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  
%------------------------------------------------------------------------------