%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 0.79s 1.02s
% Output   : Refutation 0.79s
% 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;   8 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(addition(u,u),u),
    file('KLE150+2.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiplication(zero,u),zero),
    file('KLE150+2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE150+2.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
    file('KLE150+2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ equal(addition(u,v),v)
    | leq(u,v) ),
    file('KLE150+2.p',unknown),
    [] ).

cnf(14,axiom,
    equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
    file('KLE150+2.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ leq(strong_iteration(multiplication(skc2,zero)),addition(one,multiplication(skc2,zero)))
    | ~ leq(addition(one,multiplication(skc3,zero)),strong_iteration(multiplication(skc3,zero))) ),
    file('KLE150+2.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(75,plain,
    ( ~ equal(u,u)
    | leq(u,u) ),
    inference(spl,[status(thm),theory(equality)],[2,11]),
    [iquote('0:SpL:2.0,11.0')] ).

cnf(85,plain,
    leq(u,u),
    inference(obv,[status(thm),theory(equality)],[75]),
    [iquote('0:Obv:75.0')] ).

cnf(101,plain,
    equal(addition(one,multiplication(u,multiplication(v,strong_iteration(multiplication(u,v))))),strong_iteration(multiplication(u,v))),
    inference(spr,[status(thm),theory(equality)],[14,21]),
    [iquote('0:SpR:14.0,21.0')] ).

cnf(5723,plain,
    equal(addition(one,multiplication(u,zero)),strong_iteration(multiplication(u,zero))),
    inference(spr,[status(thm),theory(equality)],[5,101]),
    [iquote('0:SpR:5.0,101.0')] ).

cnf(5743,plain,
    ( ~ leq(strong_iteration(multiplication(skc2,zero)),addition(one,multiplication(skc2,zero)))
    | ~ leq(strong_iteration(multiplication(skc3,zero)),strong_iteration(multiplication(skc3,zero))) ),
    inference(rew,[status(thm),theory(equality)],[5723,20]),
    [iquote('0:Rew:5723.0,20.1')] ).

cnf(5767,plain,
    ( ~ leq(strong_iteration(multiplication(skc2,zero)),strong_iteration(multiplication(skc2,zero)))
    | ~ leq(strong_iteration(multiplication(skc3,zero)),strong_iteration(multiplication(skc3,zero))) ),
    inference(rew,[status(thm),theory(equality)],[5723,5743]),
    [iquote('0:Rew:5723.0,5743.0')] ).

cnf(5768,plain,
    $false,
    inference(mrr,[status(thm)],[5767,85]),
    [iquote('0:MRR:5767.0,5767.1,85.0,85.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n029.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 08:42:42 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.79/1.02  
% 0.79/1.02  SPASS V 3.9 
% 0.79/1.02  SPASS beiseite: Proof found.
% 0.79/1.02  % SZS status Theorem
% 0.79/1.02  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.79/1.02  SPASS derived 4475 clauses, backtracked 0 clauses, performed 0 splits and kept 1152 clauses.
% 0.79/1.02  SPASS allocated 89462 KBytes.
% 0.79/1.02  SPASS spent	0:00:00.65 on the problem.
% 0.79/1.02  		0:00:00.03 for the input.
% 0.79/1.02  		0:00:00.03 for the FLOTTER CNF translation.
% 0.79/1.02  		0:00:00.03 for inferences.
% 0.79/1.02  		0:00:00.00 for the backtracking.
% 0.79/1.02  		0:00:00.53 for the reduction.
% 0.79/1.02  
% 0.79/1.02  
% 0.79/1.02  Here is a proof with depth 2, length 15 :
% 0.79/1.02  % SZS output start Refutation
% See solution above
% 0.79/1.02  Formulae used in the proof : idempotence left_annihilation additive_commutativity infty_unfold1 order multiplicative_associativity goals
% 0.79/1.02  
%------------------------------------------------------------------------------