%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:47:55 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(v,w)),divide(u,v)),w),
file('GRP531-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP531-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP531-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP531-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(21,plain,
equal(divide(u,divide(divide(v,divide(w,u)),v)),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(22,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(30,plain,
equal(divide(divide(u,multiply(v,w)),divide(u,v)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(31,plain,
equal(divide(divide(u,inverse(v)),divide(u,divide(w,w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(38,plain,
equal(divide(multiply(u,v),divide(u,divide(w,w))),v),
inference(rew,[status(thm),theory(equality)],[5,31]),
[iquote('0:Rew:5.0,31.0')] ).
cnf(55,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,22]),
[iquote('0:SpR:3.0,22.0')] ).
cnf(59,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[55,10]),
[iquote('0:Rew:55.0,10.0')] ).
cnf(64,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[55,5]),
[iquote('0:SpR:55.0,5.0')] ).
cnf(68,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[22,55]),
[iquote('0:SpR:22.0,55.0')] ).
cnf(71,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[68,21]),
[iquote('0:Rew:68.0,21.0')] ).
cnf(72,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,71]),
[iquote('0:Rew:5.0,71.0')] ).
cnf(80,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[72,59]),
[iquote('0:SpR:72.0,59.0')] ).
cnf(86,plain,
equal(divide(u,divide(v,w)),multiply(divide(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,72]),
[iquote('0:SpR:1.0,72.0')] ).
cnf(88,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[80,38]),
[iquote('0:Rew:80.0,38.0')] ).
cnf(93,plain,
equal(multiply(divide(divide(u,divide(v,w)),u),v),w),
inference(rew,[status(thm),theory(equality)],[86,1]),
[iquote('0:Rew:86.0,1.0')] ).
cnf(97,plain,
equal(multiply(divide(divide(u,multiply(v,w)),u),v),inverse(w)),
inference(rew,[status(thm),theory(equality)],[86,30]),
[iquote('0:Rew:86.0,30.0')] ).
cnf(98,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[86,80]),
[iquote('0:Rew:86.0,80.0')] ).
cnf(101,plain,
equal(multiply(divide(multiply(divide(u,v),w),u),v),w),
inference(rew,[status(thm),theory(equality)],[86,93]),
[iquote('0:Rew:86.0,93.0')] ).
cnf(103,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[68,97]),
[iquote('0:Rew:68.0,97.0')] ).
cnf(115,plain,
equal(multiply(multiply(multiply(divide(inverse(u),v),w),u),v),w),
inference(spr,[status(thm),theory(equality)],[5,101]),
[iquote('0:SpR:5.0,101.0')] ).
cnf(164,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[5,98]),
[iquote('0:SpR:5.0,98.0')] ).
cnf(169,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[88,98]),
[iquote('0:SpR:88.0,98.0')] ).
cnf(177,plain,
equal(multiply(u,multiply(multiply(divide(inverse(v),u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[169,115]),
[iquote('0:Rew:169.0,115.0')] ).
cnf(184,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[169,103]),
[iquote('0:Rew:169.0,103.0')] ).
cnf(189,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[169,4]),
[iquote('0:Rew:169.0,4.0')] ).
cnf(190,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[64,164]),
[iquote('0:Rew:64.0,164.0')] ).
cnf(200,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[64,184]),
[iquote('0:Rew:64.0,184.0')] ).
cnf(205,plain,
equal(multiply(u,multiply(v,multiply(divide(inverse(v),u),w))),w),
inference(rew,[status(thm),theory(equality)],[169,177]),
[iquote('0:Rew:169.0,177.0')] ).
cnf(294,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[64,169]),
[iquote('0:SpR:64.0,169.0')] ).
cnf(378,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[200,68]),
[iquote('0:SpR:200.0,68.0')] ).
cnf(395,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(u,v)),w))),w),
inference(rew,[status(thm),theory(equality)],[378,205]),
[iquote('0:Rew:378.0,205.0')] ).
cnf(401,plain,
equal(multiply(u,multiply(v,divide(w,multiply(u,v)))),w),
inference(rew,[status(thm),theory(equality)],[294,395]),
[iquote('0:Rew:294.0,395.0')] ).
cnf(583,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[190,401]),
[iquote('0:SpR:190.0,401.0')] ).
cnf(596,plain,
$false,
inference(unc,[status(thm)],[583,189]),
[iquote('0:UnC:583.0,189.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP531-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n023.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 : Tue Jun 14 09:59:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46
% 0.20/0.46 SPASS V 3.9
% 0.20/0.46 SPASS beiseite: Proof found.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 SPASS derived 397 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.46 SPASS allocated 63560 KBytes.
% 0.20/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.46 0:00:00.03 for the input.
% 0.20/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46 0:00:00.00 for inferences.
% 0.20/0.46 0:00:00.00 for the backtracking.
% 0.20/0.46 0:00:00.03 for the reduction.
% 0.20/0.46
% 0.20/0.46
% 0.20/0.46 Here is a proof with depth 4, length 40 :
% 0.20/0.46 % SZS output start Refutation
% See solution above
% 0.20/0.46 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_3
% 0.20/0.46
%------------------------------------------------------------------------------