%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:45:07 EDT 2022
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 41 unt; 0 nHn; 46 RR)
% Number of literals : 53 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(identity,u),w)))),w),v),
file('GRP067-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP067-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP067-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP067-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP067-1.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(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,4.0,1.0,3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(16,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.1')] ).
cnf(17,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[16]),
[iquote('0:Obv:16.1')] ).
cnf(18,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,17]),
[iquote('0:Rew:13.0,17.0')] ).
cnf(23,plain,
equal(divide(inverse(divide(identity,divide(u,divide(identity,v)))),v),u),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(24,plain,
equal(divide(inverse(divide(u,divide(v,identity))),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(29,plain,
equal(multiply(inverse(divide(u,divide(v,identity))),u),v),
inference(rew,[status(thm),theory(equality)],[6,24]),
[iquote('0:Rew:6.0,24.0')] ).
cnf(30,plain,
equal(multiply(inverse(divide(u,multiply(v,identity))),u),v),
inference(rew,[status(thm),theory(equality)],[15,29]),
[iquote('0:Rew:15.0,29.0')] ).
cnf(32,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,23,6]),
[iquote('0:Rew:3.0,23.0,6.0,23.0,3.0,23.0')] ).
cnf(51,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(v)))),v),u),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(52,plain,
equal(multiply(inverse(inverse(multiply(u,identity))),identity),u),
inference(spr,[status(thm),theory(equality)],[32,15]),
[iquote('0:SpR:32.0,15.0')] ).
cnf(53,plain,
equal(divide(inverse(divide(inverse(multiply(u,v)),divide(w,u))),v),w),
inference(spr,[status(thm),theory(equality)],[32,7]),
[iquote('0:SpR:32.0,7.0')] ).
cnf(59,plain,
equal(divide(inverse(inverse(u)),identity),inverse(inverse(multiply(u,identity)))),
inference(spr,[status(thm),theory(equality)],[52,32]),
[iquote('0:SpR:52.0,32.0')] ).
cnf(66,plain,
equal(multiply(inverse(inverse(u)),identity),inverse(inverse(multiply(u,identity)))),
inference(rew,[status(thm),theory(equality)],[15,59]),
[iquote('0:Rew:15.0,59.0')] ).
cnf(67,plain,
equal(inverse(inverse(multiply(multiply(u,identity),identity))),u),
inference(rew,[status(thm),theory(equality)],[66,52]),
[iquote('0:Rew:66.0,52.0')] ).
cnf(82,plain,
equal(multiply(u,inverse(multiply(multiply(v,identity),identity))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[67,6]),
[iquote('0:SpR:67.0,6.0')] ).
cnf(104,plain,
equal(inverse(divide(u,multiply(v,identity))),divide(inverse(inverse(v)),u)),
inference(spr,[status(thm),theory(equality)],[30,32]),
[iquote('0:SpR:30.0,32.0')] ).
cnf(110,plain,
equal(multiply(inverse(identity),multiply(u,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(113,plain,
equal(multiply(inverse(u),inverse(inverse(multiply(u,multiply(v,identity))))),v),
inference(spr,[status(thm),theory(equality)],[32,30]),
[iquote('0:SpR:32.0,30.0')] ).
cnf(115,plain,
equal(inverse(inverse(multiply(u,identity))),u),
inference(rew,[status(thm),theory(equality)],[13,110,9]),
[iquote('0:Rew:13.0,110.0,9.0,110.0')] ).
cnf(116,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[115,67]),
[iquote('0:Rew:115.0,67.0')] ).
cnf(120,plain,
equal(multiply(u,inverse(multiply(v,identity))),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[116,82]),
[iquote('0:Rew:116.0,82.0')] ).
cnf(125,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[116,115]),
[iquote('0:Rew:116.0,115.0')] ).
cnf(127,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[125,18]),
[iquote('0:Rew:125.0,18.0')] ).
cnf(133,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[125,51]),
[iquote('0:Rew:125.0,51.0')] ).
cnf(140,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[116,120]),
[iquote('0:Rew:116.0,120.0')] ).
cnf(141,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[140,133]),
[iquote('0:Rew:140.0,133.0')] ).
cnf(144,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[116,104,125]),
[iquote('0:Rew:116.0,104.0,125.0,104.0')] ).
cnf(150,plain,
equal(divide(divide(divide(u,v),inverse(multiply(v,w))),w),u),
inference(rew,[status(thm),theory(equality)],[144,53]),
[iquote('0:Rew:144.0,53.0')] ).
cnf(155,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[125,113,116]),
[iquote('0:Rew:125.0,113.0,116.0,113.0')] ).
cnf(159,plain,
equal(divide(multiply(divide(u,v),multiply(v,w)),w),u),
inference(rew,[status(thm),theory(equality)],[6,150]),
[iquote('0:Rew:6.0,150.0')] ).
cnf(167,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[127]),
[iquote('0:Obv:127.0')] ).
cnf(636,plain,
equal(multiply(divide(u,v),multiply(v,w)),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[159,141]),
[iquote('0:SpR:159.0,141.0')] ).
cnf(1039,plain,
equal(multiply(divide(u,inverse(v)),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[155,636]),
[iquote('0:SpR:155.0,636.0')] ).
cnf(1061,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1039]),
[iquote('0:Rew:6.0,1039.0')] ).
cnf(1062,plain,
$false,
inference(unc,[status(thm)],[1061,167]),
[iquote('0:UnC:1061.0,167.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:03:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 585 clauses, backtracked 0 clauses, performed 0 splits and kept 134 clauses.
% 0.21/0.50 SPASS allocated 64238 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.50 0:00:00.04 for the input.
% 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.01 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.07 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 5, length 46 :
% 0.21/0.50 % SZS output start Refutation
% See solution above
% 0.21/0.50 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.21/0.50
%------------------------------------------------------------------------------