TSTP Solution File: GRP448-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP448-1 : 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 11:47:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 14 RR)
% Number of literals : 14 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(divide(divide(v,v),v),w),divide(divide(divide(v,v),u),w))),v),
file('GRP448-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP448-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP448-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP448-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(6,plain,
equal(divide(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(61,plain,
equal(divide(divide(u,u),divide(divide(inverse(v),w),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(70,plain,
equal(inverse(multiply(divide(inverse(u),v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,61,5]),
[iquote('0:Rew:3.0,61.0,5.0,61.0')] ).
cnf(137,plain,
equal(inverse(multiply(inverse(u),u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7,70]),
[iquote('0:SpR:7.0,70.0')] ).
cnf(197,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[137]),
[iquote('0:SpR:137.0,137.0')] ).
cnf(229,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[197,5]),
[iquote('0:SpR:197.0,5.0')] ).
cnf(394,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[229]),
[iquote('0:SpR:229.0,229.0')] ).
cnf(426,plain,
$false,
inference(unc,[status(thm)],[394,4]),
[iquote('0:UnC:394.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 10:25:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 305 clauses, backtracked 0 clauses, performed 0 splits and kept 102 clauses.
% 0.19/0.45 SPASS allocated 63620 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.03 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 6, length 14 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.19/0.45
%------------------------------------------------------------------------------