%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP543-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:47:58 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 48 RR)
% Number of literals : 48 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(divide(divide(u,v),w),u)),w),v),
file('GRP543-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP543-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP543-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP543-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP543-1.p',unknown),
[] ).
cnf(6,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(7,plain,
equal(divide(inverse(divide(divide(divide(u,v),w),u)),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(26,plain,
equal(multiply(inverse(divide(divide(divide(u,v),inverse(w)),u)),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(30,plain,
equal(divide(inverse(divide(divide(identity,u),v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(34,plain,
equal(divide(inverse(divide(identity,u)),divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(39,plain,
equal(divide(inverse(divide(inverse(u),v)),u),v),
inference(rew,[status(thm),theory(equality)],[3,30]),
[iquote('0:Rew:3.0,30.0')] ).
cnf(40,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[3,34]),
[iquote('0:Rew:3.0,34.0')] ).
cnf(45,plain,
equal(multiply(inverse(divide(multiply(divide(u,v),w),u)),w),v),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0')] ).
cnf(54,plain,
equal(divide(inverse(divide(identity,u)),identity),u),
inference(spr,[status(thm),theory(equality)],[9,39]),
[iquote('0:SpR:9.0,39.0')] ).
cnf(60,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[15,54,3]),
[iquote('0:Rew:15.0,54.0,3.0,54.0')] ).
cnf(68,plain,
equal(divide(inverse(u),inverse(v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[40,39]),
[iquote('0:SpR:40.0,39.0')] ).
cnf(71,plain,
equal(divide(inverse(inverse(identity)),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,40]),
[iquote('0:SpR:3.0,40.0')] ).
cnf(73,plain,
equal(divide(inverse(inverse(u)),multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[6,40]),
[iquote('0:SpR:6.0,40.0')] ).
cnf(78,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,71,6,9]),
[iquote('0:Rew:13.0,71.0,6.0,71.0,9.0,71.0,9.0,71.0')] ).
cnf(80,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[78,60]),
[iquote('0:Rew:78.0,60.0')] ).
cnf(81,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[78,40]),
[iquote('0:Rew:78.0,40.0')] ).
cnf(86,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,68]),
[iquote('0:Rew:6.0,68.0')] ).
cnf(90,plain,
equal(divide(u,divide(multiply(divide(v,w),u),v)),w),
inference(rew,[status(thm),theory(equality)],[86,45]),
[iquote('0:Rew:86.0,45.0')] ).
cnf(93,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[78,73]),
[iquote('0:Rew:78.0,73.0')] ).
cnf(137,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[78,86]),
[iquote('0:SpR:78.0,86.0')] ).
cnf(139,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,137]),
[iquote('0:Rew:6.0,137.0')] ).
cnf(140,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[139,5]),
[iquote('0:Rew:139.0,5.0')] ).
cnf(155,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[139,93]),
[iquote('0:SpR:139.0,93.0')] ).
cnf(212,plain,
equal(divide(multiply(divide(u,v),w),u),divide(w,v)),
inference(spr,[status(thm),theory(equality)],[90,81]),
[iquote('0:SpR:90.0,81.0')] ).
cnf(224,plain,
equal(divide(identity,divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[80,90]),
[iquote('0:SpR:80.0,90.0')] ).
cnf(230,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,224]),
[iquote('0:Rew:3.0,224.0')] ).
cnf(245,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[230,78]),
[iquote('0:SpR:230.0,78.0')] ).
cnf(286,plain,
equal(divide(divide(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[245,81]),
[iquote('0:SpR:245.0,81.0')] ).
cnf(294,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[93,245]),
[iquote('0:SpR:93.0,245.0')] ).
cnf(295,plain,
equal(divide(inverse(u),v),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[155,245]),
[iquote('0:SpR:155.0,245.0')] ).
cnf(298,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[139,286,6]),
[iquote('0:Rew:139.0,286.0,6.0,286.0')] ).
cnf(313,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[294,295]),
[iquote('0:Rew:294.0,295.0')] ).
cnf(490,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[313,6]),
[iquote('0:SpR:313.0,6.0')] ).
cnf(524,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[6,490]),
[iquote('0:Rew:6.0,490.0')] ).
cnf(531,plain,
equal(multiply(divide(u,v),w),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[212,298]),
[iquote('0:SpR:212.0,298.0')] ).
cnf(760,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[524,139]),
[iquote('0:SpR:524.0,139.0')] ).
cnf(892,plain,
equal(multiply(u,divide(v,inverse(w))),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[6,531]),
[iquote('0:SpR:6.0,531.0')] ).
cnf(909,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[6,892]),
[iquote('0:Rew:6.0,892.0')] ).
cnf(915,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[909,760]),
[iquote('0:Rew:909.0,760.0')] ).
cnf(925,plain,
$false,
inference(unc,[status(thm)],[915,140]),
[iquote('0:UnC:915.0,140.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP543-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.07/0.28 % Computer : n032.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 600
% 0.07/0.28 % DateTime : Mon Jun 13 16:56:42 EDT 2022
% 0.07/0.28 % CPUTime :
% 0.12/0.39
% 0.12/0.39 SPASS V 3.9
% 0.12/0.39 SPASS beiseite: Proof found.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39 SPASS derived 573 clauses, backtracked 0 clauses, performed 0 splits and kept 138 clauses.
% 0.12/0.39 SPASS allocated 63877 KBytes.
% 0.12/0.39 SPASS spent 0:00:00.10 on the problem.
% 0.12/0.39 0:00:00.03 for the input.
% 0.12/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.39 0:00:00.01 for inferences.
% 0.12/0.39 0:00:00.00 for the backtracking.
% 0.12/0.39 0:00:00.05 for the reduction.
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 Here is a proof with depth 7, length 48 :
% 0.12/0.39 % SZS output start Refutation
% See solution above
% 0.12/0.39 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.12/0.39
%------------------------------------------------------------------------------