TSTP Solution File: KLE150+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 02:28:47 EDT 2022
% Result : Theorem 0.85s 1.02s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE150+1.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE150+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE150+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(addition(one,multiplication(skc1,zero)),strong_iteration(multiplication(skc1,zero))),
file('KLE150+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE150+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.0')] ).
cnf(132,plain,
equal(addition(one,multiplication(u,multiplication(v,strong_iteration(multiplication(u,v))))),strong_iteration(multiplication(u,v))),
inference(spr,[status(thm),theory(equality)],[15,21]),
[iquote('0:SpR:15.0,21.0')] ).
cnf(5852,plain,
equal(addition(one,multiplication(u,zero)),strong_iteration(multiplication(u,zero))),
inference(spr,[status(thm),theory(equality)],[5,132]),
[iquote('0:SpR:5.0,132.0')] ).
cnf(5870,plain,
$false,
inference(unc,[status(thm)],[5852,13]),
[iquote('0:UnC:5852.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 07:39:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.85/1.02
% 0.85/1.02 SPASS V 3.9
% 0.85/1.02 SPASS beiseite: Proof found.
% 0.85/1.02 % SZS status Theorem
% 0.85/1.02 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/1.02 SPASS derived 4565 clauses, backtracked 0 clauses, performed 0 splits and kept 1161 clauses.
% 0.85/1.02 SPASS allocated 89545 KBytes.
% 0.85/1.02 SPASS spent 0:00:00.65 on the problem.
% 0.85/1.02 0:00:00.04 for the input.
% 0.85/1.02 0:00:00.03 for the FLOTTER CNF translation.
% 0.85/1.02 0:00:00.03 for inferences.
% 0.85/1.02 0:00:00.00 for the backtracking.
% 0.85/1.02 0:00:00.52 for the reduction.
% 0.85/1.02
% 0.85/1.02
% 0.85/1.02 Here is a proof with depth 2, length 9 :
% 0.85/1.02 % SZS output start Refutation
% See solution above
% 0.85/1.02 Formulae used in the proof : left_annihilation additive_commutativity infty_unfold1 goals multiplicative_associativity
% 0.85/1.02
%------------------------------------------------------------------------------