TSTP Solution File: GRP421-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP421-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 18.36s 18.55s
% Output : Refutation 18.36s
% 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 : 11 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),inverse(multiply(inverse(w),w))))))),multiply(u,w))),v),
file('GRP421-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP421-1.p',unknown),
[] ).
cnf(4,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(w),inverse(multiply(inverse(v),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(w),inverse(multiply(inverse(w),w))))))),multiply(u,w))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),multiply(inverse(y),inverse(multiply(inverse(y),y))))))),multiply(x,y))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(16,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(inverse(multiply(x,v)),multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(55,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(y),inverse(multiply(inverse(y),y))))))),multiply(u,y))),multiply(inverse(multiply(z,w)),multiply(z,x))),
inference(spr,[status(thm),theory(equality)],[16,1]),
[iquote('0:SpR:16.0,1.0')] ).
cnf(65,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[1,55]),
[iquote('0:Rew:1.0,55.0')] ).
cnf(73,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(v)),multiply(inverse(w),inverse(multiply(inverse(w),w))))))),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(228,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(y,multiply(inverse(multiply(v,inverse(multiply(inverse(y),multiply(inverse(w),inverse(multiply(inverse(w),w))))))),x))),
inference(spr,[status(thm),theory(equality)],[1,65]),
[iquote('0:SpR:1.0,65.0')] ).
cnf(8307,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,w))),multiply(inverse(x),x)),
inference(spr,[status(thm),theory(equality)],[73,228]),
[iquote('0:SpR:73.0,228.0')] ).
cnf(8392,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[8307]),
[iquote('0:SpR:8307.0,8307.0')] ).
cnf(8866,plain,
$false,
inference(unc,[status(thm)],[8392,2]),
[iquote('0:UnC:8392.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP421-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 09:49:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 18.36/18.55
% 18.36/18.55 SPASS V 3.9
% 18.36/18.55 SPASS beiseite: Proof found.
% 18.36/18.55 % SZS status Theorem
% 18.36/18.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.36/18.55 SPASS derived 8277 clauses, backtracked 0 clauses, performed 0 splits and kept 2352 clauses.
% 18.36/18.55 SPASS allocated 104404 KBytes.
% 18.36/18.55 SPASS spent 0:0:17.97 on the problem.
% 18.36/18.55 0:00:00.03 for the input.
% 18.36/18.55 0:00:00.00 for the FLOTTER CNF translation.
% 18.36/18.55 0:00:00.18 for inferences.
% 18.36/18.55 0:00:00.00 for the backtracking.
% 18.36/18.55 0:0:17.74 for the reduction.
% 18.36/18.55
% 18.36/18.55
% 18.36/18.55 Here is a proof with depth 6, length 12 :
% 18.36/18.55 % SZS output start Refutation
% See solution above
% 18.36/18.55 Formulae used in the proof : single_axiom prove_these_axioms_1
% 18.36/18.55
%------------------------------------------------------------------------------