TSTP Solution File: GRP206-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% 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 11:46:19 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 8 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(identity,u),u),
file('GRP206-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(u,identity),u),
file('GRP206-1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(multiply(u,v),multiply(w,u)),multiply(u,multiply(multiply(v,w),u))),
file('GRP206-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(multiply(multiply(a,multiply(b,c)),a),multiply(multiply(a,b),multiply(c,a))),
file('GRP206-1.p',unknown),
[] ).
cnf(11,plain,
~ equal(multiply(multiply(a,multiply(b,c)),a),multiply(a,multiply(multiply(b,c),a))),
inference(rew,[status(thm),theory(equality)],[9,10]),
[iquote('0:Rew:9.0,10.0')] ).
cnf(87,plain,
equal(multiply(u,multiply(multiply(v,identity),u)),multiply(multiply(u,v),u)),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(99,plain,
equal(multiply(multiply(u,v),u),multiply(u,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[2,87]),
[iquote('0:Rew:2.0,87.0')] ).
cnf(100,plain,
$false,
inference(unc,[status(thm)],[99,11]),
[iquote('0:UnC:99.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n025.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 : Mon Jun 13 15:16:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 84 clauses, backtracked 0 clauses, performed 0 splits and kept 36 clauses.
% 0.21/0.42 SPASS allocated 63197 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.03 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 1, length 8 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : left_identity right_identity moufang4 prove_moufang1
% 0.21/0.42
%------------------------------------------------------------------------------