TSTP Solution File: GRP498-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:47:46 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 68 RR)
% Number of literals : 68 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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(double_divide(double_divide(identity,double_divide(u,double_divide(v,identity))),double_divide(double_divide(v,double_divide(w,u)),identity)),w),
file('GRP498-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP498-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP498-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP498-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP498-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[3,1,6]),
[iquote('0:Rew:3.0,1.0,6.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(44,plain,
equal(multiply(multiply(double_divide(u,v),w),double_divide(identity,double_divide(v,inverse(w)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(46,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),multiply(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(identity,double_divide(identity,inverse(u))),multiply(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(identity,identity),multiply(double_divide(u,v),v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(57,plain,
equal(double_divide(inverse(identity),multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,54]),
[iquote('0:Rew:3.0,54.0')] ).
cnf(58,plain,
equal(double_divide(identity,multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[46,57]),
[iquote('0:Rew:46.0,57.0')] ).
cnf(59,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),inverse(inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[13,50]),
[iquote('0:Rew:13.0,50.0')] ).
cnf(97,plain,
equal(double_divide(identity,multiply(identity,inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[4,58]),
[iquote('0:SpR:4.0,58.0')] ).
cnf(98,plain,
equal(double_divide(identity,multiply(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[3,58]),
[iquote('0:SpR:3.0,58.0')] ).
cnf(99,plain,
equal(double_divide(identity,multiply(identity,multiply(u,v))),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[10,58]),
[iquote('0:SpR:10.0,58.0')] ).
cnf(101,plain,
equal(double_divide(identity,inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,97]),
[iquote('0:Rew:13.0,97.0')] ).
cnf(104,plain,
equal(double_divide(identity,inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[13,99]),
[iquote('0:Rew:13.0,99.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,double_divide(identity,double_divide(inverse(u),inverse(w)))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[59,7]),
[iquote('0:SpR:59.0,7.0')] ).
cnf(125,plain,
equal(double_divide(identity,double_divide(inverse(u),inverse(v))),double_divide(identity,multiply(u,inverse(inverse(v))))),
inference(spr,[status(thm),theory(equality)],[59,58]),
[iquote('0:SpR:59.0,58.0')] ).
cnf(130,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[46,59]),
[iquote('0:SpR:46.0,59.0')] ).
cnf(137,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[6,130,3,46]),
[iquote('0:Rew:6.0,130.0,3.0,130.0,3.0,130.0,46.0,130.0')] ).
cnf(144,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,double_divide(identity,multiply(u,inverse(inverse(w))))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[125,122]),
[iquote('0:Rew:125.0,122.0')] ).
cnf(147,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[137,10]),
[iquote('0:SpR:137.0,10.0')] ).
cnf(161,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[137,98]),
[iquote('0:SpR:137.0,98.0')] ).
cnf(163,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[161,101]),
[iquote('0:Rew:161.0,101.0')] ).
cnf(166,plain,
equal(double_divide(inverse(double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[161,7]),
[iquote('0:Rew:161.0,7.0')] ).
cnf(168,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,inverse(multiply(u,inverse(inverse(w))))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[161,144]),
[iquote('0:Rew:161.0,144.0')] ).
cnf(170,plain,
equal(double_divide(identity,double_divide(inverse(u),inverse(v))),inverse(multiply(u,inverse(inverse(v))))),
inference(rew,[status(thm),theory(equality)],[161,125]),
[iquote('0:Rew:161.0,125.0')] ).
cnf(174,plain,
equal(double_divide(inverse(inverse(inverse(u))),u),identity),
inference(rew,[status(thm),theory(equality)],[161,147]),
[iquote('0:Rew:161.0,147.0')] ).
cnf(176,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[161,104]),
[iquote('0:Rew:161.0,104.0')] ).
cnf(177,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[161,51]),
[iquote('0:Rew:161.0,51.0')] ).
cnf(184,plain,
equal(multiply(multiply(double_divide(u,v),w),inverse(double_divide(v,inverse(w)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[161,44]),
[iquote('0:Rew:161.0,44.0')] ).
cnf(193,plain,
equal(double_divide(inverse(inverse(inverse(u))),multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[161,177]),
[iquote('0:Rew:161.0,177.0')] ).
cnf(194,plain,
equal(double_divide(multiply(inverse(u),v),multiply(double_divide(w,v),u)),w),
inference(rew,[status(thm),theory(equality)],[6,166]),
[iquote('0:Rew:6.0,166.0')] ).
cnf(195,plain,
equal(inverse(double_divide(inverse(u),inverse(v))),inverse(multiply(u,inverse(inverse(v))))),
inference(rew,[status(thm),theory(equality)],[161,170]),
[iquote('0:Rew:161.0,170.0')] ).
cnf(196,plain,
equal(inverse(multiply(u,inverse(inverse(v)))),multiply(inverse(v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,195]),
[iquote('0:Rew:6.0,195.0')] ).
cnf(200,plain,
equal(multiply(multiply(double_divide(u,v),w),multiply(inverse(w),v)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[6,184]),
[iquote('0:Rew:6.0,184.0')] ).
cnf(207,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,multiply(inverse(w),inverse(u))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[161,168,196]),
[iquote('0:Rew:161.0,168.0,196.0,168.0')] ).
cnf(283,plain,
equal(double_divide(multiply(inverse(u),v),multiply(identity,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[174,194]),
[iquote('0:SpR:174.0,194.0')] ).
cnf(296,plain,
equal(double_divide(multiply(inverse(u),v),inverse(inverse(u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,283]),
[iquote('0:Rew:13.0,283.0')] ).
cnf(358,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[163,193]),
[iquote('0:SpR:163.0,193.0')] ).
cnf(379,plain,
equal(double_divide(u,multiply(identity,inverse(u))),identity),
inference(spr,[status(thm),theory(equality)],[46,358]),
[iquote('0:SpR:46.0,358.0')] ).
cnf(384,plain,
equal(double_divide(u,inverse(inverse(inverse(u)))),identity),
inference(rew,[status(thm),theory(equality)],[13,379]),
[iquote('0:Rew:13.0,379.0')] ).
cnf(397,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(inverse(v)))),multiply(identity,u)),v),
inference(spr,[status(thm),theory(equality)],[384,194]),
[iquote('0:SpR:384.0,194.0')] ).
cnf(402,plain,
equal(double_divide(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[163,384]),
[iquote('0:SpR:163.0,384.0')] ).
cnf(410,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(inverse(v)))),inverse(inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[13,397]),
[iquote('0:Rew:13.0,397.0')] ).
cnf(411,plain,
equal(inverse(inverse(inverse(inverse(inverse(inverse(u)))))),u),
inference(rew,[status(thm),theory(equality)],[296,410]),
[iquote('0:Rew:296.0,410.0')] ).
cnf(412,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[163,411]),
[iquote('0:Rew:163.0,411.0')] ).
cnf(417,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[412,13]),
[iquote('0:Rew:412.0,13.0')] ).
cnf(420,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[412,196]),
[iquote('0:Rew:412.0,196.0')] ).
cnf(428,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[412,176]),
[iquote('0:Rew:412.0,176.0')] ).
cnf(439,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(u,v)),
inference(rew,[status(thm),theory(equality)],[428,420]),
[iquote('0:Rew:428.0,420.0')] ).
cnf(440,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,u)),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[439,207]),
[iquote('0:Rew:439.0,207.0')] ).
cnf(496,plain,
equal(multiply(multiply(identity,u),multiply(inverse(u),v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[402,200]),
[iquote('0:SpR:402.0,200.0')] ).
cnf(507,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[417,496,412]),
[iquote('0:Rew:417.0,496.0,412.0,496.0')] ).
cnf(698,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[412,439]),
[iquote('0:SpR:412.0,439.0')] ).
cnf(705,plain,
equal(multiply(u,inverse(multiply(double_divide(v,double_divide(w,u)),inverse(w)))),v),
inference(rew,[status(thm),theory(equality)],[698,440]),
[iquote('0:Rew:698.0,440.0')] ).
cnf(720,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[428,705]),
[iquote('0:Rew:428.0,705.0')] ).
cnf(721,plain,
equal(multiply(u,multiply(v,inverse(double_divide(w,double_divide(v,u))))),w),
inference(rew,[status(thm),theory(equality)],[698,720]),
[iquote('0:Rew:698.0,720.0')] ).
cnf(722,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,721]),
[iquote('0:Rew:6.0,721.0')] ).
cnf(869,plain,
equal(multiply(inverse(double_divide(u,v)),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[507,722]),
[iquote('0:SpR:507.0,722.0')] ).
cnf(884,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,869]),
[iquote('0:Rew:6.0,869.0')] ).
cnf(885,plain,
$false,
inference(unc,[status(thm)],[884,5]),
[iquote('0:UnC:884.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 15:16:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 554 clauses, backtracked 0 clauses, performed 0 splits and kept 158 clauses.
% 0.21/0.47 SPASS allocated 63900 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.01 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.05 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 7, length 68 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.21/0.47
%------------------------------------------------------------------------------