%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM846+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 14:31:01 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(8,axiom,
    equal(vplus(u,v),vplus(v,u)),
    file('NUM846+2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(vplus(vmul(u,v),u),vmul(u,vsucc(v))),
    file('NUM846+2.p',unknown),
    [] ).

cnf(20,axiom,
    equal(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vmul(vd436,vplus(vd437,vd439))),
    file('NUM846+2.p',unknown),
    [] ).

cnf(23,axiom,
    ~ equal(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vplus(vd437,vd439)),vd436)),
    file('NUM846+2.p',unknown),
    [] ).

cnf(26,plain,
    equal(vplus(u,vmul(u,v)),vmul(u,vsucc(v))),
    inference(rew,[status(thm),theory(equality)],[8,17]),
    [iquote('0:Rew:8.0,17.0')] ).

cnf(32,plain,
    ~ equal(vmul(vd436,vsucc(vplus(vd437,vd439))),vmul(vd436,vsucc(vplus(vd437,vd439)))),
    inference(rew,[status(thm),theory(equality)],[26,23,8,20]),
    [iquote('0:Rew:26.0,23.0,8.0,23.0,20.0,23.0,26.0,23.0,8.0,23.0')] ).

cnf(33,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[32]),
    [iquote('0:Obv:32.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % 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 : Tue Jul  5 14:29:02 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.20/0.44  SPASS allocated 85115 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.03 for the input.
% 0.20/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 0, length 7 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_32_a41__a44__a32_and_a40_holds_a40_definiens_a40_249_a41__a44__a32_399_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_249_a41__a44__a32_398_a44__a32_0_a41__a41__a41_ holds_a40_285_a44__a32_440_a44__a32_0_a41_ holds_a40_286_a44__a32_441_a44__a32_2_a41_
% 0.20/0.44  
%------------------------------------------------------------------------------