%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (  10 unt;   0 nHn;  10 RR)
%            Number of literals    :   10 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(strong_iteration(zero),one),
    file('KLE138+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(addition(u,zero),u),
    file('KLE138+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiplication(zero,u),zero),
    file('KLE138+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE138+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
    file('KLE138+1.p',unknown),
    [] ).

cnf(21,plain,
    equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
    inference(rew,[status(thm),theory(equality)],[7,10]),
    [iquote('0:Rew:7.0,10.0')] ).

cnf(30,plain,
    equal(addition(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[7,2]),
    [iquote('0:SpR:7.0,2.0')] ).

cnf(46,plain,
    equal(addition(one,zero),strong_iteration(zero)),
    inference(spr,[status(thm),theory(equality)],[6,21]),
    [iquote('0:SpR:6.0,21.0')] ).

cnf(48,plain,
    equal(strong_iteration(zero),one),
    inference(rew,[status(thm),theory(equality)],[30,46,7]),
    [iquote('0:Rew:30.0,46.0,7.0,46.0')] ).

cnf(49,plain,
    $false,
    inference(mrr,[status(thm)],[48,1]),
    [iquote('0:MRR:48.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun 16 12:49:09 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.21/0.45  SPASS allocated 85135 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.04 for the input.
% 0.21/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 1, length 10 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : goals additive_identity left_annihilation additive_commutativity infty_unfold1
% 0.21/0.45  
%------------------------------------------------------------------------------