TSTP Solution File: GRP521-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:47:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(v,divide(w,divide(u,v)))),w),
file('GRP521-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP521-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP521-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP521-1.p',unknown),
[] ).
cnf(5,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(8,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(51,plain,
equal(inverse(divide(u,divide(v,divide(divide(w,w),u)))),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(70,plain,
equal(divide(u,inverse(divide(v,divide(u,divide(w,w))))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(75,plain,
equal(inverse(divide(u,multiply(v,u))),v),
inference(rew,[status(thm),theory(equality)],[5,51,3]),
[iquote('0:Rew:5.0,51.0,3.0,51.0')] ).
cnf(78,plain,
equal(multiply(u,divide(v,divide(u,divide(w,w)))),v),
inference(rew,[status(thm),theory(equality)],[5,70]),
[iquote('0:Rew:5.0,70.0')] ).
cnf(99,plain,
equal(inverse(divide(u,inverse(inverse(u)))),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[10,75]),
[iquote('0:SpR:10.0,75.0')] ).
cnf(106,plain,
equal(inverse(multiply(u,inverse(u))),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[5,99]),
[iquote('0:Rew:5.0,99.0')] ).
cnf(128,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[106]),
[iquote('0:SpR:106.0,106.0')] ).
cnf(140,plain,
equal(divide(u,divide(u,divide(v,inverse(multiply(w,inverse(w)))))),v),
inference(spr,[status(thm),theory(equality)],[106,1]),
[iquote('0:SpR:106.0,1.0')] ).
cnf(143,plain,
equal(divide(u,divide(v,inverse(multiply(w,inverse(w))))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[106,1]),
[iquote('0:SpR:106.0,1.0')] ).
cnf(149,plain,
equal(divide(u,divide(u,multiply(v,multiply(w,inverse(w))))),v),
inference(rew,[status(thm),theory(equality)],[5,140]),
[iquote('0:Rew:5.0,140.0')] ).
cnf(150,plain,
equal(divide(u,multiply(v,multiply(w,inverse(w)))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[5,143]),
[iquote('0:Rew:5.0,143.0')] ).
cnf(151,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[150,149]),
[iquote('0:Rew:150.0,149.0')] ).
cnf(165,plain,
equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
inference(spr,[status(thm),theory(equality)],[128,1]),
[iquote('0:SpR:128.0,1.0')] ).
cnf(187,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[151,165]),
[iquote('0:Rew:151.0,165.0')] ).
cnf(188,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[187,78]),
[iquote('0:Rew:187.0,78.0')] ).
cnf(321,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[151,188]),
[iquote('0:SpR:151.0,188.0')] ).
cnf(404,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[8,321]),
[iquote('0:SpR:8.0,321.0')] ).
cnf(408,plain,
$false,
inference(unc,[status(thm)],[404,4]),
[iquote('0:UnC:404.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.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 08:39:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 313 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.45 SPASS allocated 63406 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.02 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 5, length 25 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.20/0.45
%------------------------------------------------------------------------------