TSTP Solution File: GRP488-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP488-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 44 RR)
% Number of literals : 44 ( 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('GRP488-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP488-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP488-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP488-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP488-1.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(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
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(54,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
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(56,plain,
equal(double_divide(u,inverse(multiply(double_divide(inverse(u),double_divide(identity,v)),identity))),v),
inference(rew,[status(thm),theory(equality)],[6,54]),
[iquote('0:Rew:6.0,54.0')] ).
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(102,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),inverse(identity))))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[85,7]),
[iquote('0:SpR:85.0,7.0')] ).
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(110,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,identity)),
inference(rew,[status(thm),theory(equality)],[105,69]),
[iquote('0:Rew:105.0,69.0')] ).
cnf(116,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,110]),
[iquote('0:Rew:3.0,110.0')] ).
cnf(123,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),multiply(inverse(v),identity)),
inference(rew,[status(thm),theory(equality)],[105,102]),
[iquote('0:Rew:105.0,102.0')] ).
cnf(124,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[55,123,3]),
[iquote('0:Rew:55.0,123.0,3.0,123.0')] ).
cnf(125,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[124,116]),
[iquote('0:Rew:124.0,116.0')] ).
cnf(136,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,inverse(identity)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[105,55]),
[iquote('0:SpR:105.0,55.0')] ).
cnf(144,plain,
equal(double_divide(identity,multiply(u,identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[105,136,3]),
[iquote('0:Rew:105.0,136.0,3.0,136.0,105.0,136.0')] ).
cnf(148,plain,
equal(multiply(multiply(u,v),identity),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,124]),
[iquote('0:SpR:6.0,124.0')] ).
cnf(163,plain,
equal(inverse(inverse(multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,125]),
[iquote('0:SpR:6.0,125.0')] ).
cnf(166,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[144,6]),
[iquote('0:SpR:144.0,6.0')] ).
cnf(172,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[124,144]),
[iquote('0:SpR:124.0,144.0')] ).
cnf(175,plain,
equal(double_divide(u,multiply(v,inverse(inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[172,55]),
[iquote('0:Rew:172.0,55.0')] ).
cnf(185,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[148,166]),
[iquote('0:Rew:148.0,166.0')] ).
cnf(189,plain,
equal(double_divide(u,inverse(inverse(inverse(double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(rew,[status(thm),theory(equality)],[185,56]),
[iquote('0:Rew:185.0,56.0')] ).
cnf(193,plain,
equal(double_divide(u,multiply(v,inverse(u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[125,175]),
[iquote('0:Rew:125.0,175.0')] ).
cnf(196,plain,
equal(double_divide(u,inverse(inverse(multiply(double_divide(identity,v),inverse(u))))),v),
inference(rew,[status(thm),theory(equality)],[6,189]),
[iquote('0:Rew:6.0,189.0')] ).
cnf(197,plain,
equal(inverse(double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[193,196,163]),
[iquote('0:Rew:193.0,196.0,163.0,196.0')] ).
cnf(198,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,197]),
[iquote('0:Rew:6.0,197.0')] ).
cnf(199,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[185,198]),
[iquote('0:Rew:185.0,198.0')] ).
cnf(200,plain,
$false,
inference(unc,[status(thm)],[199,14]),
[iquote('0:UnC:199.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP488-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 08:38:54 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 123 clauses, backtracked 0 clauses, performed 0 splits and kept 53 clauses.
% 0.21/0.45 SPASS allocated 63321 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.45 0:00:00.04 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.01 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 6, length 44 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.21/0.45
%------------------------------------------------------------------------------