TSTP Solution File: GRP533-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:47:55 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP533-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP533-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP533-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP533-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(16,plain,
~ equal(multiply(inverse(a1),a1),identity),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(17,plain,
~ equal(identity,identity),
inference(rew,[status(thm),theory(equality)],[12,16]),
[iquote('0:Rew:12.0,16.0')] ).
cnf(18,plain,
$false,
inference(obv,[status(thm),theory(equality)],[17]),
[iquote('0:Obv:17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP533-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n024.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 04:20:48 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.21/0.42 SPASS allocated 63096 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.05 on the problem.
% 0.21/0.42 0:00:00.03 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 1, length 10 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : multiply inverse identity prove_these_axioms_1
% 0.21/0.42
%------------------------------------------------------------------------------