TSTP Solution File: GRP582-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 47 RR)
% Number of literals : 47 ( 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(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,identity)),w),
file('GRP582-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP582-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP582-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP582-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP582-1.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(identity,v),double_divide(w,double_divide(v,u)))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew: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(50,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),double_divide(v,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(identity,double_divide(double_divide(identity,u),double_divide(v,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(53,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(inverse(identity),u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(67,plain,
equal(double_divide(double_divide(inverse(u),identity),inverse(identity)),double_divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,55]),
[iquote('0:SpR:4.0,55.0')] ).
cnf(68,plain,
equal(double_divide(double_divide(inverse(double_divide(double_divide(identity,u),double_divide(v,double_divide(u,identity)))),v),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[7,55]),
[iquote('0:SpR:7.0,55.0')] ).
cnf(70,plain,
equal(double_divide(inverse(inverse(u)),inverse(identity)),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,67]),
[iquote('0:Rew:3.0,67.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,68,3]),
[iquote('0:Rew:6.0,68.0,3.0,68.0')] ).
cnf(79,plain,
equal(double_divide(inverse(multiply(u,v)),inverse(identity)),double_divide(identity,double_divide(v,u))),
inference(spr,[status(thm),theory(equality)],[6,70]),
[iquote('0:SpR:6.0,70.0')] ).
cnf(107,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,51]),
[iquote('0:SpR:4.0,51.0')] ).
cnf(114,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[6,107,3]),
[iquote('0:Rew:6.0,107.0,3.0,107.0')] ).
cnf(143,plain,
equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,114]),
[iquote('0:SpR:12.0,114.0')] ).
cnf(145,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,143]),
[iquote('0:Rew:4.0,143.0,4.0,143.0')] ).
cnf(148,plain,
equal(double_divide(inverse(inverse(u)),identity),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[145,70]),
[iquote('0:Rew:145.0,70.0')] ).
cnf(151,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),identity),u),
inference(rew,[status(thm),theory(equality)],[145,114]),
[iquote('0:Rew:145.0,114.0')] ).
cnf(152,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(identity,u)))),identity),v),
inference(rew,[status(thm),theory(equality)],[145,53]),
[iquote('0:Rew:145.0,53.0')] ).
cnf(157,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),identity),identity),
inference(rew,[status(thm),theory(equality)],[145,73]),
[iquote('0:Rew:145.0,73.0')] ).
cnf(158,plain,
equal(double_divide(inverse(multiply(u,v)),identity),double_divide(identity,double_divide(v,u))),
inference(rew,[status(thm),theory(equality)],[145,79]),
[iquote('0:Rew:145.0,79.0')] ).
cnf(172,plain,
equal(inverse(inverse(inverse(u))),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,148]),
[iquote('0:Rew:3.0,148.0')] ).
cnf(175,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[6,151,3]),
[iquote('0:Rew:6.0,151.0,3.0,151.0')] ).
cnf(190,plain,
equal(double_divide(identity,double_divide(u,v)),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[3,158]),
[iquote('0:Rew:3.0,158.0')] ).
cnf(204,plain,
equal(multiply(double_divide(identity,double_divide(u,double_divide(identity,v))),v),u),
inference(rew,[status(thm),theory(equality)],[6,152,3]),
[iquote('0:Rew:6.0,152.0,3.0,152.0')] ).
cnf(205,plain,
equal(multiply(inverse(inverse(multiply(double_divide(identity,u),v))),u),v),
inference(rew,[status(thm),theory(equality)],[190,204]),
[iquote('0:Rew:190.0,204.0')] ).
cnf(208,plain,
equal(multiply(u,multiply(double_divide(u,inverse(v)),double_divide(identity,v))),identity),
inference(rew,[status(thm),theory(equality)],[6,157,3]),
[iquote('0:Rew:6.0,157.0,3.0,157.0')] ).
cnf(256,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(double_divide(identity,u)))),
inference(spr,[status(thm),theory(equality)],[172]),
[iquote('0:SpR:172.0,172.0')] ).
cnf(258,plain,
equal(double_divide(identity,inverse(u)),inverse(double_divide(identity,u))),
inference(spr,[status(thm),theory(equality)],[172]),
[iquote('0:SpR:172.0,172.0')] ).
cnf(263,plain,
equal(double_divide(identity,inverse(u)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[6,258]),
[iquote('0:Rew:6.0,258.0')] ).
cnf(266,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[6,256]),
[iquote('0:Rew:6.0,256.0')] ).
cnf(267,plain,
equal(multiply(inverse(u),identity),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[263,266]),
[iquote('0:Rew:263.0,266.0')] ).
cnf(375,plain,
equal(inverse(multiply(double_divide(u,v),identity)),multiply(multiply(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,267]),
[iquote('0:SpR:6.0,267.0')] ).
cnf(444,plain,
equal(multiply(u,multiply(identity,double_divide(identity,u))),identity),
inference(spr,[status(thm),theory(equality)],[4,208]),
[iquote('0:SpR:4.0,208.0')] ).
cnf(447,plain,
equal(multiply(u,inverse(multiply(u,identity))),identity),
inference(rew,[status(thm),theory(equality)],[6,444,13]),
[iquote('0:Rew:6.0,444.0,13.0,444.0')] ).
cnf(462,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),multiply(inverse(inverse(identity)),u)),
inference(spr,[status(thm),theory(equality)],[447,205]),
[iquote('0:SpR:447.0,205.0')] ).
cnf(475,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,462,145]),
[iquote('0:Rew:13.0,462.0,145.0,462.0,145.0,462.0')] ).
cnf(476,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[375,475]),
[iquote('0:Rew:375.0,475.0')] ).
cnf(477,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[175,476]),
[iquote('0:Rew:175.0,476.0')] ).
cnf(478,plain,
$false,
inference(unc,[status(thm)],[477,14]),
[iquote('0:UnC:477.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP582-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 09:47:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 257 clauses, backtracked 0 clauses, performed 0 splits and kept 91 clauses.
% 0.18/0.43 SPASS allocated 63655 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 47 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.18/0.43
%------------------------------------------------------------------------------