TSTP Solution File: GRP566-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:48:04 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 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(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,identity)),v),
file('GRP566-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP566-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP566-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP566-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP566-1.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(v,double_divide(u,w)),double_divide(identity,w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
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(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,inverse(identity))),identity)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,identity)),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,50,3]),
[iquote('0:Rew:6.0,50.0,3.0,50.0')] ).
cnf(56,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,inverse(u)),inverse(identity))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,51]),
[iquote('0:Rew:3.0,51.0')] ).
cnf(69,plain,
equal(double_divide(double_divide(identity,multiply(identity,u)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,55]),
[iquote('0:SpR:4.0,55.0')] ).
cnf(71,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[13,69]),
[iquote('0:Rew:13.0,69.0')] ).
cnf(116,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(identity))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,56]),
[iquote('0:SpR:4.0,56.0')] ).
cnf(121,plain,
equal(double_divide(double_divide(inverse(u),u),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[71,56]),
[iquote('0:SpR:71.0,56.0')] ).
cnf(123,plain,
equal(double_divide(inverse(u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,116,4]),
[iquote('0:Rew:3.0,116.0,4.0,116.0')] ).
cnf(162,plain,
equal(double_divide(inverse(inverse(identity)),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,121]),
[iquote('0:SpR:3.0,121.0')] ).
cnf(164,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[123,162]),
[iquote('0:Rew:123.0,162.0')] ).
cnf(170,plain,
equal(double_divide(inverse(u),identity),u),
inference(rew,[status(thm),theory(equality)],[164,123]),
[iquote('0:Rew:164.0,123.0')] ).
cnf(185,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,170]),
[iquote('0:Rew:3.0,170.0')] ).
cnf(186,plain,
$false,
inference(unc,[status(thm)],[185,14]),
[iquote('0:UnC:185.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:34:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 128 clauses, backtracked 0 clauses, performed 0 splits and kept 57 clauses.
% 0.19/0.43 SPASS allocated 63351 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 4, length 23 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.19/0.43
%------------------------------------------------------------------------------