TSTP Solution File: GRP540-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:47:57 EDT 2022
% Result : Unsatisfiable 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 0 equ; 1 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,v),divide(divide(u,w),v)),w),
file('GRP540-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP540-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP540-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP540-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP540-1.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(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(30,plain,
equal(divide(divide(u,v),divide(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(34,plain,
equal(divide(divide(u,divide(u,v)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(37,plain,
equal(divide(identity,divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(41,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[7,30,6]),
[iquote('0:Rew:7.0,30.0,6.0,30.0')] ).
cnf(42,plain,
equal(multiply(divide(u,divide(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,34]),
[iquote('0:Rew:15.0,34.0')] ).
cnf(43,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[6,37]),
[iquote('0:Rew:6.0,37.0')] ).
cnf(52,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[4,41]),
[iquote('0:SpR:4.0,41.0')] ).
cnf(54,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[7,41]),
[iquote('0:SpR:7.0,41.0')] ).
cnf(57,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,52]),
[iquote('0:Rew:13.0,52.0')] ).
cnf(61,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[57,7]),
[iquote('0:SpR:57.0,7.0')] ).
cnf(64,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[61,54]),
[iquote('0:Rew:61.0,54.0')] ).
cnf(89,plain,
equal(inverse(divide(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[6,43]),
[iquote('0:SpR:6.0,43.0')] ).
cnf(97,plain,
equal(inverse(multiply(inverse(u),identity)),u),
inference(rew,[status(thm),theory(equality)],[15,89]),
[iquote('0:Rew:15.0,89.0')] ).
cnf(104,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(spr,[status(thm),theory(equality)],[97,57]),
[iquote('0:SpR:97.0,57.0')] ).
cnf(121,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[57,104]),
[iquote('0:SpR:57.0,104.0')] ).
cnf(125,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[121,42]),
[iquote('0:Rew:121.0,42.0')] ).
cnf(144,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[125,41]),
[iquote('0:SpR:125.0,41.0')] ).
cnf(174,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[64,144]),
[iquote('0:SpR:64.0,144.0')] ).
cnf(176,plain,
$false,
inference(unc,[status(thm)],[174,5]),
[iquote('0:UnC:174.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 12:43:20 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.44
% 0.22/0.44 SPASS V 3.9
% 0.22/0.44 SPASS beiseite: Proof found.
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.44 SPASS derived 137 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.22/0.44 SPASS allocated 63227 KBytes.
% 0.22/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.22/0.44 0:00:00.03 for the input.
% 0.22/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.44 0:00:00.00 for inferences.
% 0.22/0.44 0:00:00.00 for the backtracking.
% 0.22/0.44 0:00:00.01 for the reduction.
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 Here is a proof with depth 4, length 29 :
% 0.22/0.44 % SZS output start Refutation
% See solution above
% 0.22/0.44 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.22/0.44
%------------------------------------------------------------------------------