%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 02:27:57 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   6 unt;   0 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    test__dfg(skc1),
    file('KLE006+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(addition(skc1,c(skc1)),one),
    file('KLE006+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE006+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ complement(u,v)
    | equal(addition(v,u),one) ),
    file('KLE006+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ test__dfg(u)
    | ~ equal(c(u),v)
    | complement(u,v) ),
    file('KLE006+1.p',unknown),
    [] ).

cnf(25,plain,
    ( ~ equal(c(skc1),u)
    | complement(skc1,u) ),
    inference(res,[status(thm),theory(equality)],[1,20]),
    [iquote('0:Res:1.0,20.0')] ).

cnf(55,plain,
    ( ~ complement(u,v)
    | equal(addition(u,v),one) ),
    inference(spr,[status(thm),theory(equality)],[17,11]),
    [iquote('0:SpR:17.1,11.0')] ).

cnf(79,plain,
    complement(skc1,c(skc1)),
    inference(eqr,[status(thm),theory(equality)],[25]),
    [iquote('0:EqR:25.0')] ).

cnf(101,plain,
    ( ~ complement(skc1,c(skc1))
    | ~ equal(one,one) ),
    inference(spl,[status(thm),theory(equality)],[55,10]),
    [iquote('0:SpL:55.1,10.0')] ).

cnf(102,plain,
    ~ complement(skc1,c(skc1)),
    inference(obv,[status(thm),theory(equality)],[101]),
    [iquote('0:Obv:101.1')] ).

cnf(103,plain,
    $false,
    inference(mrr,[status(thm)],[102,79]),
    [iquote('0:MRR:102.0,79.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 09:51:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  
% 0.20/0.46  SPASS V 3.9 
% 0.20/0.46  SPASS beiseite: Proof found.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.46  SPASS derived 76 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.20/0.46  SPASS allocated 97654 KBytes.
% 0.20/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.20/0.46  		0:00:00.04 for the input.
% 0.20/0.46  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.46  		0:00:00.00 for inferences.
% 0.20/0.46  		0:00:00.00 for the backtracking.
% 0.20/0.46  		0:00:00.00 for the reduction.
% 0.20/0.46  
% 0.20/0.46  
% 0.20/0.46  Here is a proof with depth 2, length 11 :
% 0.20/0.46  % SZS output start Refutation
% See solution above
% 0.20/0.46  Formulae used in the proof : goals additive_commutativity test_2 test_3
% 0.20/0.46  
%------------------------------------------------------------------------------