TSTP Solution File: GRP487-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:47:42 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 22 ( 0 equ; 2 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(double_divide(u,double_divide(double_divide(double_divide(identity,double_divide(double_divide(u,identity),double_divide(v,w))),v),identity)),w),
file('GRP487-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP487-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP487-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP487-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(a1),a1),identity),
file('GRP487-1.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(u,multiply(v,double_divide(identity,double_divide(inverse(u),double_divide(v,w))))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0,3.0,1.0')] ).
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(14,plain,
~ equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(16,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(50,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(55,plain,
equal(double_divide(u,multiply(v,double_divide(identity,inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(68,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,inverse(inverse(u)))))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[13,55]),
[iquote('0:SpR:13.0,55.0')] ).
cnf(69,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[16,55]),
[iquote('0:SpR:16.0,55.0')] ).
cnf(71,plain,
equal(double_divide(u,inverse(multiply(inverse(inverse(u)),identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[6,68]),
[iquote('0:Rew:6.0,68.0')] ).
cnf(72,plain,
equal(double_divide(u,double_divide(u,inverse(identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[69,71]),
[iquote('0:Rew:69.0,71.0')] ).
cnf(80,plain,
equal(double_divide(u,multiply(inverse(u),double_divide(identity,inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[72,7]),
[iquote('0:SpR:72.0,7.0')] ).
cnf(85,plain,
equal(double_divide(u,multiply(inverse(u),identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[4,80]),
[iquote('0:Rew:4.0,80.0')] ).
cnf(104,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,85]),
[iquote('0:SpR:12.0,85.0')] ).
cnf(105,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,104]),
[iquote('0:Rew:4.0,104.0')] ).
cnf(106,plain,
$false,
inference(mrr,[status(thm)],[105,14]),
[iquote('0:MRR:105.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.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 : Tue Jun 14 02:15:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 68 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.19/0.41 SPASS allocated 63240 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.01 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 4, length 22 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.19/0.41
%------------------------------------------------------------------------------