%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP425-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:24 EDT 2022
% Result : Unsatisfiable 1.30s 1.48s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(w),w))),v),
file('GRP425-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP425-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(x),multiply(inverse(w),w))))),v)),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(59,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),w)))),multiply(u,inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(68,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(77,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(w),w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(101,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x)))))),inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))),multiply(w,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(x),x)))),x)))),
inference(spr,[status(thm),theory(equality)],[59,1]),
[iquote('0:SpR:59.0,1.0')] ).
cnf(183,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),multiply(inverse(multiply(y,inverse(v))),multiply(y,inverse(multiply(w,inverse(x)))))),
inference(spr,[status(thm),theory(equality)],[59,68]),
[iquote('0:SpR:59.0,68.0')] ).
cnf(270,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[5,183]),
[iquote('0:SpR:5.0,183.0')] ).
cnf(351,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))))),multiply(u,inverse(multiply(y,inverse(x)))))),inverse(multiply(inverse(multiply(y,inverse(x))),multiply(y,inverse(x))))),multiply(y,inverse(w))),
inference(spr,[status(thm),theory(equality)],[270,1]),
[iquote('0:SpR:270.0,1.0')] ).
cnf(388,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),multiply(inverse(x),multiply(inverse(multiply(inverse(multiply(y,inverse(multiply(inverse(x),v)))),multiply(y,inverse(v)))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1,270]),
[iquote('0:SpR:1.0,270.0')] ).
cnf(394,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))),inverse(multiply(inverse(x),x)))),x))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[101,351]),
[iquote('0:Rew:101.0,351.0')] ).
cnf(423,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(w),w))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(y)))),inverse(multiply(inverse(y),y)))),y)),
inference(spr,[status(thm),theory(equality)],[394,77]),
[iquote('0:SpR:394.0,77.0')] ).
cnf(468,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w)))),inverse(multiply(inverse(w),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[77,423]),
[iquote('0:Rew:77.0,423.0')] ).
cnf(635,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[1,388]),
[iquote('0:SpR:1.0,388.0')] ).
cnf(730,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[635]),
[iquote('0:SpR:635.0,635.0')] ).
cnf(743,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y)))))),v),
inference(spr,[status(thm),theory(equality)],[635,1]),
[iquote('0:SpR:635.0,1.0')] ).
cnf(767,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y))))))),v)),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[635,5]),
[iquote('0:SpR:635.0,5.0')] ).
cnf(820,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[743,767]),
[iquote('0:Rew:743.0,767.0')] ).
cnf(837,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),v),v),
inference(spr,[status(thm),theory(equality)],[730,468]),
[iquote('0:SpR:730.0,468.0')] ).
cnf(878,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),x)))),multiply(u,inverse(x))),v),
inference(spr,[status(thm),theory(equality)],[730,59]),
[iquote('0:SpR:730.0,59.0')] ).
cnf(908,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),w))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[730,59]),
[iquote('0:SpR:730.0,59.0')] ).
cnf(927,plain,
~ equal(multiply(multiply(inverse(u),u),a2),a2),
inference(spl,[status(thm),theory(equality)],[730,2]),
[iquote('0:SpL:730.0,2.0')] ).
cnf(968,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),multiply(inverse(multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(inverse(v)),inverse(v))))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[837,270]),
[iquote('0:SpR:837.0,270.0')] ).
cnf(971,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),w),w),
inference(spr,[status(thm),theory(equality)],[730,837]),
[iquote('0:SpR:730.0,837.0')] ).
cnf(977,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),inverse(w))),
inference(rew,[status(thm),theory(equality)],[971,968]),
[iquote('0:Rew:971.0,968.0')] ).
cnf(982,plain,
equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(v),v)))),w))),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[977,878]),
[iquote('0:Rew:977.0,878.0')] ).
cnf(1200,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[982,908]),
[iquote('0:Rew:982.0,908.0')] ).
cnf(1206,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),u))),multiply(inverse(u),u)),
inference(rew,[status(thm),theory(equality)],[1200,820]),
[iquote('0:Rew:1200.0,820.0')] ).
cnf(1216,plain,
equal(inverse(multiply(inverse(u),u)),multiply(inverse(u),u)),
inference(rew,[status(thm),theory(equality)],[1200,1206]),
[iquote('0:Rew:1200.0,1206.0')] ).
cnf(1225,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[1216,1200]),
[iquote('0:Rew:1216.0,1200.0')] ).
cnf(1227,plain,
$false,
inference(unc,[status(thm)],[1225,927]),
[iquote('0:UnC:1225.0,927.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP425-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % 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 : Tue Jun 14 04:23:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.30/1.48
% 1.30/1.48 SPASS V 3.9
% 1.30/1.48 SPASS beiseite: Proof found.
% 1.30/1.48 % SZS status Theorem
% 1.30/1.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.30/1.48 SPASS derived 1202 clauses, backtracked 0 clauses, performed 0 splits and kept 542 clauses.
% 1.30/1.48 SPASS allocated 71692 KBytes.
% 1.30/1.48 SPASS spent 0:00:01.07 on the problem.
% 1.30/1.48 0:00:00.03 for the input.
% 1.30/1.48 0:00:00.00 for the FLOTTER CNF translation.
% 1.30/1.48 0:00:00.03 for inferences.
% 1.30/1.48 0:00:00.00 for the backtracking.
% 1.30/1.48 0:00:00.99 for the reduction.
% 1.30/1.48
% 1.30/1.48
% 1.30/1.48 Here is a proof with depth 9, length 33 :
% 1.30/1.48 % SZS output start Refutation
% See solution above
% 1.30/1.48 Formulae used in the proof : single_axiom prove_these_axioms_2
% 1.30/1.48
%------------------------------------------------------------------------------