%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:48:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 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(inverse(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(w))))),v),w),
file('GRP592-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP592-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP592-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(multiply(multiply(inverse(u),v),double_divide(v,w)),w),u),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(u,multiply(multiply(inverse(v),w),double_divide(w,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),w),double_divide(w,x))),v),x),u),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(50,plain,
equal(double_divide(multiply(inverse(u),u),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(51,plain,
equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[50,2]),
[iquote('0:SpR:50.0,2.0')] ).
cnf(52,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(inverse(v),v)),w),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[50,4]),
[iquote('0:SpR:50.0,4.0')] ).
cnf(53,plain,
equal(multiply(inverse(u),multiply(multiply(inverse(v),multiply(inverse(w),w)),u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[50,6]),
[iquote('0:SpR:50.0,6.0')] ).
cnf(60,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[51,52]),
[iquote('0:Rew:51.0,52.0')] ).
cnf(61,plain,
equal(multiply(inverse(u),multiply(inverse(v),u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[51,53]),
[iquote('0:Rew:51.0,53.0')] ).
cnf(98,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(v),v))),u),
inference(spr,[status(thm),theory(equality)],[51,60]),
[iquote('0:SpR:51.0,60.0')] ).
cnf(101,plain,
equal(double_divide(inverse(multiply(inverse(u),u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[51,50]),
[iquote('0:SpR:51.0,50.0')] ).
cnf(128,plain,
equal(double_divide(multiply(multiply(inverse(u),inverse(v)),v),inverse(multiply(inverse(w),w))),u),
inference(spr,[status(thm),theory(equality)],[98,4]),
[iquote('0:SpR:98.0,4.0')] ).
cnf(137,plain,
equal(double_divide(multiply(u,v),inverse(multiply(inverse(w),w))),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,98]),
[iquote('0:SpR:2.0,98.0')] ).
cnf(138,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[137,128]),
[iquote('0:Rew:137.0,128.0')] ).
cnf(192,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[101,98]),
[iquote('0:SpR:101.0,98.0')] ).
cnf(205,plain,
equal(double_divide(multiply(multiply(inverse(u),u),double_divide(v,w)),w),v),
inference(spr,[status(thm),theory(equality)],[192,4]),
[iquote('0:SpR:192.0,4.0')] ).
cnf(219,plain,
equal(double_divide(u,multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[192,138]),
[iquote('0:SpR:192.0,138.0')] ).
cnf(246,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[219,2]),
[iquote('0:SpR:219.0,2.0')] ).
cnf(261,plain,
equal(double_divide(u,inverse(multiply(inverse(v),v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[51,219]),
[iquote('0:SpR:51.0,219.0')] ).
cnf(269,plain,
equal(double_divide(inverse(inverse(double_divide(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[246,205]),
[iquote('0:Rew:246.0,205.0')] ).
cnf(271,plain,
equal(double_divide(inverse(multiply(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[2,269]),
[iquote('0:Rew:2.0,269.0')] ).
cnf(272,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[261,98]),
[iquote('0:Rew:261.0,98.0')] ).
cnf(273,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[261,137]),
[iquote('0:Rew:261.0,137.0')] ).
cnf(278,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[273,271]),
[iquote('0:Rew:273.0,271.0')] ).
cnf(375,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[272,61]),
[iquote('0:SpR:272.0,61.0')] ).
cnf(500,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[375]),
[iquote('0:SpR:375.0,375.0')] ).
cnf(512,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[273,500]),
[iquote('0:Rew:273.0,500.0')] ).
cnf(664,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[278,512]),
[iquote('0:SpR:278.0,512.0')] ).
cnf(665,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,664]),
[iquote('0:Rew:2.0,664.0')] ).
cnf(666,plain,
$false,
inference(unc,[status(thm)],[665,3]),
[iquote('0:UnC:665.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 12:18:24 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 553 clauses, backtracked 0 clauses, performed 0 splits and kept 265 clauses.
% 0.20/0.52 SPASS allocated 64171 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.52 0:00:00.04 for the input.
% 0.20/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.09 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 7, length 33 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.20/0.52
%------------------------------------------------------------------------------