TSTP Solution File: NUM434+3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM434+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 01:34:46 EDT 2024

% Result   : Theorem 8.90s 2.96s
% Output   : Refutation 9.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :   29 (  14 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  140 (  11   ~;   3   |;  11   &; 115   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :    8 (   0   ^   3   !;   5   ?;   8   :)

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

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

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

thf(sk2_type,type,
    sk2: $i ).

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/sandbox2/benchmark/theBenchmark.p',m__1003) ).

thf(64,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(69,plain,
    ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ sk2 )
    = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ),
    inference(cnf,[status(esa)],[64]) ).

thf(70,plain,
    ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
    = ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ sk2 ) ),
    inference(lifteq,[status(thm)],[69]) ).

thf(67,plain,
    aInteger0 @ sk2,
    inference(cnf,[status(esa)],[64]) ).

thf(1,conjecture,
    ? [A: $i] :
      ( ( aInteger0 @ A )
      & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
        = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

thf(27,plain,
    ~ ? [A: $i] :
        ( ( aInteger0 @ A )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
          = ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(28,plain,
    ! [A: $i] :
      ( ~ ( aInteger0 @ A )
      | ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(29,plain,
    ! [A: $i] :
      ( ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
      | ~ ( aInteger0 @ A ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(133,plain,
    ! [A: $i] :
      ( ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ A )
       != ( sdtpldt0 @ xa @ ( smndt0 @ xb ) ) )
      | ( ( aInteger0 @ sk2 )
       != ( aInteger0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67,29]) ).

thf(134,plain,
    ( ( sdtpldt0 @ xa @ ( smndt0 @ xb ) )
   != ( sdtasdt0 @ ( sdtasdt0 @ xp @ xq ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( sk2 ))]]) ).

thf(1124,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[70,134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : NUM434+3 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 04:40:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.89/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.12/1.02  % [INFO] 	 Parsing done (128ms). 
% 1.12/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.26  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.31  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.72/1.32  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.91/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 24 axioms. Running axiom selection ... 
% 2.03/1.39  % [INFO] 	 Axiom selection finished. Selected 24 axioms (removed 0 axioms). 
% 2.03/1.39  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.03/1.40  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.03/1.42  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.03/1.43  % [INFO] 	 Type checking passed. 
% 2.03/1.43  % [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 ... 
% 8.90/2.95  % [INFO] 	 Killing All external provers ... 
% 8.90/2.96  % Time passed: 2409ms (effective reasoning time: 1920ms)
% 8.90/2.96  % 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)>
% 8.90/2.96  % Axioms used in derivation (1): m__1003
% 8.90/2.96  % No. of inferences in proof: 13
% 8.90/2.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2409 ms resp. 1920 ms w/o parsing
% 9.03/3.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.03/3.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------