TSTP Solution File: GRP544-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 11:47:58 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(divide(divide(u,v),w),u)),w),v),
file('GRP544-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP544-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP544-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP544-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP544-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(divide(divide(u,v),w),u)),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(30,plain,
equal(divide(inverse(divide(divide(identity,u),v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(34,plain,
equal(divide(inverse(divide(identity,u)),divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(39,plain,
equal(divide(inverse(divide(inverse(u),v)),u),v),
inference(rew,[status(thm),theory(equality)],[3,30]),
[iquote('0:Rew:3.0,30.0')] ).
cnf(40,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,34]),
[iquote('0:Rew:3.0,34.0')] ).
cnf(68,plain,
equal(divide(inverse(u),inverse(v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[40,39]),
[iquote('0:SpR:40.0,39.0')] ).
cnf(71,plain,
equal(divide(inverse(inverse(identity)),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(78,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,71,6,9]),
[iquote('0:Rew:13.0,71.0,6.0,71.0,9.0,71.0,9.0,71.0')] ).
cnf(86,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,68]),
[iquote('0:Rew:6.0,68.0')] ).
cnf(137,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[78,86]),
[iquote('0:SpR:78.0,86.0')] ).
cnf(139,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,137]),
[iquote('0:Rew:6.0,137.0')] ).
cnf(140,plain,
$false,
inference(unc,[status(thm)],[139,5]),
[iquote('0:UnC:139.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 12:00:24 EDT 2022
% 0.12/0.33 % 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 98 clauses, backtracked 0 clauses, performed 0 splits and kept 47 clauses.
% 0.20/0.41 SPASS allocated 63240 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.03 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 0:00:00.01 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 20 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.20/0.41
%------------------------------------------------------------------------------