u,unit))),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[3190,3383]),
[iquote('0:Rew:3190.0,3383.0')] ).
cnf(4264,plain,
equal(ld(rd(ld(u,ld(v,unit)),v),w),mult(mult(v,mult(v,u)),w)),
inference(spr,[status(thm),theory(equality)],[3424,1854]),
[iquote('0:SpR:3424.0,1854.0')] ).
cnf(4298,plain,
equal(ld(ld(u,ld(v,ld(v,unit))),w),mult(mult(v,mult(v,u)),w)),
inference(rew,[status(thm),theory(equality)],[3304,4264]),
[iquote('0:Rew:3304.0,4264.0')] ).
cnf(11386,plain,
equal(ld(rd(ld(u,unit),mult(v,v)),w),mult(v,mult(v,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[1499,1480]),
[iquote('0:SpR:1499.0,1480.0')] ).
cnf(11421,plain,
equal(ld(ld(u,ld(v,ld(v,unit))),w),mult(v,mult(v,mult(u,w)))),
inference(rew,[status(thm),theory(equality)],[3300,11386]),
[iquote('0:Rew:3300.0,11386.0')] ).
cnf(11422,plain,
equal(mult(mult(u,mult(u,v)),w),mult(u,mult(u,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[4298,11421]),
[iquote('0:Rew:4298.0,11421.0')] ).
cnf(11423,plain,
$false,
inference(unc,[status(thm)],[11422,67]),
[iquote('0:UnC:11422.0,67.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP686-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 18:38:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 14.61/14.86
% 14.61/14.86 SPASS V 3.9
% 14.61/14.86 SPASS beiseite: Proof found.
% 14.61/14.86 % SZS status Theorem
% 14.61/14.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.61/14.86 SPASS derived 5553 clauses, backtracked 0 clauses, performed 0 splits and kept 2048 clauses.
% 14.61/14.86 SPASS allocated 91994 KBytes.
% 14.61/14.86 SPASS spent 0:0:14.31 on the problem.
% 14.61/14.86 0:00:00.03 for the input.
% 14.61/14.86 0:00:00.00 for the FLOTTER CNF translation.
% 14.61/14.86 0:00:00.10 for inferences.
% 14.61/14.86 0:00:00.00 for the backtracking.
% 14.61/14.86 0:0:14.14 for the reduction.
% 14.61/14.86
% 14.61/14.86
% 14.61/14.86 Here is a proof with depth 13, length 84 :
% 14.61/14.86 % SZS output start Refutation
% See solution above
% 14.61/14.87 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 goals
% 14.61/14.87
%------------------------------------------------------------------------------