%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP065-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of clauses : 52 ( 47 unt; 0 nHn; 52 RR)
% Number of literals : 60 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 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; 12 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(divide(u,u),u),w)))),w),v),
file('GRP065-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP065-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP065-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ 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('GRP065-1.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(6,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(9,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(11,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(12,plain,
equal(divide(inverse(inverse(divide(u,u))),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(20,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(22,plain,
( ~ 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)],[20,4]),
[iquote('0:Rew:20.0,4.2')] ).
cnf(24,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,v))),w),x),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(28,plain,
equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(29,plain,
equal(divide(inverse(divide(u,inverse(divide(inverse(u),v)))),v),divide(w,w)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(35,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,28,5]),
[iquote('0:Rew:3.0,28.0,5.0,28.0')] ).
cnf(38,plain,
equal(divide(inverse(multiply(u,divide(inverse(u),v))),v),divide(w,w)),
inference(rew,[status(thm),theory(equality)],[5,29]),
[iquote('0:Rew:5.0,29.0')] ).
cnf(51,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(v)))),v),u),
inference(spr,[status(thm),theory(equality)],[35,5]),
[iquote('0:SpR:35.0,5.0')] ).
cnf(55,plain,
equal(divide(inverse(inverse(inverse(inverse(u)))),u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[11,35]),
[iquote('0:SpR:11.0,35.0')] ).
cnf(99,plain,
equal(inverse(inverse(multiply(u,inverse(v)))),divide(inverse(inverse(u)),v)),
inference(spr,[status(thm),theory(equality)],[51,35]),
[iquote('0:SpR:51.0,35.0')] ).
cnf(104,plain,
equal(multiply(inverse(inverse(inverse(inverse(inverse(u))))),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[20,51]),
[iquote('0:SpR:20.0,51.0')] ).
cnf(105,plain,
equal(multiply(divide(inverse(inverse(u)),v),v),u),
inference(rew,[status(thm),theory(equality)],[99,51]),
[iquote('0:Rew:99.0,51.0')] ).
cnf(108,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[105,11]),
[iquote('0:SpR:105.0,11.0')] ).
cnf(116,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[108,104]),
[iquote('0:Rew:108.0,104.0')] ).
cnf(120,plain,
equal(divide(u,u),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[108,55]),
[iquote('0:Rew:108.0,55.0')] ).
cnf(161,plain,
equal(multiply(u,inverse(inverse(inverse(v)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[108,5]),
[iquote('0:SpR:108.0,5.0')] ).
cnf(168,plain,
equal(multiply(divide(u,v),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[108,105]),
[iquote('0:SpR:108.0,105.0')] ).
cnf(516,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(inverse(multiply(x,v)))),
inference(spr,[status(thm),theory(equality)],[35,24]),
[iquote('0:SpR:35.0,24.0')] ).
cnf(519,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,x))),w),inverse(multiply(y,divide(inverse(y),v)))),
inference(spr,[status(thm),theory(equality)],[38,24]),
[iquote('0:SpR:38.0,24.0')] ).
cnf(523,plain,
equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(divide(y,divide(x,divide(inverse(y),v))))),
inference(spr,[status(thm),theory(equality)],[6,24]),
[iquote('0:SpR:6.0,24.0')] ).
cnf(609,plain,
equal(inverse(divide(u,divide(v,divide(inverse(u),w)))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[516,523]),
[iquote('0:Rew:516.0,523.0')] ).
cnf(614,plain,
equal(inverse(inverse(multiply(divide(u,u),v))),inverse(multiply(w,divide(inverse(w),v)))),
inference(rew,[status(thm),theory(equality)],[516,519]),
[iquote('0:Rew:516.0,519.0')] ).
cnf(615,plain,
equal(inverse(multiply(u,divide(inverse(u),v))),v),
inference(rew,[status(thm),theory(equality)],[108,614,11]),
[iquote('0:Rew:108.0,614.0,11.0,614.0')] ).
cnf(790,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[615,35]),
[iquote('0:SpR:615.0,35.0')] ).
cnf(802,plain,
equal(inverse(multiply(u,divide(v,v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[120,615]),
[iquote('0:SpR:120.0,615.0')] ).
cnf(858,plain,
equal(inverse(divide(inverse(u),inverse(divide(v,v)))),u),
inference(spr,[status(thm),theory(equality)],[790,12]),
[iquote('0:SpR:790.0,12.0')] ).
cnf(876,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[35,790]),
[iquote('0:SpR:35.0,790.0')] ).
cnf(927,plain,
equal(inverse(inverse(multiply(u,inverse(v)))),inverse(multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[876,99]),
[iquote('0:Rew:876.0,99.0')] ).
cnf(930,plain,
equal(inverse(divide(u,divide(v,inverse(multiply(w,u))))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[876,609]),
[iquote('0:Rew:876.0,609.0')] ).
cnf(939,plain,
equal(inverse(multiply(inverse(u),divide(v,v))),u),
inference(rew,[status(thm),theory(equality)],[5,858]),
[iquote('0:Rew:5.0,858.0')] ).
cnf(940,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[802,939]),
[iquote('0:Rew:802.0,939.0')] ).
cnf(942,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[940,168]),
[iquote('0:Rew:940.0,168.0')] ).
cnf(943,plain,
( ~ 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)],[940,22]),
[iquote('0:Rew:940.0,22.2')] ).
cnf(961,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[940,161]),
[iquote('0:Rew:940.0,161.0')] ).
cnf(1027,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[940,927,961]),
[iquote('0:Rew:940.0,927.0,961.0,927.0,961.0,927.0')] ).
cnf(1072,plain,
equal(inverse(divide(u,multiply(v,multiply(w,u)))),inverse(inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[5,930]),
[iquote('0:Rew:5.0,930.0')] ).
cnf(1073,plain,
equal(divide(multiply(u,multiply(v,w)),w),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[1027,1072,940]),
[iquote('0:Rew:1027.0,1072.0,940.0,1072.0')] ).
cnf(1116,plain,
( ~ 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)],[943]),
[iquote('0:Obv:943.2')] ).
cnf(1453,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1073,942]),
[iquote('0:SpR:1073.0,942.0')] ).
cnf(1474,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[1453,1116]),
[iquote('0:Rew:1453.0,1116.1')] ).
cnf(1567,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[1474]),
[iquote('0:Obv:1474.1')] ).
cnf(1568,plain,
$false,
inference(unc,[status(thm)],[1567,116]),
[iquote('0:UnC:1567.0,116.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP065-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n016.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 : Mon Jun 13 22:31:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 1038 clauses, backtracked 0 clauses, performed 0 splits and kept 246 clauses.
% 0.20/0.54 SPASS allocated 64501 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.54 0:00:00.03 for the input.
% 0.20/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.01 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.11 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 6, length 52 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms
% 0.20/0.54
%------------------------------------------------------------------------------