TSTP Solution File: GRP497-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 38 ( 0 equ; 2 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(identity,double_divide(u,double_divide(v,identity))),double_divide(double_divide(v,double_divide(w,u)),identity)),w),
file('GRP497-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP497-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP497-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP497-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP497-1.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(identity,double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[3,1,6]),
[iquote('0:Rew:3.0,1.0,6.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(47,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),multiply(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(identity,identity),multiply(double_divide(u,v),v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(58,plain,
equal(double_divide(inverse(identity),multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,55]),
[iquote('0:Rew:3.0,55.0')] ).
cnf(59,plain,
equal(double_divide(identity,multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[47,58]),
[iquote('0:Rew:47.0,58.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),inverse(inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[13,51]),
[iquote('0:Rew:13.0,51.0')] ).
cnf(98,plain,
equal(double_divide(identity,multiply(identity,inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[4,59]),
[iquote('0:SpR:4.0,59.0')] ).
cnf(99,plain,
equal(double_divide(identity,multiply(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[3,59]),
[iquote('0:SpR:3.0,59.0')] ).
cnf(102,plain,
equal(double_divide(identity,inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,98]),
[iquote('0:Rew:13.0,98.0')] ).
cnf(118,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[47,60]),
[iquote('0:SpR:47.0,60.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,double_divide(identity,inverse(u))),inverse(inverse(u))),identity),
inference(spr,[status(thm),theory(equality)],[47,60]),
[iquote('0:SpR:47.0,60.0')] ).
cnf(125,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[6,118,3,47]),
[iquote('0:Rew:6.0,118.0,3.0,118.0,3.0,118.0,47.0,118.0')] ).
cnf(133,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[125,10]),
[iquote('0:SpR:125.0,10.0')] ).
cnf(161,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[125,99]),
[iquote('0:SpR:125.0,99.0')] ).
cnf(163,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[161,102]),
[iquote('0:Rew:161.0,102.0')] ).
cnf(166,plain,
equal(double_divide(inverse(double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[161,7]),
[iquote('0:Rew:161.0,7.0')] ).
cnf(174,plain,
equal(double_divide(inverse(inverse(inverse(u))),u),identity),
inference(rew,[status(thm),theory(equality)],[161,133]),
[iquote('0:Rew:161.0,133.0')] ).
cnf(178,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[161,122]),
[iquote('0:Rew:161.0,122.0')] ).
cnf(192,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[161,178]),
[iquote('0:Rew:161.0,178.0')] ).
cnf(194,plain,
equal(double_divide(multiply(inverse(u),v),multiply(double_divide(w,v),u)),w),
inference(rew,[status(thm),theory(equality)],[6,166]),
[iquote('0:Rew:6.0,166.0')] ).
cnf(283,plain,
equal(double_divide(multiply(inverse(u),v),multiply(identity,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[174,194]),
[iquote('0:SpR:174.0,194.0')] ).
cnf(296,plain,
equal(double_divide(multiply(inverse(u),v),inverse(inverse(u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,283]),
[iquote('0:Rew:13.0,283.0')] ).
cnf(346,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(v))),multiply(identity,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[192,194]),
[iquote('0:SpR:192.0,194.0')] ).
cnf(363,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(v))),inverse(inverse(u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,346]),
[iquote('0:Rew:13.0,346.0')] ).
cnf(364,plain,
equal(inverse(inverse(inverse(inverse(inverse(u))))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[296,363]),
[iquote('0:Rew:296.0,363.0')] ).
cnf(365,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[163,364]),
[iquote('0:Rew:163.0,364.0')] ).
cnf(366,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[365,163]),
[iquote('0:Rew:365.0,163.0')] ).
cnf(376,plain,
$false,
inference(unc,[status(thm)],[366,14]),
[iquote('0:UnC:366.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.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 08:01:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 245 clauses, backtracked 0 clauses, performed 0 splits and kept 96 clauses.
% 0.20/0.43 SPASS allocated 63491 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.02 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 5, length 38 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.20/0.43
%------------------------------------------------------------------------------