%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 02:28:43 EDT 2022

% Result   : Theorem 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  10 unt;   0 nHn;  15 RR)
%            Number of literals    :   20 (   0 equ;   7 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(addition(u,u),u),
    file('KLE141+2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiplication(u,one),u),
    file('KLE141+2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiplication(one,u),u),
    file('KLE141+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ equal(addition(u,v),v)
    | leq(u,v) ),
    file('KLE141+2.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(addition(u,v),w),addition(u,addition(v,w))),
    file('KLE141+2.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ leq(u,addition(multiplication(v,u),w))
    | leq(u,multiplication(strong_iteration(v),w)) ),
    file('KLE141+2.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),skc3))
    | ~ leq(multiplication(strong_iteration(one),skc2),strong_iteration(one)) ),
    file('KLE141+2.p',unknown),
    [] ).

cnf(150,plain,
    equal(addition(u,addition(u,v)),addition(u,v)),
    inference(spr,[status(thm),theory(equality)],[2,13]),
    [iquote('0:SpR:2.0,13.0')] ).

cnf(192,plain,
    ( ~ equal(addition(u,v),addition(u,v))
    | leq(u,addition(u,v)) ),
    inference(spl,[status(thm),theory(equality)],[150,11]),
    [iquote('0:SpL:150.0,11.0')] ).

cnf(197,plain,
    leq(u,addition(u,v)),
    inference(obv,[status(thm),theory(equality)],[192]),
    [iquote('0:Obv:192.0')] ).

cnf(474,plain,
    ( ~ leq(u,addition(u,v))
    | leq(u,multiplication(strong_iteration(one),v)) ),
    inference(spl,[status(thm),theory(equality)],[4,19]),
    [iquote('0:SpL:4.0,19.0')] ).

cnf(495,plain,
    leq(u,multiplication(strong_iteration(one),v)),
    inference(mrr,[status(thm)],[474,197]),
    [iquote('0:MRR:474.0,197.0')] ).

cnf(496,plain,
    ~ leq(multiplication(strong_iteration(one),skc2),strong_iteration(one)),
    inference(mrr,[status(thm)],[20,495]),
    [iquote('0:MRR:20.0,495.0')] ).

cnf(500,plain,
    leq(u,strong_iteration(one)),
    inference(spr,[status(thm),theory(equality)],[3,495]),
    [iquote('0:SpR:3.0,495.0')] ).

cnf(504,plain,
    $false,
    inference(unc,[status(thm)],[500,496]),
    [iquote('0:UnC:500.0,496.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.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 15:12:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.46  
% 0.19/0.46  SPASS V 3.9 
% 0.19/0.46  SPASS beiseite: Proof found.
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.46  SPASS derived 394 clauses, backtracked 0 clauses, performed 0 splits and kept 188 clauses.
% 0.19/0.46  SPASS allocated 85551 KBytes.
% 0.19/0.46  SPASS spent	0:00:00.12 on the problem.
% 0.19/0.46  		0:00:00.03 for the input.
% 0.19/0.46  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.46  		0:00:00.00 for inferences.
% 0.19/0.46  		0:00:00.00 for the backtracking.
% 0.19/0.46  		0:00:00.03 for the reduction.
% 0.19/0.46  
% 0.19/0.46  
% 0.19/0.46  Here is a proof with depth 2, length 15 :
% 0.19/0.46  % SZS output start Refutation
% See solution above
% 0.19/0.46  Formulae used in the proof : idempotence multiplicative_right_identity multiplicative_left_identity order additive_associativity infty_coinduction goals
% 0.19/0.46  
%------------------------------------------------------------------------------