TSTP Solution File: NUM436+3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : NUM436+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Fri May 19 11:40:34 EDT 2023

% Result   : Theorem 4.60s 2.08s
% Output   : Refutation 4.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   69 (   6 unt;  13 typ;   0 def)
%            Number of atoms       :  223 (  72 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  685 (  19   ~;  14   |; 102   &; 499   @)
%                                         (   2 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :   90 (   0   ^;  79   !;  11   ?;  90   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aInteger0_type,type,
    aInteger0: $i > $o ).

thf(aDivisorOf0_type,type,
    aDivisorOf0: $i > $i > $o ).

thf(sz00_type,type,
    sz00: $i ).

thf(sdtasdt0_type,type,
    sdtasdt0: $i > $i > $i ).

thf(sdteqdtlpzmzozddtrp0_type,type,
    sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).

thf(sdtpldt0_type,type,
    sdtpldt0: $i > $i > $i ).

thf(smndt0_type,type,
    smndt0: $i > $i ).

thf(xp_type,type,
    xp: $i ).

thf(xa_type,type,
    xa: $i ).

thf(xb_type,type,
    xb: $i ).

thf(xq_type,type,
    xq: $i ).

thf(sz10_type,type,
    sz10: $i ).

thf(xm_type,type,
    xm: $i ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
        = ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

thf(115,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) )
        = ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 )
        & ( aInteger0 @ D ) )
     => ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
          & ( sdteqdtlpzmzozddtrp0 @ B @ D @ C ) )
       => ( sdteqdtlpzmzozddtrp0 @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).

thf(106,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 )
        & ( aInteger0 @ D ) )
     => ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
          & ( sdteqdtlpzmzozddtrp0 @ B @ D @ C ) )
       => ( sdteqdtlpzmzozddtrp0 @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(17,axiom,
    aInteger0 @ sz10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).

thf(102,plain,
    aInteger0 @ sz10,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz00 )
          = A )
        & ( A
          = ( sdtpldt0 @ sz00 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

thf(97,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz00 )
          = A )
        & ( A
          = ( sdtpldt0 @ sz00 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( B != sz00 ) )
     => ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).

thf(141,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( B != sz00 ) )
     => ( sdteqdtlpzmzozddtrp0 @ A @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 ) )
     => ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
       => ( sdteqdtlpzmzozddtrp0 @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).

thf(109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 ) )
     => ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
       => ( sdteqdtlpzmzozddtrp0 @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(11,axiom,
    ( ( ( sdtasdt0 @ xp @ xq )
     != sz00 )
    & ? [A: $i] :
        ( ( aInteger0 @ A )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
          = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
    & ( aDivisorOf0 @ ( sdtasdt0 @ xp @ xq ) @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
    & ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ ( sdtasdt0 @ xp @ xq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1003) ).

thf(73,plain,
    ( ( ( sdtasdt0 @ xp @ xq )
     != sz00 )
    & ? [A: $i] :
        ( ( aInteger0 @ A )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
          = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
    & ( aDivisorOf0 @ ( sdtasdt0 @ xp @ xq ) @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
    & ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ ( sdtasdt0 @ xp @ xq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ B )
          = sz00 )
       => ( ( A = sz00 )
          | ( B = sz00 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).

thf(112,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ B )
          = sz00 )
       => ( ( A = sz00 )
          | ( B = sz00 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

thf(127,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ! [B: $i] :
          ( ( aDivisorOf0 @ B @ A )
        <=> ( ( aInteger0 @ B )
            & ( B != sz00 )
            & ? [C: $i] :
                ( ( aInteger0 @ C )
                & ( ( sdtasdt0 @ B @ C )
                  = A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).

thf(47,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ! [B: $i] :
          ( ( ( aDivisorOf0 @ B @ A )
           => ( ( aInteger0 @ B )
              & ( B != sz00 )
              & ? [C: $i] :
                  ( ( aInteger0 @ C )
                  & ( ( sdtasdt0 @ B @ C )
                    = A ) ) ) )
          & ( ( ( aInteger0 @ B )
              & ( B != sz00 )
              & ? [C: $i] :
                  ( ( aInteger0 @ C )
                  & ( ( sdtasdt0 @ B @ C )
                    = A ) ) )
           => ( aDivisorOf0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntegers) ).

thf(46,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ( ( ? [A: $i] :
          ( ( aInteger0 @ A )
          & ( ( sdtasdt0 @ xp @ A )
            = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
      | ( aDivisorOf0 @ xp @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
      | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xp ) )
    & ( ? [A: $i] :
          ( ( aInteger0 @ A )
          & ( ( sdtasdt0 @ xq @ A )
            = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
      | ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
      | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( ( ? [A: $i] :
            ( ( aInteger0 @ A )
            & ( ( sdtasdt0 @ xp @ A )
              = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
        | ( aDivisorOf0 @ xp @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
        | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xp ) )
      & ( ? [A: $i] :
            ( ( aInteger0 @ A )
            & ( ( sdtasdt0 @ xq @ A )
              = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
        | ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
        | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(29,plain,
    ~ ( ( ? [A: $i] :
            ( ( aInteger0 @ A )
            & ( ( sdtasdt0 @ xp @ A )
              = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
        | ( aDivisorOf0 @ xp @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
        | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xp ) )
      & ( ? [A: $i] :
            ( ( aInteger0 @ A )
            & ( ( sdtasdt0 @ xq @ A )
              = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) )
        | ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
        | ( sdteqdtlpzmzozddtrp0 @ xa @ xb @ xq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).

thf(61,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(25,axiom,
    ( ( aInteger0 @ xm )
    & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ xm )
      = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1032) ).

thf(132,plain,
    ( ( aInteger0 @ xm )
    & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ xm )
      = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).

thf(44,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( aInteger0 @ ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( aInteger0 @ ( smndt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).

thf(59,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( aInteger0 @ ( smndt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(23,axiom,
    ( ( aInteger0 @ xa )
    & ( aInteger0 @ xb )
    & ( aInteger0 @ xp )
    & ( xp != sz00 )
    & ( aInteger0 @ xq )
    & ( xq != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).

thf(118,plain,
    ( ( aInteger0 @ xa )
    & ( aInteger0 @ xb )
    & ( aInteger0 @ xp )
    & ( xp != sz00 )
    & ( aInteger0 @ xq )
    & ( xq != sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).

thf(71,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( aInteger0 @ ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(28,axiom,
    aInteger0 @ sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

thf(144,plain,
    aInteger0 @ sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(13,axiom,
    ( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xm ) )
      = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
    & ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
      = ( sdtasdt0 @ xq @ ( sdtasdt0 @ xp @ xm ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1071) ).

thf(86,plain,
    ( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xm ) )
      = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
    & ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
      = ( sdtasdt0 @ xq @ ( sdtasdt0 @ xp @ xm ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

thf(81,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
          = ( smndt0 @ A ) )
        & ( ( smndt0 @ A )
          = ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).

thf(39,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
          = ( smndt0 @ A ) )
        & ( ( smndt0 @ A )
          = ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( sdtasdt0 @ A @ B )
        = ( sdtasdt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

thf(103,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( sdtasdt0 @ A @ B )
        = ( sdtasdt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
        = ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

thf(91,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C ) )
     => ( ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) )
        = ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 ) )
     => ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
      <=> ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).

thf(66,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B )
        & ( aInteger0 @ C )
        & ( C != sz00 ) )
     => ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
         => ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) ) )
        & ( ( aDivisorOf0 @ C @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) )
         => ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz10 )
          = A )
        & ( A
          = ( sdtasdt0 @ sz10 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).

thf(136,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz10 )
          = A )
        & ( A
          = ( sdtasdt0 @ sz10 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( sdtpldt0 @ A @ B )
        = ( sdtpldt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

thf(94,plain,
    ! [A: $i,B: $i] :
      ( ( ( aInteger0 @ A )
        & ( aInteger0 @ B ) )
     => ( ( sdtpldt0 @ A @ B )
        = ( sdtpldt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(190,plain,
    $false,
    inference(cvc4,[status(thm)],[115,106,102,97,141,109,73,112,127,47,46,29,61,132,44,59,118,71,144,86,81,39,103,91,66,136,94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM436+3 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 16:06:46 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.85/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.30/0.97  % [INFO] 	 Parsing done (133ms). 
% 1.30/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.23  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.91/1.23  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.95/1.26  % [INFO] 	 Found a conjecture and 26 axioms. Running axiom selection ... 
% 1.95/1.31  % [INFO] 	 Axiom selection finished. Selected 26 axioms (removed 0 axioms). 
% 2.16/1.31  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.34  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.16/1.35  % [INFO] 	 Type checking passed. 
% 2.16/1.35  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.60/2.08  % External prover 'cvc4' found a proof!
% 4.60/2.08  % [INFO] 	 Killing All external provers ... 
% 4.60/2.08  % Time passed: 1563ms (effective reasoning time: 1096ms)
% 4.60/2.08  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.60/2.08  % Axioms used in derivation (26): mEquModTrn, mAddNeg, mMulOne, mAddZero, mAddAsso, mIntMult, mDivisor, mMulMinOne, m__1032, mMulComm, mAddComm, m__1071, mMulZero, mEquMod, mZeroDiv, mDistrib, mMulAsso, m__1003, mEquModSym, mIntPlus, mIntNeg, m__979, mEquModRef, mIntegers, mIntOne, mIntZero
% 4.60/2.08  % No. of inferences in proof: 56
% 4.60/2.08  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1563 ms resp. 1096 ms w/o parsing
% 4.71/2.11  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.71/2.11  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------