TSTP Solution File: RNG109+4 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG109+4 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Tue May 21 02:37:53 EDT 2024

% Result   : Theorem 12.12s 4.08s
% Output   : Refutation 12.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   68
% Syntax   : Number of formulae    :  114 (  11 unt;  24 typ;   0 def)
%            Number of atoms       :  521 ( 119 equ;   0 cnn)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives : 1411 (  17   ~;  15   |; 248   &; 963   @)
%                                         (  19 <=>; 149  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;   8 con; 0-3 aty)
%            Number of variables   :  247 (   0   ^ 176   !;  71   ?; 247   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aSet0_type,type,
    aSet0: $i > $o ).

thf(sdtpldt1_type,type,
    sdtpldt1: $i > $i > $i ).

thf(aElementOf0_type,type,
    aElementOf0: $i > $i > $o ).

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

thf(sdtasasdt0_type,type,
    sdtasasdt0: $i > $i > $i ).

thf(aIdeal0_type,type,
    aIdeal0: $i > $o ).

thf(aElement0_type,type,
    aElement0: $i > $o ).

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

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

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

thf(doDivides0_type,type,
    doDivides0: $i > $i > $o ).

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

thf(aGcdOfAnd0_type,type,
    aGcdOfAnd0: $i > $i > $i > $o ).

thf(misRelativelyPrime0_type,type,
    misRelativelyPrime0: $i > $i > $o ).

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

thf(slsdtgt0_type,type,
    slsdtgt0: $i > $i ).

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

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

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

thf(aNaturalNumber0_type,type,
    aNaturalNumber0: $i > $o ).

thf(iLess0_type,type,
    iLess0: $i > $i > $o ).

thf(xI_type,type,
    xI: $i ).

thf(sbrdtbr0_type,type,
    sbrdtbr0: $i > $i ).

thf(xc_type,type,
    xc: $i ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( aIdeal0 @ ( sdtasasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).

thf(69,plain,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( aIdeal0 @ ( sdtasasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
          = ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).

thf(185,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
          = ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
          = ( smndt0 @ A ) )
        & ( ( smndt0 @ A )
          = ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).

thf(164,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ A )
          = ( smndt0 @ A ) )
        & ( ( smndt0 @ A )
          = ( sdtasdt0 @ A @ ( smndt0 @ sz10 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

thf(201,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( aDivisorOf0 @ B @ A )
        <=> ( ( aElement0 @ B )
            & ( doDivides0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).

thf(192,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( aDivisorOf0 @ B @ A )
           => ( ( aElement0 @ B )
              & ( doDivides0 @ B @ A ) ) )
          & ( ( ( aElement0 @ B )
              & ( doDivides0 @ B @ A ) )
           => ( aDivisorOf0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( doDivides0 @ A @ B )
      <=> ? [C: $i] :
            ( ( aElement0 @ C )
            & ( ( sdtasdt0 @ A @ C )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

thf(298,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( ( doDivides0 @ A @ B )
         => ? [C: $i] :
              ( ( aElement0 @ C )
              & ( ( sdtasdt0 @ A @ C )
                = B ) ) )
        & ( ? [C: $i] :
              ( ( aElement0 @ C )
              & ( ( sdtasdt0 @ A @ C )
                = B ) )
         => ( doDivides0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).

thf(306,plain,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( aIdeal0 @ ( sdtpldt1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( aIdeal0 @ ( slsdtgt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).

thf(162,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( aIdeal0 @ ( slsdtgt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ! [C: $i] :
          ( ( C
            = ( sdtpldt1 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ? [E: $i,F: $i] :
                    ( ( aElementOf0 @ E @ A )
                    & ( aElementOf0 @ F @ B )
                    & ( ( sdtpldt0 @ E @ F )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).

thf(231,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ! [C: $i] :
          ( ( ( C
              = ( sdtpldt1 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ? [E: $i,F: $i] :
                        ( ( aElementOf0 @ E @ A )
                        & ( aElementOf0 @ F @ B )
                        & ( ( sdtpldt0 @ E @ F )
                          = D ) ) )
                  & ( ? [E: $i,F: $i] :
                        ( ( aElementOf0 @ E @ A )
                        & ( aElementOf0 @ F @ B )
                        & ( ( sdtpldt0 @ E @ F )
                          = D ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ? [E: $i,F: $i] :
                        ( ( aElementOf0 @ E @ A )
                        & ( aElementOf0 @ F @ B )
                        & ( ( sdtpldt0 @ E @ F )
                          = D ) ) )
                  & ( ? [E: $i,F: $i] :
                        ( ( aElementOf0 @ E @ A )
                        & ( aElementOf0 @ F @ B )
                        & ( ( sdtpldt0 @ E @ F )
                          = D ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( sdtpldt1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aIdeal0 @ C ) )
     => ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
      <=> ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMod) ).

thf(139,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aIdeal0 @ C ) )
     => ( ( ( sdteqdtlpzmzozddtrp0 @ A @ B @ C )
         => ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C ) )
        & ( ( aElementOf0 @ ( sdtpldt0 @ A @ ( smndt0 @ B ) ) @ C )
         => ( sdteqdtlpzmzozddtrp0 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

thf(190,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( aElement0 @ ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( aElement0 @ ( smndt0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).

thf(131,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( aElement0 @ ( smndt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz00 )
          = A )
        & ( A
          = ( sdtpldt0 @ sz00 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

thf(308,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz00 )
          = A )
        & ( A
          = ( sdtpldt0 @ sz00 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( ! [C: $i] :
            ( ( aElement0 @ C )
           => ( aElementOf0 @ C @ ( sdtpldt1 @ A @ B ) ) )
       => ! [C: $i,D: $i] :
            ( ( ( aElement0 @ C )
              & ( aElement0 @ D ) )
           => ? [E: $i] :
                ( ( aElement0 @ E )
                & ( sdteqdtlpzmzozddtrp0 @ E @ C @ A )
                & ( sdteqdtlpzmzozddtrp0 @ E @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).

thf(379,plain,
    ! [A: $i,B: $i] :
      ( ( ( aIdeal0 @ A )
        & ( aIdeal0 @ B ) )
     => ( ! [C: $i] :
            ( ( aElement0 @ C )
           => ( aElementOf0 @ C @ ( sdtpldt1 @ A @ B ) ) )
       => ! [C: $i,D: $i] :
            ( ( ( aElement0 @ C )
              & ( aElement0 @ D ) )
           => ? [E: $i] :
                ( ( aElement0 @ E )
                & ( sdteqdtlpzmzozddtrp0 @ E @ C @ A )
                & ( sdteqdtlpzmzozddtrp0 @ E @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( B
            = ( slsdtgt0 @ A ) )
        <=> ( ( aSet0 @ B )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ B )
              <=> ? [D: $i] :
                    ( ( aElement0 @ D )
                    & ( ( sdtasdt0 @ A @ D )
                      = C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).

thf(269,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ! [B: $i] :
          ( ( ( B
              = ( slsdtgt0 @ A ) )
           => ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ B )
                   => ? [D: $i] :
                        ( ( aElement0 @ D )
                        & ( ( sdtasdt0 @ A @ D )
                          = C ) ) )
                  & ( ? [D: $i] :
                        ( ( aElement0 @ D )
                        & ( ( sdtasdt0 @ A @ D )
                          = C ) )
                   => ( aElementOf0 @ C @ B ) ) ) ) )
          & ( ( ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ B )
                   => ? [D: $i] :
                        ( ( aElement0 @ D )
                        & ( ( sdtasdt0 @ A @ D )
                          = C ) ) )
                  & ( ? [D: $i] :
                        ( ( aElement0 @ D )
                        & ( ( sdtasdt0 @ A @ D )
                          = C ) )
                   => ( aElementOf0 @ C @ B ) ) ) )
           => ( B
              = ( slsdtgt0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( misRelativelyPrime0 @ A @ B )
      <=> ( aGcdOfAnd0 @ sz10 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRel) ).

thf(385,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( ( misRelativelyPrime0 @ A @ B )
         => ( aGcdOfAnd0 @ sz10 @ A @ B ) )
        & ( ( aGcdOfAnd0 @ sz10 @ A @ B )
         => ( misRelativelyPrime0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( aGcdOfAnd0 @ C @ A @ B )
        <=> ( ( aDivisorOf0 @ C @ A )
            & ( aDivisorOf0 @ C @ B )
            & ! [D: $i] :
                ( ( ( aDivisorOf0 @ D @ A )
                  & ( aDivisorOf0 @ D @ B ) )
               => ( doDivides0 @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefGCD) ).

thf(142,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ! [C: $i] :
          ( ( ( aGcdOfAnd0 @ C @ A @ B )
           => ( ( aDivisorOf0 @ C @ A )
              & ( aDivisorOf0 @ C @ B )
              & ! [D: $i] :
                  ( ( ( aDivisorOf0 @ D @ A )
                    & ( aDivisorOf0 @ D @ B ) )
                 => ( doDivides0 @ D @ C ) ) ) )
          & ( ( ( aDivisorOf0 @ C @ A )
              & ( aDivisorOf0 @ C @ B )
              & ! [D: $i] :
                  ( ( ( aDivisorOf0 @ D @ A )
                    & ( aDivisorOf0 @ D @ B ) )
                 => ( doDivides0 @ D @ C ) ) )
           => ( aGcdOfAnd0 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ B )
          = sz00 )
       => ( ( A = sz00 )
          | ( B = sz00 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).

thf(153,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ B )
          = sz00 )
       => ( ( A = sz00 )
          | ( B = sz00 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    ? [A: $i] :
      ( ( ! [B: $i] :
            ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
          <=> ? [C: $i] :
                ( ( aElement0 @ C )
                & ( ( sdtasdt0 @ xa @ C )
                  = B ) ) )
       => ( ! [B: $i] :
              ( ( aElementOf0 @ B @ ( slsdtgt0 @ xb ) )
            <=> ? [C: $i] :
                  ( ( aElement0 @ C )
                  & ( ( sdtasdt0 @ xb @ C )
                    = B ) ) )
         => ( ? [B: $i,C: $i] :
                ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
                & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
                & ( ( sdtpldt0 @ B @ C )
                  = A ) )
            | ( aElementOf0 @ A @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) ) )
      & ( A != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ? [A: $i] :
        ( ( ! [B: $i] :
              ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
            <=> ? [C: $i] :
                  ( ( aElement0 @ C )
                  & ( ( sdtasdt0 @ xa @ C )
                    = B ) ) )
         => ( ! [B: $i] :
                ( ( aElementOf0 @ B @ ( slsdtgt0 @ xb ) )
              <=> ? [C: $i] :
                    ( ( aElement0 @ C )
                    & ( ( sdtasdt0 @ xb @ C )
                      = B ) ) )
           => ( ? [B: $i,C: $i] :
                  ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
                  & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
                  & ( ( sdtpldt0 @ B @ C )
                    = A ) )
              | ( aElementOf0 @ A @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) ) )
        & ( A != sz00 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(46,plain,
    ~ ? [A: $i] :
        ( ( ! [B: $i] :
              ( ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
               => ? [C: $i] :
                    ( ( aElement0 @ C )
                    & ( ( sdtasdt0 @ xa @ C )
                      = B ) ) )
              & ( ? [C: $i] :
                    ( ( aElement0 @ C )
                    & ( ( sdtasdt0 @ xa @ C )
                      = B ) )
               => ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) ) ) )
         => ( ! [B: $i] :
                ( ( ( aElementOf0 @ B @ ( slsdtgt0 @ xb ) )
                 => ? [C: $i] :
                      ( ( aElement0 @ C )
                      & ( ( sdtasdt0 @ xb @ C )
                        = B ) ) )
                & ( ? [C: $i] :
                      ( ( aElement0 @ C )
                      & ( ( sdtasdt0 @ xb @ C )
                        = B ) )
                 => ( aElementOf0 @ B @ ( slsdtgt0 @ xb ) ) ) )
           => ( ? [B: $i,C: $i] :
                  ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
                  & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
                  & ( ( sdtpldt0 @ B @ C )
                    = A ) )
              | ( aElementOf0 @ A @ ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) ) )
        & ( A != sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

thf(228,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( aElement0 @ ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( sdtpldt0 @ A @ B )
        = ( sdtpldt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

thf(133,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( sdtpldt0 @ A @ B )
        = ( sdtpldt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(7,axiom,
    ( ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xa @ A )
          = sz00 ) )
    & ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xa @ A )
          = xa ) )
    & ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xb @ A )
          = sz00 ) )
    & ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xb @ A )
          = xb ) )
    & ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).

thf(74,plain,
    ( ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xa @ A )
          = sz00 ) )
    & ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xa @ A )
          = xa ) )
    & ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xb @ A )
          = sz00 ) )
    & ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xb @ A )
          = xb ) )
    & ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( aIdeal0 @ A )
    <=> ( ( aSet0 @ A )
        & ! [B: $i] :
            ( ( aElementOf0 @ B @ A )
           => ( ! [C: $i] :
                  ( ( aElementOf0 @ C @ A )
                 => ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
              & ! [C: $i] :
                  ( ( aElement0 @ C )
                 => ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

thf(206,plain,
    ! [A: $i] :
      ( ( ( aIdeal0 @ A )
       => ( ( aSet0 @ A )
          & ! [B: $i] :
              ( ( aElementOf0 @ B @ A )
             => ( ! [C: $i] :
                    ( ( aElementOf0 @ C @ A )
                   => ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
                & ! [C: $i] :
                    ( ( aElement0 @ C )
                   => ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ) )
      & ( ( ( aSet0 @ A )
          & ! [B: $i] :
              ( ( aElementOf0 @ B @ A )
             => ( ! [C: $i] :
                    ( ( aElementOf0 @ C @ A )
                   => ( aElementOf0 @ ( sdtpldt0 @ B @ C ) @ A ) )
                & ! [C: $i] :
                    ( ( aElement0 @ C )
                   => ( aElementOf0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) )
       => ( aIdeal0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(16,axiom,
    sz10 != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).

thf(156,plain,
    sz10 != sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( ( aElement0 @ A )
        & ( A != sz00 ) )
     => ( aNaturalNumber0 @ ( sbrdtbr0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEucSort) ).

thf(169,plain,
    ! [A: $i] :
      ( ( ( aElement0 @ A )
        & ( A != sz00 ) )
     => ( aNaturalNumber0 @ ( sbrdtbr0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( aElement0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

thf(339,plain,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => ! [B: $i] :
          ( ( aElementOf0 @ B @ A )
         => ( aElement0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(9,axiom,
    ( ( aSet0 @ xI )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ xI )
       => ( ! [B: $i] :
              ( ( aElementOf0 @ B @ xI )
             => ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xI ) )
          & ! [B: $i] :
              ( ( aElement0 @ B )
             => ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xI ) ) ) )
    & ( aIdeal0 @ xI )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ ( slsdtgt0 @ xa ) )
      <=> ? [B: $i] :
            ( ( aElement0 @ B )
            & ( ( sdtasdt0 @ xa @ B )
              = A ) ) )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ ( slsdtgt0 @ xb ) )
      <=> ? [B: $i] :
            ( ( aElement0 @ B )
            & ( ( sdtasdt0 @ xb @ B )
              = A ) ) )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ xI )
      <=> ? [B: $i,C: $i] :
            ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ B @ C )
              = A ) ) )
    & ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

thf(96,plain,
    ( ( aSet0 @ xI )
    & ! [A: $i] :
        ( ( aElementOf0 @ A @ xI )
       => ( ! [B: $i] :
              ( ( aElementOf0 @ B @ xI )
             => ( aElementOf0 @ ( sdtpldt0 @ A @ B ) @ xI ) )
          & ! [B: $i] :
              ( ( aElement0 @ B )
             => ( aElementOf0 @ ( sdtasdt0 @ B @ A ) @ xI ) ) ) )
    & ( aIdeal0 @ xI )
    & ! [A: $i] :
        ( ( ( aElementOf0 @ A @ ( slsdtgt0 @ xa ) )
         => ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ xa @ B )
                = A ) ) )
        & ( ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ xa @ B )
                = A ) )
         => ( aElementOf0 @ A @ ( slsdtgt0 @ xa ) ) ) )
    & ! [A: $i] :
        ( ( ( aElementOf0 @ A @ ( slsdtgt0 @ xb ) )
         => ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ xb @ B )
                = A ) ) )
        & ( ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ xb @ B )
                = A ) )
         => ( aElementOf0 @ A @ ( slsdtgt0 @ xb ) ) ) )
    & ! [A: $i] :
        ( ( ( aElementOf0 @ A @ xI )
         => ? [B: $i,C: $i] :
              ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
              & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
              & ( ( sdtpldt0 @ B @ C )
                = A ) ) )
        & ( ? [B: $i,C: $i] :
              ( ( aElementOf0 @ B @ ( slsdtgt0 @ xa ) )
              & ( aElementOf0 @ C @ ( slsdtgt0 @ xb ) )
              & ( ( sdtpldt0 @ B @ C )
                = A ) )
         => ( aElementOf0 @ A @ xI ) ) )
    & ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( aSet0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).

thf(73,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
        = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

thf(266,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
        = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).

thf(71,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(40,axiom,
    ( ( aElement0 @ xc )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xc @ A )
          = xa ) )
    & ( doDivides0 @ xc @ xa )
    & ( aDivisorOf0 @ xc @ xa )
    & ( aElement0 @ xc )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xc @ A )
          = xb ) )
    & ( doDivides0 @ xc @ xb )
    & ( aDivisorOf0 @ xc @ xb )
    & ! [A: $i] :
        ( ( ( ( ( aElement0 @ A )
              & ( ? [B: $i] :
                    ( ( aElement0 @ B )
                    & ( ( sdtasdt0 @ A @ B )
                      = xa ) )
                | ( doDivides0 @ A @ xa ) ) )
            | ( aDivisorOf0 @ A @ xa ) )
          & ( ? [B: $i] :
                ( ( aElement0 @ B )
                & ( ( sdtasdt0 @ A @ B )
                  = xb ) )
            | ( doDivides0 @ A @ xb )
            | ( aDivisorOf0 @ A @ xb ) ) )
       => ( ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ A @ B )
                = xc ) )
          & ( doDivides0 @ A @ xc ) ) )
    & ( aGcdOfAnd0 @ xc @ xa @ xb ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).

thf(313,plain,
    ( ( aElement0 @ xc )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xc @ A )
          = xa ) )
    & ( doDivides0 @ xc @ xa )
    & ( aDivisorOf0 @ xc @ xa )
    & ( aElement0 @ xc )
    & ? [A: $i] :
        ( ( aElement0 @ A )
        & ( ( sdtasdt0 @ xc @ A )
          = xb ) )
    & ( doDivides0 @ xc @ xb )
    & ( aDivisorOf0 @ xc @ xb )
    & ! [A: $i] :
        ( ( ( ( ( aElement0 @ A )
              & ( ? [B: $i] :
                    ( ( aElement0 @ B )
                    & ( ( sdtasdt0 @ A @ B )
                      = xa ) )
                | ( doDivides0 @ A @ xa ) ) )
            | ( aDivisorOf0 @ A @ xa ) )
          & ( ? [B: $i] :
                ( ( aElement0 @ B )
                & ( ( sdtasdt0 @ A @ B )
                  = xb ) )
            | ( doDivides0 @ A @ xb )
            | ( aDivisorOf0 @ A @ xb ) ) )
       => ( ? [B: $i] :
              ( ( aElement0 @ B )
              & ( ( sdtasdt0 @ A @ B )
                = xc ) )
          & ( doDivides0 @ A @ xc ) ) )
    & ( aGcdOfAnd0 @ xc @ xa @ xb ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ! [C: $i] :
          ( ( C
            = ( sdtasasdt0 @ A @ B ) )
        <=> ( ( aSet0 @ C )
            & ! [D: $i] :
                ( ( aElementOf0 @ D @ C )
              <=> ( ( aElementOf0 @ D @ A )
                  & ( aElementOf0 @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).

thf(350,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ! [C: $i] :
          ( ( ( C
              = ( sdtasasdt0 @ A @ B ) )
           => ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElementOf0 @ D @ A )
                      & ( aElementOf0 @ D @ B ) ) )
                  & ( ( ( aElementOf0 @ D @ A )
                      & ( aElementOf0 @ D @ B ) )
                   => ( aElementOf0 @ D @ C ) ) ) ) )
          & ( ( ( aSet0 @ C )
              & ! [D: $i] :
                  ( ( ( aElementOf0 @ D @ C )
                   => ( ( aElementOf0 @ D @ A )
                      & ( aElementOf0 @ D @ B ) ) )
                  & ( ( ( aElementOf0 @ D @ A )
                      & ( aElementOf0 @ D @ B ) )
                   => ( aElementOf0 @ D @ C ) ) ) )
           => ( C
              = ( sdtasasdt0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( sdtasdt0 @ A @ B )
        = ( sdtasdt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

thf(159,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B ) )
     => ( ( sdtasdt0 @ A @ B )
        = ( sdtasdt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(21,axiom,
    ( ( xa != sz00 )
    | ( xb != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).

thf(172,plain,
    ( ( xa != sz00 )
    | ( xb != sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(32,axiom,
    aElement0 @ sz10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

thf(230,plain,
    aElement0 @ sz10,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

thf(91,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(26,axiom,
    ( ( aElement0 @ xa )
    & ( aElement0 @ xb ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

thf(198,plain,
    ( ( aElement0 @ xa )
    & ( aElement0 @ xb ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( iLess0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatLess) ).

thf(72,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( B != sz00 ) )
     => ? [C: $i,D: $i] :
          ( ( aElement0 @ C )
          & ( aElement0 @ D )
          & ( A
            = ( sdtpldt0 @ ( sdtasdt0 @ C @ B ) @ D ) )
          & ( ( D != sz00 )
           => ( iLess0 @ ( sbrdtbr0 @ D ) @ ( sbrdtbr0 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).

thf(175,plain,
    ! [A: $i,B: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( B != sz00 ) )
     => ? [C: $i,D: $i] :
          ( ( aElement0 @ C )
          & ( aElement0 @ D )
          & ( A
            = ( sdtpldt0 @ ( sdtasdt0 @ C @ B ) @ D ) )
          & ( ( D != sz00 )
           => ( iLess0 @ ( sbrdtbr0 @ D ) @ ( sbrdtbr0 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).

thf(305,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
        = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

thf(136,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aElement0 @ A )
        & ( aElement0 @ B )
        & ( aElement0 @ C ) )
     => ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
        = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ( ( ! [C: $i] :
              ( ( aElementOf0 @ C @ A )
             => ( aElementOf0 @ C @ B ) )
          & ! [C: $i] :
              ( ( aElementOf0 @ C @ B )
             => ( aElementOf0 @ C @ A ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).

thf(341,plain,
    ! [A: $i,B: $i] :
      ( ( ( aSet0 @ A )
        & ( aSet0 @ B ) )
     => ( ( ! [C: $i] :
              ( ( aElementOf0 @ C @ A )
             => ( aElementOf0 @ C @ B ) )
          & ! [C: $i] :
              ( ( aElementOf0 @ C @ B )
             => ( aElementOf0 @ C @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(30,axiom,
    aElement0 @ sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

thf(227,plain,
    aElement0 @ sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz10 )
          = A )
        & ( A
          = ( sdtasdt0 @ sz10 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).

thf(222,plain,
    ! [A: $i] :
      ( ( aElement0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz10 )
          = A )
        & ( A
          = ( sdtasdt0 @ sz10 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(1543,plain,
    $false,
    inference(cvc4,[status(thm)],[69,185,164,201,192,298,306,162,231,139,190,131,308,379,269,385,142,153,46,228,133,74,206,156,169,339,96,73,266,71,313,350,159,172,230,91,198,72,175,305,136,341,227,222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG109+4 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n021.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  : 300
% 0.14/0.35  % DateTime : Sat May 18 12:20:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.84/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/0.98  % [INFO] 	 Parsing done (160ms). 
% 1.35/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.98/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.98/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.98/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.33  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.34  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.35  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.35  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.16/1.36  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.31/1.37  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.31/1.37  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.31/1.38  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.31/1.38  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.31/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ... 
% 2.65/1.54  % [INFO] 	 Axiom selection finished. Selected 43 axioms (removed 0 axioms). 
% 2.69/1.57  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.57  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.59  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.59  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.60  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.60  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.69/1.60  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.89/1.63  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.89/1.63  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.89/1.63  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.89/1.65  % [INFO] 	 Type checking passed. 
% 2.89/1.65  % [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 ... 
% 12.12/4.08  % External prover 'cvc4' found a proof!
% 12.12/4.08  % [INFO] 	 Killing All external provers ... 
% 12.12/4.08  % Time passed: 3583ms (effective reasoning time: 3075ms)
% 12.12/4.08  % 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)>
% 12.12/4.08  % Axioms used in derivation (43): mAddComm, mIdeInt, mMulZero, mNatLess, mSetSort, mDivision, m__2091, mDefSSum, mMulUnit, mAddInvr, m__2110, mDefMod, mSortsC, mDefIdeal, mEucSort, mDefPrIdeal, mDefDvs, m__2174, mSortsC_01, mEOfElem, m__2129, mAddZero, mIdeSum, mDefSInt, mAddAsso, mMulAsso, mDefDiv, mDefRel, mMulMnOne, mPrIdeal, mCancel, mSortsB_02, mSortsU, mDefGCD, mSetEq, mAMDistr, mElmSort, mUnNeZr, mChineseRemainder, mSortsB, mNatSort, mMulComm, m__2203
% 12.12/4.08  % No. of inferences in proof: 90
% 12.12/4.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3583 ms resp. 3075 ms w/o parsing
% 12.71/4.17  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.71/4.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------