TSTP Solution File: GRP418-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP418-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:47:23 EDT 2022
% Result : Unsatisfiable 46.55s 46.78s
% Output : Refutation 46.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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),inverse(multiply(w,inverse(multiply(inverse(w),w)))))))),multiply(u,w))),v),
file('GRP418-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP418-1.p',unknown),
[] ).
cnf(5,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(v,inverse(multiply(w,inverse(multiply(inverse(w),w)))))))),multiply(u,w))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),inverse(multiply(y,inverse(multiply(inverse(y),y)))))))),multiply(x,y))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(8,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(v)),inverse(multiply(w,inverse(multiply(inverse(w),w)))))))),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(82,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(v)),inverse(multiply(w,inverse(multiply(inverse(w),w)))))))),inverse(multiply(inverse(x),inverse(multiply(multiply(u,w),inverse(multiply(inverse(multiply(u,w)),multiply(u,w))))))))),v)),x),
inference(spr,[status(thm),theory(equality)],[8,1]),
[iquote('0:SpR:8.0,1.0')] ).
cnf(516,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(multiply(x,inverse(multiply(inverse(inverse(inverse(multiply(w,inverse(multiply(inverse(w),w)))))),inverse(multiply(y,inverse(multiply(inverse(y),y)))))))),inverse(multiply(inverse(v),inverse(multiply(multiply(x,y),inverse(multiply(inverse(multiply(x,y)),multiply(x,y))))))))),
inference(spr,[status(thm),theory(equality)],[82,1]),
[iquote('0:SpR:82.0,1.0')] ).
cnf(728,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)],[516]),
[iquote('0:SpR:516.0,516.0')] ).
cnf(970,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(v,w)),multiply(v,x)))),inverse(multiply(y,inverse(multiply(inverse(y),y)))))))),multiply(u,y)),multiply(inverse(multiply(z,w)),multiply(z,x))),
inference(spr,[status(thm),theory(equality)],[728,8]),
[iquote('0:SpR:728.0,8.0')] ).
cnf(1040,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[8,970]),
[iquote('0:Rew:8.0,970.0')] ).
cnf(1316,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(y,multiply(inverse(multiply(v,inverse(multiply(inverse(y),inverse(multiply(w,inverse(multiply(inverse(w),w)))))))),x))),
inference(spr,[status(thm),theory(equality)],[1,1040]),
[iquote('0:SpR:1.0,1040.0')] ).
cnf(6262,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,w))),multiply(inverse(x),x)),
inference(spr,[status(thm),theory(equality)],[8,1316]),
[iquote('0:SpR:8.0,1316.0')] ).
cnf(6311,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[6262]),
[iquote('0:SpR:6262.0,6262.0')] ).
cnf(6716,plain,
$false,
inference(unc,[status(thm)],[6311,2]),
[iquote('0:UnC:6311.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP418-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Tue Jun 14 08:27:49 EDT 2022
% 0.15/0.35 % CPUTime :
% 46.55/46.78
% 46.55/46.78 SPASS V 3.9
% 46.55/46.78 SPASS beiseite: Proof found.
% 46.55/46.78 % SZS status Theorem
% 46.55/46.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.55/46.78 SPASS derived 6159 clauses, backtracked 0 clauses, performed 0 splits and kept 2533 clauses.
% 46.55/46.78 SPASS allocated 122047 KBytes.
% 46.55/46.78 SPASS spent 0:0:45.95 on the problem.
% 46.55/46.78 0:00:00.03 for the input.
% 46.55/46.78 0:00:00.00 for the FLOTTER CNF translation.
% 46.55/46.78 0:00:00.19 for inferences.
% 46.55/46.78 0:00:00.00 for the backtracking.
% 46.55/46.78 0:0:45.71 for the reduction.
% 46.55/46.78
% 46.55/46.78
% 46.55/46.78 Here is a proof with depth 9, length 13 :
% 46.55/46.78 % SZS output start Refutation
% See solution above
% 46.55/46.78 Formulae used in the proof : single_axiom prove_these_axioms_1
% 46.55/46.78
%------------------------------------------------------------------------------