TSTP Solution File: GRP588-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP588-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:48:10 EDT 2022
% Result : Unsatisfiable 0.47s 0.65s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 39 RR)
% Number of literals : 39 ( 0 equ; 1 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(u,inverse(double_divide(inverse(double_divide(double_divide(u,v),inverse(w))),v))),w),
file('GRP588-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP588-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP588-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(u,multiply(v,multiply(inverse(w),double_divide(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,multiply(inverse(v),double_divide(w,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(multiply(v,multiply(inverse(w),double_divide(u,v))),multiply(inverse(x),w))),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(double_divide(u,multiply(v,multiply(multiply(w,x),double_divide(u,v)))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(44,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(45,plain,
equal(multiply(inverse(u),multiply(inverse(v),u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[44,2]),
[iquote('0:SpR:44.0,2.0')] ).
cnf(56,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(u),v))),v),
inference(spr,[status(thm),theory(equality)],[45,44]),
[iquote('0:SpR:45.0,44.0')] ).
cnf(58,plain,
equal(multiply(inverse(multiply(inverse(u),v)),inverse(u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[45]),
[iquote('0:SpR:45.0,45.0')] ).
cnf(94,plain,
equal(double_divide(inverse(u),inverse(inverse(v))),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[45,56]),
[iquote('0:SpR:45.0,56.0')] ).
cnf(119,plain,
equal(double_divide(inverse(u),inverse(multiply(v,w))),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[2,94]),
[iquote('0:SpR:2.0,94.0')] ).
cnf(121,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[119,56]),
[iquote('0:Rew:119.0,56.0')] ).
cnf(124,plain,
equal(multiply(inverse(u),double_divide(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[121,6]),
[iquote('0:SpR:121.0,6.0')] ).
cnf(127,plain,
equal(double_divide(u,inverse(double_divide(v,w))),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[121,9]),
[iquote('0:SpR:121.0,9.0')] ).
cnf(134,plain,
equal(double_divide(u,multiply(v,w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[2,127]),
[iquote('0:Rew:2.0,127.0')] ).
cnf(161,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(spr,[status(thm),theory(equality)],[124,4]),
[iquote('0:SpR:124.0,4.0')] ).
cnf(165,plain,
equal(double_divide(inverse(u),inverse(double_divide(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[124,44]),
[iquote('0:SpR:124.0,44.0')] ).
cnf(167,plain,
equal(multiply(inverse(u),u),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[124,121]),
[iquote('0:SpR:124.0,121.0')] ).
cnf(176,plain,
equal(double_divide(inverse(u),multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[2,165]),
[iquote('0:Rew:2.0,165.0')] ).
cnf(205,plain,
equal(multiply(double_divide(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[167,121]),
[iquote('0:SpR:167.0,121.0')] ).
cnf(217,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[167,94]),
[iquote('0:SpR:167.0,94.0')] ).
cnf(248,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[94,205]),
[iquote('0:SpR:94.0,205.0')] ).
cnf(312,plain,
equal(double_divide(u,multiply(inverse(v),double_divide(u,multiply(inverse(w),w)))),v),
inference(spr,[status(thm),theory(equality)],[248,4]),
[iquote('0:SpR:248.0,4.0')] ).
cnf(324,plain,
equal(double_divide(inverse(u),multiply(multiply(inverse(v),v),multiply(inverse(w),u))),w),
inference(spr,[status(thm),theory(equality)],[176,4]),
[iquote('0:SpR:176.0,4.0')] ).
cnf(334,plain,
equal(double_divide(inverse(u),multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[248,324]),
[iquote('0:Rew:248.0,324.0')] ).
cnf(335,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[134,334]),
[iquote('0:Rew:134.0,334.0')] ).
cnf(547,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[335,176]),
[iquote('0:SpR:335.0,176.0')] ).
cnf(550,plain,
equal(double_divide(u,multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[217,335]),
[iquote('0:SpR:217.0,335.0')] ).
cnf(553,plain,
equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[58,335]),
[iquote('0:SpR:58.0,335.0')] ).
cnf(571,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[550,312]),
[iquote('0:Rew:550.0,312.0')] ).
cnf(607,plain,
equal(double_divide(u,double_divide(u,inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[553,161]),
[iquote('0:Rew:553.0,161.0')] ).
cnf(694,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[547,571,553]),
[iquote('0:Rew:547.0,571.0,553.0,571.0')] ).
cnf(701,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[547,607]),
[iquote('0:Rew:547.0,607.0')] ).
cnf(962,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[694,701]),
[iquote('0:SpR:694.0,701.0')] ).
cnf(1019,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[962,2]),
[iquote('0:SpR:962.0,2.0')] ).
cnf(1029,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,1019]),
[iquote('0:Rew:2.0,1019.0')] ).
cnf(1030,plain,
$false,
inference(unc,[status(thm)],[1029,3]),
[iquote('0:UnC:1029.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP588-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 22:05:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/0.65
% 0.47/0.65 SPASS V 3.9
% 0.47/0.65 SPASS beiseite: Proof found.
% 0.47/0.65 % SZS status Theorem
% 0.47/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.65 SPASS derived 639 clauses, backtracked 0 clauses, performed 0 splits and kept 329 clauses.
% 0.47/0.65 SPASS allocated 64866 KBytes.
% 0.47/0.65 SPASS spent 0:00:00.27 on the problem.
% 0.47/0.65 0:00:00.03 for the input.
% 0.47/0.65 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.65 0:00:00.01 for inferences.
% 0.47/0.65 0:00:00.00 for the backtracking.
% 0.47/0.65 0:00:00.20 for the reduction.
% 0.47/0.65
% 0.47/0.65
% 0.47/0.65 Here is a proof with depth 11, length 39 :
% 0.47/0.65 % SZS output start Refutation
% See solution above
% 0.47/0.65 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.47/0.65
%------------------------------------------------------------------------------