%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP085-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:45:14 EDT 2022
% Result : Unsatisfiable 0.41s 0.59s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of clauses : 57 ( 49 unt; 0 nHn; 57 RR)
% Number of literals : 73 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(multiply(u,v),w),inverse(multiply(u,w))),v),
file('GRP085-1.p',unknown),
[] ).
cnf(2,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('GRP085-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(multiply(multiply(multiply(multiply(u,v),w),x),inverse(multiply(u,w))),inverse(v)),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),inverse(multiply(v,w))))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(8,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),inverse(multiply(multiply(x,w),inverse(multiply(x,u))))),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(10,plain,
equal(multiply(u,inverse(multiply(v,inverse(multiply(multiply(w,multiply(v,x)),inverse(multiply(w,u))))))),x),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(11,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),inverse(w)))),inverse(multiply(multiply(x,v),inverse(multiply(x,w))))),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(21,plain,
equal(multiply(multiply(u,inverse(multiply(multiply(multiply(v,w),x),inverse(multiply(v,x))))),inverse(u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(33,plain,
equal(multiply(multiply(u,inverse(v)),inverse(u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1,21]),
[iquote('0:Rew:1.0,21.0')] ).
cnf(42,plain,
equal(multiply(inverse(u),inverse(multiply(v,inverse(u)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[33]),
[iquote('0:SpR:33.0,33.0')] ).
cnf(43,plain,
equal(multiply(inverse(u),inverse(multiply(v,inverse(v)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[33,1]),
[iquote('0:SpR:33.0,1.0')] ).
cnf(47,plain,
equal(multiply(multiply(inverse(u),inverse(multiply(v,inverse(u)))),inverse(w)),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[33,3]),
[iquote('0:SpR:33.0,3.0')] ).
cnf(48,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(w)),u),inverse(inverse(w))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[33,5]),
[iquote('0:SpR:33.0,5.0')] ).
cnf(50,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(u,w)))),multiply(w,inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,33]),
[iquote('0:SpR:5.0,33.0')] ).
cnf(51,plain,
equal(multiply(u,inverse(multiply(multiply(v,u),w))),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1,33]),
[iquote('0:SpR:1.0,33.0')] ).
cnf(54,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(u,w)))),inverse(multiply(v,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[51,11]),
[iquote('0:Rew:51.0,11.0')] ).
cnf(60,plain,
equal(multiply(u,inverse(multiply(v,multiply(u,inverse(multiply(v,w)))))),w),
inference(rew,[status(thm),theory(equality)],[50,10]),
[iquote('0:Rew:50.0,10.0')] ).
cnf(61,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,v))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[50,8]),
[iquote('0:Rew:50.0,8.0')] ).
cnf(64,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[61,1]),
[iquote('0:Rew:61.0,1.0')] ).
cnf(67,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[50,54]),
[iquote('0:Rew:50.0,54.0')] ).
cnf(68,plain,
equal(multiply(inverse(u),multiply(v,inverse(v))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[67,43]),
[iquote('0:Rew:67.0,43.0')] ).
cnf(69,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[67,42]),
[iquote('0:Rew:67.0,42.0')] ).
cnf(78,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[69,47,67]),
[iquote('0:Rew:69.0,47.0,67.0,47.0')] ).
cnf(79,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[51,48,67]),
[iquote('0:Rew:51.0,48.0,67.0,48.0')] ).
cnf(94,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[79]),
[iquote('0:SpR:79.0,79.0')] ).
cnf(96,plain,
equal(multiply(u,inverse(multiply(u,v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[67,94,78]),
[iquote('0:Rew:67.0,94.0,78.0,94.0')] ).
cnf(97,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[96,64]),
[iquote('0:SpR:96.0,64.0')] ).
cnf(98,plain,
equal(multiply(u,inverse(inverse(v))),inverse(inverse(multiply(u,v)))),
inference(spr,[status(thm),theory(equality)],[96]),
[iquote('0:SpR:96.0,96.0')] ).
cnf(103,plain,
equal(multiply(u,inverse(inverse(v))),inverse(inverse(multiply(v,u)))),
inference(spr,[status(thm),theory(equality)],[79,96]),
[iquote('0:SpR:79.0,96.0')] ).
cnf(104,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[78,97]),
[iquote('0:Rew:78.0,97.0')] ).
cnf(110,plain,
equal(inverse(inverse(multiply(u,v))),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[98,103]),
[iquote('0:Rew:98.0,103.0')] ).
cnf(119,plain,
equal(multiply(multiply(multiply(u,v),w),inverse(multiply(v,u))),w),
inference(spr,[status(thm),theory(equality)],[104,64]),
[iquote('0:SpR:104.0,64.0')] ).
cnf(138,plain,
equal(multiply(u,multiply(v,inverse(u))),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[67,96]),
[iquote('0:SpR:67.0,96.0')] ).
cnf(146,plain,
equal(multiply(multiply(u,v),inverse(u)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[96,67]),
[iquote('0:SpR:96.0,67.0')] ).
cnf(149,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[64,146]),
[iquote('0:Rew:64.0,146.0')] ).
cnf(151,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[149,138]),
[iquote('0:Rew:149.0,138.0')] ).
cnf(153,plain,
equal(inverse(inverse(multiply(u,v))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[149,110]),
[iquote('0:Rew:149.0,110.0')] ).
cnf(158,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[149,153]),
[iquote('0:Rew:149.0,153.0')] ).
cnf(159,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(multiply(a2,multiply(inverse(b2),b2)),a2) ),
inference(rew,[status(thm),theory(equality)],[158,2]),
[iquote('0:Rew:158.0,2.3')] ).
cnf(163,plain,
equal(multiply(inverse(multiply(u,v)),multiply(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[158,119]),
[iquote('0:Rew:158.0,119.0')] ).
cnf(184,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),
inference(rew,[status(thm),theory(equality)],[158,159]),
[iquote('0:Rew:158.0,159.3,158.0,159.2,158.0,159.1,158.0,159.1,158.0,159.0')] ).
cnf(185,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),
inference(obv,[status(thm),theory(equality)],[184]),
[iquote('0:Obv:184.0')] ).
cnf(216,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[158,151]),
[iquote('0:SpR:158.0,151.0')] ).
cnf(300,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[68,216]),
[iquote('0:SpR:68.0,216.0')] ).
cnf(308,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[149,68]),
[iquote('0:SpR:149.0,68.0')] ).
cnf(309,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[308,185]),
[iquote('0:Rew:308.0,185.2')] ).
cnf(321,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[309]),
[iquote('0:Obv:309.2')] ).
cnf(540,plain,
equal(inverse(multiply(u,multiply(inverse(v),inverse(multiply(u,w))))),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[60,216]),
[iquote('0:SpR:60.0,216.0')] ).
cnf(586,plain,
equal(multiply(inverse(u),multiply(v,multiply(u,w))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[158,540,67,78]),
[iquote('0:Rew:158.0,540.0,67.0,540.0,78.0,540.0')] ).
cnf(638,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[163,216]),
[iquote('0:SpR:163.0,216.0')] ).
cnf(719,plain,
equal(multiply(multiply(u,v),w),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[638,158]),
[iquote('0:SpR:638.0,158.0')] ).
cnf(797,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[719,158]),
[iquote('0:SpR:719.0,158.0')] ).
cnf(1618,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[586,216]),
[iquote('0:SpR:586.0,216.0')] ).
cnf(1680,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1618,321]),
[iquote('0:Rew:1618.0,321.1')] ).
cnf(1769,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[797,1680]),
[iquote('0:Rew:797.0,1680.1')] ).
cnf(1770,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[1769]),
[iquote('0:Obv:1769.1')] ).
cnf(1771,plain,
$false,
inference(unc,[status(thm)],[1770,300]),
[iquote('0:UnC:1770.0,300.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP085-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:10:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.41/0.59
% 0.41/0.59 SPASS V 3.9
% 0.41/0.59 SPASS beiseite: Proof found.
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.59 SPASS derived 1162 clauses, backtracked 0 clauses, performed 0 splits and kept 218 clauses.
% 0.41/0.59 SPASS allocated 64708 KBytes.
% 0.41/0.59 SPASS spent 0:00:00.22 on the problem.
% 0.41/0.59 0:00:00.04 for the input.
% 0.41/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.59 0:00:00.01 for inferences.
% 0.41/0.59 0:00:00.00 for the backtracking.
% 0.41/0.59 0:00:00.15 for the reduction.
% 0.41/0.59
% 0.41/0.59
% 0.41/0.59 Here is a proof with depth 9, length 57 :
% 0.41/0.59 % SZS output start Refutation
% See solution above
% 0.41/0.59 Formulae used in the proof : single_axiom prove_these_axioms
% 0.41/0.59
%------------------------------------------------------------------------------