TSTP Solution File: GRP517-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:47:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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('GRP517-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP517-1.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(8,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)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
cnf(25,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(w,v))),w),u),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
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(70,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(spr,[status(thm),theory(equality)],[55,8]),
[iquote('0:SpR:55.0,8.0')] ).
cnf(74,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[8,55]),
[iquote('0:SpR:8.0,55.0')] ).
cnf(77,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(w,v))),w),
inference(rew,[status(thm),theory(equality)],[74,8]),
[iquote('0:Rew:74.0,8.0')] ).
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)],[74,70]),
[iquote('0:Rew:74.0,70.0')] ).
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(128,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)],[128,116]),
[iquote('0:Rew:128.0,116.0')] ).
cnf(142,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[131,84]),
[iquote('0:SpR:131.0,84.0')] ).
cnf(143,plain,
$false,
inference(unc,[status(thm)],[142,2]),
[iquote('0:UnC:142.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:18:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 110 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.18/0.43 SPASS allocated 63409 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.02 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 21 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : single_axiom prove_these_axioms_1
% 0.18/0.43
%------------------------------------------------------------------------------