TSTP Solution File: GRP424-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP424-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 1.13s 1.31s
% Output : Refutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 1 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('GRP424-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP424-1.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(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(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(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(817,plain,
$false,
inference(unc,[status(thm)],[730,2]),
[iquote('0:UnC:730.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP424-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 08:31:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.13/1.31
% 1.13/1.31 SPASS V 3.9
% 1.13/1.31 SPASS beiseite: Proof found.
% 1.13/1.31 % SZS status Theorem
% 1.13/1.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.13/1.31 SPASS derived 828 clauses, backtracked 0 clauses, performed 0 splits and kept 452 clauses.
% 1.13/1.31 SPASS allocated 70562 KBytes.
% 1.13/1.31 SPASS spent 0:00:00.93 on the problem.
% 1.13/1.31 0:00:00.03 for the input.
% 1.13/1.31 0:00:00.00 for the FLOTTER CNF translation.
% 1.13/1.31 0:00:00.03 for inferences.
% 1.13/1.31 0:00:00.00 for the backtracking.
% 1.13/1.31 0:00:00.85 for the reduction.
% 1.13/1.31
% 1.13/1.31
% 1.13/1.31 Here is a proof with depth 7, length 12 :
% 1.13/1.31 % SZS output start Refutation
% See solution above
% 1.13/1.31 Formulae used in the proof : single_axiom prove_these_axioms_1
% 1.13/1.31
%------------------------------------------------------------------------------