%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE002+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 02:27:56 EDT 2022

% Result   : Theorem 0.46s 0.71s
% Output   : Refutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (  11 unt;   0 nHn;  14 RR)
%            Number of literals    :   17 (   0 equ;   4 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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    leq(skc3,skc4),
    file('KLE002+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(addition(u,u),u),
    file('KLE002+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ leq(multiplication(skc3,skc5),multiplication(skc4,skc5)),
    file('KLE002+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ leq(u,v)
    | equal(addition(u,v),v) ),
    file('KLE002+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ equal(addition(u,v),v)
    | leq(u,v) ),
    file('KLE002+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(addition(addition(u,v),w),addition(u,addition(v,w))),
    file('KLE002+1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE002+1.p',unknown),
    [] ).

cnf(16,plain,
    equal(addition(skc3,skc4),skc4),
    inference(res,[status(thm),theory(equality)],[1,10]),
    [iquote('0:Res:1.0,10.0')] ).

cnf(87,plain,
    equal(addition(u,addition(u,v)),addition(u,v)),
    inference(spr,[status(thm),theory(equality)],[3,12]),
    [iquote('0:SpR:3.0,12.0')] ).

cnf(127,plain,
    equal(addition(multiplication(skc3,u),multiplication(skc4,u)),multiplication(skc4,u)),
    inference(spr,[status(thm),theory(equality)],[16,15]),
    [iquote('0:SpR:16.0,15.0')] ).

cnf(448,plain,
    ( ~ equal(addition(u,v),addition(u,v))
    | leq(u,addition(u,v)) ),
    inference(spl,[status(thm),theory(equality)],[87,11]),
    [iquote('0:SpL:87.0,11.0')] ).

cnf(453,plain,
    leq(u,addition(u,v)),
    inference(obv,[status(thm),theory(equality)],[448]),
    [iquote('0:Obv:448.0')] ).

cnf(3061,plain,
    leq(multiplication(skc3,u),multiplication(skc4,u)),
    inference(spr,[status(thm),theory(equality)],[127,453]),
    [iquote('0:SpR:127.0,453.0')] ).

cnf(3101,plain,
    $false,
    inference(unc,[status(thm)],[3061,9]),
    [iquote('0:UnC:3061.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n005.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun 16 13:10:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.46/0.71  
% 0.46/0.71  SPASS V 3.9 
% 0.46/0.71  SPASS beiseite: Proof found.
% 0.46/0.71  % SZS status Theorem
% 0.46/0.71  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.46/0.71  SPASS derived 2432 clauses, backtracked 0 clauses, performed 0 splits and kept 504 clauses.
% 0.46/0.71  SPASS allocated 87497 KBytes.
% 0.46/0.71  SPASS spent	0:00:00.35 on the problem.
% 0.46/0.71  		0:00:00.04 for the input.
% 0.46/0.71  		0:00:00.03 for the FLOTTER CNF translation.
% 0.46/0.71  		0:00:00.02 for inferences.
% 0.46/0.71  		0:00:00.00 for the backtracking.
% 0.46/0.71  		0:00:00.25 for the reduction.
% 0.46/0.71  
% 0.46/0.71  
% 0.46/0.71  Here is a proof with depth 3, length 14 :
% 0.46/0.71  % SZS output start Refutation
% See solution above
% 0.46/0.71  Formulae used in the proof : goals additive_idempotence order additive_associativity left_distributivity
% 0.46/0.71  
%------------------------------------------------------------------------------