TSTP Solution File: GRP536-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:47:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(divide(u,v),w)),v),w),
file('GRP536-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP536-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP536-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP536-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP536-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(27,plain,
equal(multiply(divide(u,divide(divide(u,identity),v)),identity),v),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(31,plain,
equal(divide(divide(u,divide(identity,v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(35,plain,
equal(divide(divide(u,identity),v),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(39,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[7,31,6]),
[iquote('0:Rew:7.0,31.0,6.0,31.0')] ).
cnf(40,plain,
equal(divide(multiply(u,identity),v),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[15,35]),
[iquote('0:Rew:15.0,35.0')] ).
cnf(43,plain,
equal(multiply(divide(u,divide(multiply(u,identity),v)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,27]),
[iquote('0:Rew:15.0,27.0')] ).
cnf(44,plain,
equal(multiply(divide(u,divide(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[40,43]),
[iquote('0:Rew:40.0,43.0')] ).
cnf(52,plain,
equal(multiply(multiply(identity,u),identity),u),
inference(spr,[status(thm),theory(equality)],[39,15]),
[iquote('0:SpR:39.0,15.0')] ).
cnf(54,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,39]),
[iquote('0:SpR:12.0,39.0')] ).
cnf(56,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,54,7]),
[iquote('0:Rew:13.0,54.0,7.0,54.0')] ).
cnf(57,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[56,13]),
[iquote('0:Rew:56.0,13.0')] ).
cnf(58,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[57,52]),
[iquote('0:Rew:57.0,52.0')] ).
cnf(60,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[58,44]),
[iquote('0:Rew:58.0,44.0')] ).
cnf(65,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[56,7]),
[iquote('0:SpR:56.0,7.0')] ).
cnf(109,plain,
equal(divide(multiply(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[39,60]),
[iquote('0:SpR:39.0,60.0')] ).
cnf(123,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[109,7]),
[iquote('0:SpR:109.0,7.0')] ).
cnf(130,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[65,123]),
[iquote('0:Rew:65.0,123.0')] ).
cnf(137,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[39,130]),
[iquote('0:SpR:39.0,130.0')] ).
cnf(142,plain,
$false,
inference(unc,[status(thm)],[137,5]),
[iquote('0:UnC:137.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 12:50:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 103 clauses, backtracked 0 clauses, performed 0 splits and kept 39 clauses.
% 0.20/0.42 SPASS allocated 63209 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 6, length 30 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.20/0.42
%------------------------------------------------------------------------------