TSTP Solution File: GRP409-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:47:14 EDT 2022
% Result : Unsatisfiable 0.84s 1.02s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),v),
file('GRP409-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP409-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(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(6,plain,
equal(multiply(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(v,w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(60,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),w)))),multiply(u,inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(61,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(multiply(v,w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(73,plain,
equal(multiply(multiply(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)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(108,plain,
equal(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))),inverse(multiply(w,inverse(multiply(multiply(v,inverse(multiply(inverse(x),x))),x))))),
inference(spr,[status(thm),theory(equality)],[60,1]),
[iquote('0:SpR:60.0,1.0')] ).
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)],[60,61]),
[iquote('0:SpR:60.0,61.0')] ).
cnf(268,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)],[3,183]),
[iquote('0:SpR:3.0,183.0')] ).
cnf(360,plain,
equal(multiply(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))))),inverse(multiply(y,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[268,1]),
[iquote('0:SpR:268.0,1.0')] ).
cnf(390,plain,
equal(inverse(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x))),inverse(multiply(inverse(x),x))),x)))),inverse(multiply(u,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[108,360]),
[iquote('0:Rew:108.0,360.0')] ).
cnf(422,plain,
equal(multiply(multiply(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(multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(y))),inverse(multiply(inverse(y),y))),y)),
inference(spr,[status(thm),theory(equality)],[390,73]),
[iquote('0:SpR:390.0,73.0')] ).
cnf(463,plain,
equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),w),v),
inference(rew,[status(thm),theory(equality)],[73,422]),
[iquote('0:Rew:73.0,422.0')] ).
cnf(529,plain,
equal(multiply(multiply(multiply(inverse(u),multiply(multiply(inverse(multiply(v,inverse(multiply(u,w)))),multiply(v,inverse(w))),inverse(x))),inverse(multiply(inverse(x),x))),x),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[1,463]),
[iquote('0:SpR:1.0,463.0')] ).
cnf(615,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),multiply(inverse(v),v)),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[1,529]),
[iquote('0:SpR:1.0,529.0')] ).
cnf(687,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)],[615,60]),
[iquote('0:SpR:615.0,60.0')] ).
cnf(715,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[687]),
[iquote('0:SpR:687.0,687.0')] ).
cnf(806,plain,
$false,
inference(unc,[status(thm)],[715,2]),
[iquote('0:UnC:715.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:42:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.84/1.02
% 0.84/1.02 SPASS V 3.9
% 0.84/1.02 SPASS beiseite: Proof found.
% 0.84/1.02 % SZS status Theorem
% 0.84/1.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.02 SPASS derived 746 clauses, backtracked 0 clauses, performed 0 splits and kept 390 clauses.
% 0.84/1.02 SPASS allocated 68569 KBytes.
% 0.84/1.02 SPASS spent 0:00:00.65 on the problem.
% 0.84/1.02 0:00:00.03 for the input.
% 0.84/1.02 0:00:00.00 for the FLOTTER CNF translation.
% 0.84/1.02 0:00:00.02 for inferences.
% 0.84/1.02 0:00:00.00 for the backtracking.
% 0.84/1.02 0:00:00.57 for the reduction.
% 0.84/1.02
% 0.84/1.02
% 0.84/1.02 Here is a proof with depth 10, length 19 :
% 0.84/1.02 % SZS output start Refutation
% See solution above
% 0.84/1.02 Formulae used in the proof : single_axiom prove_these_axioms_1
% 0.84/1.02
%------------------------------------------------------------------------------