TSTP Solution File: GRP518-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:47:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 1 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(multiply(inverse(multiply(u,v)),w),v)),w),
file('GRP518-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP518-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(multiply(inverse(multiply(inverse(multiply(u,v)),w)),x),w),multiply(u,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,multiply(multiply(inverse(v),w),multiply(multiply(inverse(multiply(u,x)),v),x))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(9,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,v))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(24,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(w,x)))),multiply(u,w)),inverse(multiply(v,x))),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(25,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(w,v))),w),u),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(55,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(71,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(spr,[status(thm),theory(equality)],[55,9]),
[iquote('0:SpR:55.0,9.0')] ).
cnf(74,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[9,55]),
[iquote('0:SpR:9.0,55.0')] ).
cnf(77,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(w,v))),w),
inference(rew,[status(thm),theory(equality)],[74,9]),
[iquote('0:Rew:74.0,9.0')] ).
cnf(81,plain,
equal(multiply(u,multiply(inverse(multiply(u,multiply(v,multiply(w,x)))),w)),inverse(multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[74,24]),
[iquote('0:Rew:74.0,24.0')] ).
cnf(83,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[74,71]),
[iquote('0:Rew:74.0,71.0')] ).
cnf(84,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[83,77]),
[iquote('0:Rew:83.0,77.0')] ).
cnf(95,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),v),inverse(multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[83,81]),
[iquote('0:Rew:83.0,81.0')] ).
cnf(96,plain,
equal(inverse(multiply(inverse(multiply(u,v)),v)),u),
inference(rew,[status(thm),theory(equality)],[95,25]),
[iquote('0:Rew:95.0,25.0')] ).
cnf(116,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(spr,[status(thm),theory(equality)],[84,1]),
[iquote('0:SpR:84.0,1.0')] ).
cnf(127,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[55,96]),
[iquote('0:SpR:55.0,96.0')] ).
cnf(131,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[127,116]),
[iquote('0:Rew:127.0,116.0')] ).
cnf(134,plain,
$false,
inference(unc,[status(thm)],[131,2]),
[iquote('0:UnC:131.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 13:06:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 104 clauses, backtracked 0 clauses, performed 0 splits and kept 58 clauses.
% 0.20/0.44 SPASS allocated 63402 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 4, length 20 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom prove_these_axioms_2
% 0.20/0.45
%------------------------------------------------------------------------------