%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 14:30:59 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    6 (   6 unt;   0 nHn;   6 RR)
%            Number of literals    :    6 (   0 equ;   2 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(8,axiom,
    equal(vplus(u,v),vplus(v,u)),
    file('NUM844+2.p',unknown),
    [] ).

cnf(12,axiom,
    equal(vplus(vsucc(u),v),vsucc(vplus(u,v))),
    file('NUM844+2.p',unknown),
    [] ).

cnf(13,axiom,
    equal(vplus(u,vsucc(v)),vsucc(vplus(u,v))),
    file('NUM844+2.p',unknown),
    [] ).

cnf(22,axiom,
    ~ equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))),
    file('NUM844+2.p',unknown),
    [] ).

cnf(30,plain,
    ~ equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))),
    inference(rew,[status(thm),theory(equality)],[13,22,12,8]),
    [iquote('0:Rew:13.0,22.0,12.0,22.0,13.0,22.0,8.0,22.0,13.0,22.0')] ).

cnf(31,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[30]),
    [iquote('0:Obv:30.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n021.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 : Tue Jul  5 04:46:02 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.19/0.43  SPASS allocated 85113 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.00 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 0, length 6 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_52_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_3_a41__a44__a32_and_a40_holds_a40_definiens_a40_29_a41__a44__a32_45_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_29_a41__a44__a32_44_a44__a32_0_a41__a41__a41_ holds_a40_266_a44__a32_415_a44__a32_3_a41_
% 0.19/0.43  
%------------------------------------------------------------------------------