TSTP Solution File: KLE001+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 : Sun Jul 17 02:27:55 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE001+1.p',unknown),
[] ).
cnf(9,axiom,
~ leq(addition(skc3,skc4),addition(skc3,skc4)),
file('KLE001+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE001+1.p',unknown),
[] ).
cnf(53,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpL:3.0,11.0')] ).
cnf(59,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[53]),
[iquote('0:Obv:53.0')] ).
cnf(60,plain,
$false,
inference(unc,[status(thm)],[59,9]),
[iquote('0:UnC:59.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 : Thu Jun 16 14:44:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 41 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.18/0.43 SPASS allocated 85097 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 1, length 6 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : additive_idempotence goals order
% 0.18/0.43
%------------------------------------------------------------------------------