%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 : Mon Jul 18 14:30:53 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     :    9 (   5 unt;   3 nHn;   9 RR)
%            Number of literals    :   16 (   0 equ;   5 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 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(vd151,vd165),
    file('NUM835+2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(vplus(vd151,u),vd165),
    file('NUM835+2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(vplus(vd165,u),vd151),
    file('NUM835+2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equal(u,v)
    | m(v) ),
    file('NUM835+2.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ m(u)
    | equal(v,u)
    | equal(vplus(u,skf2(u,v)),v)
    | equal(vplus(v,skf3(v,u)),u) ),
    file('NUM835+2.p',unknown),
    [] ).

cnf(30,plain,
    m(u),
    inference(aed,[status(thm),theory(equality)],[1,5]),
    [iquote('0:AED:1.0,5.0')] ).

cnf(32,plain,
    ( equal(u,v)
    | equal(vplus(u,skf3(u,v)),v)
    | equal(vplus(v,skf2(v,u)),u) ),
    inference(mrr,[status(thm)],[28,30]),
    [iquote('0:MRR:28.0,30.0')] ).

cnf(35,plain,
    ( equal(vd151,vd165)
    | equal(vplus(vd151,skf2(vd151,vd165)),vd165) ),
    inference(res,[status(thm),theory(equality)],[32,4]),
    [iquote('0:Res:32.2,4.0')] ).

cnf(43,plain,
    $false,
    inference(mrr,[status(thm)],[35,1,3]),
    [iquote('0:MRR:35.0,35.1,1.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n011.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 : Wed Jul  6 07:47:53 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 6 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.21/0.45  SPASS allocated 97687 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.03 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 9 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : dis_a40_case_distinction_a40_conseq_a40_110_a41__a41__a41_ def_a40_cond_a40_conseq_a40_105_a41__a44__a32_0_a41__a44__a32_1_a41_
% 0.21/0.45  
%------------------------------------------------------------------------------