TSTP Solution File: NUM423+3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM423+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 01:34:43 EDT 2024

% Result   : Theorem 92.47s 12.13s
% Output   : Refutation 92.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   37 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :   62 (  27 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  179 (  21   ~;  15   |;  11   &; 128   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   16 (   0   ^  13   !;   3   ?;  16   :)

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

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

thf(20,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

thf(93,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtasdt0 @ A @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(94,plain,
    ! [A: $i] :
      ( ~ ( aInteger0 @ A )
      | ( ( sdtasdt0 @ A @ sz00 )
        = sz00 ) ),
    inference(cnf,[status(esa)],[93]) ).

thf(96,plain,
    ! [A: $i] :
      ( ( ( sdtasdt0 @ A @ sz00 )
        = sz00 )
      | ~ ( aInteger0 @ A ) ),
    inference(lifteq,[status(thm)],[94]) ).

thf(22,axiom,
    aInteger0 @ sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).

thf(103,plain,
    aInteger0 @ sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

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

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

thf(23,plain,
    ~ ( ? [A: $i] :
          ( ( aInteger0 @ A )
          & ( ( sdtasdt0 @ xq @ A )
            = ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) ) )
      | ( aDivisorOf0 @ xq @ ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
      | ( sdteqdtlpzmzozddtrp0 @ xa @ xa @ xq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( aInteger0 @ A )
      | ( ( sdtasdt0 @ xq @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(27,plain,
    ! [A: $i] :
      ( ( ( sdtasdt0 @ xq @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
      | ~ ( aInteger0 @ A ) ),
    inference(lifteq,[status(thm)],[26]) ).

thf(110,plain,
    ! [A: $i] :
      ( ( ( sdtasdt0 @ xq @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xa ) ) )
      | ( ( aInteger0 @ sz00 )
       != ( aInteger0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[103,27]) ).

thf(111,plain,
    ( ( sdtpldt0 @ xa @ ( smndt0 @ xa ) )
   != ( sdtasdt0 @ xq @ sz00 ) ),
    inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( sz00 ))]]) ).

thf(18,axiom,
    ( ( aInteger0 @ xa )
    & ( aInteger0 @ xq )
    & ( xq != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).

thf(83,plain,
    ( ( aInteger0 @ xa )
    & ( aInteger0 @ xq )
    & ( xq != sz00 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(86,plain,
    aInteger0 @ xa,
    inference(cnf,[status(esa)],[83]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

thf(88,plain,
    ! [A: $i] :
      ( ( aInteger0 @ A )
     => ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(89,plain,
    ! [A: $i] :
      ( ~ ( aInteger0 @ A )
      | ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
        = sz00 ) ),
    inference(cnf,[status(esa)],[88]) ).

thf(91,plain,
    ! [A: $i] :
      ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
        = sz00 )
      | ~ ( aInteger0 @ A ) ),
    inference(lifteq,[status(thm)],[89]) ).

thf(17684,plain,
    ! [A: $i] :
      ( ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
        = sz00 )
      | ( ( aInteger0 @ xa )
       != ( aInteger0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[86,91]) ).

thf(17685,plain,
    ( ( sdtpldt0 @ xa @ ( smndt0 @ xa ) )
    = sz00 ),
    inference(pattern_uni,[status(thm)],[17684:[bind(A,$thf( xa ))]]) ).

thf(18356,plain,
    ( ( sdtasdt0 @ xq @ sz00 )
   != sz00 ),
    inference(rewrite,[status(thm)],[111,17685]) ).

thf(19715,plain,
    ! [A: $i] :
      ( ~ ( aInteger0 @ A )
      | ( ( sdtasdt0 @ A @ sz00 )
       != ( sdtasdt0 @ xq @ sz00 ) ) ),
    inference(paramod_ordered,[status(thm)],[96,18356]) ).

thf(19716,plain,
    ~ ( aInteger0 @ xq ),
    inference(pattern_uni,[status(thm)],[19715:[bind(A,$thf( xq ))]]) ).

thf(85,plain,
    aInteger0 @ xq,
    inference(cnf,[status(esa)],[83]) ).

thf(19957,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[19716,85]) ).

thf(19958,plain,
    $false,
    inference(simp,[status(thm)],[19957]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM423+3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n012.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % 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 : Mon May 20 04:32:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.96/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/0.98  % [INFO] 	 Parsing done (134ms). 
% 1.32/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.31  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.80/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.80/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ... 
% 2.02/1.38  % [INFO] 	 Axiom selection finished. Selected 20 axioms (removed 0 axioms). 
% 2.02/1.39  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.02/1.39  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.02/1.41  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.02/1.41  % [INFO] 	 Type checking passed. 
% 2.02/1.42  % [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 ... 
% 92.47/12.12  % [INFO] 	 Killing All external provers ... 
% 92.47/12.13  % Time passed: 11612ms (effective reasoning time: 11119ms)
% 92.47/12.13  % 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)>
% 92.47/12.13  % Axioms used in derivation (4): mMulZero, mIntZero, m__671, mAddNeg
% 92.47/12.13  % No. of inferences in proof: 28
% 92.47/12.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11612 ms resp. 11119 ms w/o parsing
% 92.47/12.17  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 92.47/12.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------