TSTP Solution File: GRP012-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:44:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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,identity),u),
file('GRP012-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(u,inverse(u)),identity),
file('GRP012-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b),inverse(a)),inverse(multiply(a,b))),
file('GRP012-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP012-4.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP012-4.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP012-4.p',unknown),
[] ).
cnf(18,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,v)))),identity),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(22,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(27,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,22]),
[iquote('0:Rew:4.0,22.0')] ).
cnf(71,plain,
equal(multiply(u,inverse(multiply(v,u))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[18,27]),
[iquote('0:SpR:18.0,27.0')] ).
cnf(93,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1,71]),
[iquote('0:Rew:1.0,71.0')] ).
cnf(108,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[93,27]),
[iquote('0:SpR:93.0,27.0')] ).
cnf(122,plain,
$false,
inference(unc,[status(thm)],[108,3]),
[iquote('0:UnC:108.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 : Tue Jun 14 14:19:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 81 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.20/0.41 SPASS allocated 63197 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 13 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : right_identity right_inverse prove_inverse_of_product_is_product_of_inverses left_identity left_inverse associativity
% 0.20/0.41
%------------------------------------------------------------------------------