%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP089-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:45:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of clauses : 41 ( 30 unt; 0 nHn; 41 RR)
% Number of literals : 63 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(u,v),divide(w,v))),w),
file('GRP089-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP089-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP089-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP089-1.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(8,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(19,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.0,5.0')] ).
cnf(21,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[19,4]),
[iquote('0:Rew:19.0,4.3')] ).
cnf(28,plain,
equal(divide(divide(u,divide(v,w)),w),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(37,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(38,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,37]),
[iquote('0:Rew:5.0,37.0')] ).
cnf(51,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[5,38]),
[iquote('0:SpR:5.0,38.0')] ).
cnf(53,plain,
equal(multiply(u,inverse(u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[3,38]),
[iquote('0:SpR:3.0,38.0')] ).
cnf(59,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[53]),
[iquote('0:SpR:53.0,53.0')] ).
cnf(60,plain,
equal(multiply(inverse(inverse(u)),divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[53,51]),
[iquote('0:SpR:53.0,51.0')] ).
cnf(67,plain,
equal(divide(u,divide(divide(u,v),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[53,1]),
[iquote('0:SpR:53.0,1.0')] ).
cnf(70,plain,
equal(divide(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[53,1]),
[iquote('0:SpR:53.0,1.0')] ).
cnf(72,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[70,67]),
[iquote('0:Rew:70.0,67.0')] ).
cnf(87,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[59,38]),
[iquote('0:SpR:59.0,38.0')] ).
cnf(101,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[87,60]),
[iquote('0:Rew:87.0,60.0')] ).
cnf(102,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[101,21]),
[iquote('0:Rew:101.0,21.3')] ).
cnf(116,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[102]),
[iquote('0:Obv:102.3')] ).
cnf(143,plain,
equal(multiply(divide(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[72,38]),
[iquote('0:SpR:72.0,38.0')] ).
cnf(145,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,72]),
[iquote('0:SpR:5.0,72.0')] ).
cnf(214,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[143,51]),
[iquote('0:SpR:143.0,51.0')] ).
cnf(225,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),divide(b1,b1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[214,116]),
[iquote('0:Rew:214.0,116.1')] ).
cnf(226,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[214,51]),
[iquote('0:Rew:214.0,51.0')] ).
cnf(244,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[214,225]),
[iquote('0:Rew:214.0,225.1')] ).
cnf(250,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[226,38]),
[iquote('0:SpR:226.0,38.0')] ).
cnf(256,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[250,244]),
[iquote('0:Rew:250.0,244.2')] ).
cnf(258,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[250,256]),
[iquote('0:Rew:250.0,256.0')] ).
cnf(259,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[258]),
[iquote('0:Obv:258.0')] ).
cnf(338,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[38,145]),
[iquote('0:SpR:38.0,145.0')] ).
cnf(374,plain,
equal(divide(u,divide(v,w)),multiply(w,divide(u,v))),
inference(spr,[status(thm),theory(equality)],[28,38]),
[iquote('0:SpR:28.0,38.0')] ).
cnf(451,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,338]),
[iquote('0:SpR:5.0,338.0')] ).
cnf(547,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(v,divide(u,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[451,374]),
[iquote('0:SpR:451.0,374.0')] ).
cnf(566,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[5,547]),
[iquote('0:Rew:5.0,547.0,5.0,547.0')] ).
cnf(567,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[566,259]),
[iquote('0:Rew:566.0,259.1')] ).
cnf(570,plain,
( ~ equal(divide(b1,b1),divide(a1,a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[250,567]),
[iquote('0:Rew:250.0,567.1')] ).
cnf(571,plain,
~ equal(divide(b1,b1),divide(a1,a1)),
inference(obv,[status(thm),theory(equality)],[570]),
[iquote('0:Obv:570.1')] ).
cnf(572,plain,
$false,
inference(unc,[status(thm)],[571,59]),
[iquote('0:UnC:571.0,59.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP089-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 17:38:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 401 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses.
% 0.19/0.43 SPASS allocated 63487 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.03 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 7, length 41 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms
% 0.19/0.43
%------------------------------------------------------------------------------