TSTP Solution File: GRP580-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:48:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 45 RR)
% Number of literals : 45 ( 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(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP580-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP580-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP580-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP580-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP580-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),inverse(v))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(20,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,v),inverse(u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(22,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),inverse(double_divide(v,u))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(23,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(v,u)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,22]),
[iquote('0:Rew:6.0,22.0')] ).
cnf(25,plain,
equal(double_divide(double_divide(u,double_divide(multiply(u,v),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,23]),
[iquote('0:Rew:6.0,23.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[4,24]),
[iquote('0:SpR:4.0,24.0')] ).
cnf(73,plain,
equal(double_divide(inverse(u),inverse(identity)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[3,72]),
[iquote('0:Rew:3.0,72.0')] ).
cnf(82,plain,
equal(double_divide(multiply(u,v),inverse(identity)),multiply(double_divide(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,73]),
[iquote('0:SpR:6.0,73.0')] ).
cnf(136,plain,
equal(double_divide(double_divide(inverse(double_divide(identity,u)),identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpR:4.0,20.0')] ).
cnf(138,plain,
equal(double_divide(double_divide(inverse(identity),multiply(identity,u)),inverse(identity)),double_divide(identity,inverse(u))),
inference(spr,[status(thm),theory(equality)],[24,20]),
[iquote('0:SpR:24.0,20.0')] ).
cnf(139,plain,
equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(multiply(identity,u),inverse(u))),
inference(spr,[status(thm),theory(equality)],[25,20]),
[iquote('0:SpR:25.0,20.0')] ).
cnf(141,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[73,136,3,6]),
[iquote('0:Rew:73.0,136.0,3.0,136.0,6.0,136.0')] ).
cnf(143,plain,
equal(double_divide(double_divide(inverse(identity),inverse(inverse(u))),inverse(identity)),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,138]),
[iquote('0:Rew:13.0,138.0')] ).
cnf(144,plain,
equal(double_divide(inverse(inverse(u)),inverse(u)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[12,139,73,3,13]),
[iquote('0:Rew:12.0,139.0,73.0,139.0,3.0,139.0,13.0,139.0')] ).
cnf(158,plain,
equal(multiply(inverse(inverse(identity)),identity),identity),
inference(spr,[status(thm),theory(equality)],[13,141]),
[iquote('0:SpR:13.0,141.0')] ).
cnf(161,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),double_divide(identity,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[158,82]),
[iquote('0:SpR:158.0,82.0')] ).
cnf(167,plain,
equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),identity),
inference(rew,[status(thm),theory(equality)],[4,161]),
[iquote('0:Rew:4.0,161.0')] ).
cnf(173,plain,
equal(double_divide(identity,inverse(inverse(identity))),multiply(identity,identity)),
inference(spr,[status(thm),theory(equality)],[167,141]),
[iquote('0:SpR:167.0,141.0')] ).
cnf(175,plain,
equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))),
inference(rew,[status(thm),theory(equality)],[13,173]),
[iquote('0:Rew:13.0,173.0')] ).
cnf(185,plain,
equal(multiply(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[175,6]),
[iquote('0:SpR:175.0,6.0')] ).
cnf(192,plain,
equal(inverse(inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[158,185]),
[iquote('0:Rew:158.0,185.0')] ).
cnf(246,plain,
equal(double_divide(inverse(identity),identity),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[192,144]),
[iquote('0:SpR:192.0,144.0')] ).
cnf(250,plain,
equal(inverse(inverse(identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[3,246]),
[iquote('0:Rew:3.0,246.0')] ).
cnf(253,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[250,192]),
[iquote('0:Rew:250.0,192.0')] ).
cnf(261,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[250,253]),
[iquote('0:Rew:250.0,253.0')] ).
cnf(265,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),identity),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[261,24]),
[iquote('0:Rew:261.0,24.0')] ).
cnf(266,plain,
equal(double_divide(inverse(u),identity),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[261,73]),
[iquote('0:Rew:261.0,73.0')] ).
cnf(293,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[261,143]),
[iquote('0:Rew:261.0,143.0')] ).
cnf(318,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,266]),
[iquote('0:Rew:3.0,266.0')] ).
cnf(319,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[318,141]),
[iquote('0:Rew:318.0,141.0')] ).
cnf(322,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[318,319]),
[iquote('0:Rew:318.0,319.0')] ).
cnf(352,plain,
equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,265,3]),
[iquote('0:Rew:6.0,265.0,3.0,265.0')] ).
cnf(360,plain,
equal(multiply(inverse(inverse(u)),identity),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,293,3]),
[iquote('0:Rew:6.0,293.0,3.0,293.0')] ).
cnf(361,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[322,360,318]),
[iquote('0:Rew:322.0,360.0,318.0,360.0')] ).
cnf(362,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[361,352]),
[iquote('0:Rew:361.0,352.0')] ).
cnf(365,plain,
$false,
inference(unc,[status(thm)],[362,5]),
[iquote('0:UnC:362.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 20:08:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 226 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.19/0.44 SPASS allocated 63652 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.03 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 7, length 45 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.19/0.44
%------------------------------------------------------------------------------