TSTP Solution File: KLE137+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 02:28:41 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 14 RR)
% Number of literals : 18 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 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,
~ leq(skc1,strong_iteration(one)),
file('KLE137+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE137+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE137+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE137+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE137+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE137+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE137+1.p',unknown),
[] ).
cnf(136,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(193,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[136,12]),
[iquote('0:SpL:136.0,12.0')] ).
cnf(198,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[193]),
[iquote('0:Obv:193.0')] ).
cnf(467,plain,
( ~ leq(u,addition(u,v))
| leq(u,multiplication(strong_iteration(one),v)) ),
inference(spl,[status(thm),theory(equality)],[5,20]),
[iquote('0:SpL:5.0,20.0')] ).
cnf(488,plain,
leq(u,multiplication(strong_iteration(one),v)),
inference(mrr,[status(thm)],[467,198]),
[iquote('0:MRR:467.0,198.0')] ).
cnf(500,plain,
leq(u,strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[4,488]),
[iquote('0:SpR:4.0,488.0')] ).
cnf(504,plain,
$false,
inference(unc,[status(thm)],[500,1]),
[iquote('0:UnC:500.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.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 08:40:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 393 clauses, backtracked 0 clauses, performed 0 splits and kept 187 clauses.
% 0.18/0.48 SPASS allocated 85550 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.48 0:00:00.03 for the input.
% 0.18/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.03 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 2, length 14 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : goals idempotence multiplicative_right_identity multiplicative_left_identity order additive_associativity infty_coinduction
% 0.18/0.48
%------------------------------------------------------------------------------