TSTP Solution File: SEU503^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU503^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 03:37:51 EDT 2024

% Result   : Theorem 2.62s 1.51s
% Output   : Refutation 2.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   44 (  21 unt;  21 typ;  19 def)
%            Number of atoms       :  169 (  29 equ;   0 cnn)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  247 (   7   ~;   3   |;  17   &; 151   @)
%                                         (   0 <=>;  69  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  29 usr;  30 con; 0-2 aty)
%            Number of variables   :   66 (   0   ^  54   !;  12   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(setextAx_type,type,
    setextAx: $o ).

thf(setextAx_def,definition,
    ( setextAx
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
              = ( in @ C @ B ) )
         => ( A = B ) ) ) ) ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(emptysetAx_type,type,
    emptysetAx: $o ).

thf(emptysetAx_def,definition,
    ( emptysetAx
    = ( ! [A: $i] :
          ~ ( in @ A @ emptyset ) ) ) ).

thf(setadjoinAx_type,type,
    setadjoinAx: $o ).

thf(setadjoinAx_def,definition,
    ( setadjoinAx
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
          = ( ( C = A )
            | ( in @ C @ B ) ) ) ) ) ).

thf(powersetAx_type,type,
    powersetAx: $o ).

thf(powersetAx_def,definition,
    ( powersetAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
          = ( ! [C: $i] :
                ( ( in @ C @ B )
               => ( in @ C @ A ) ) ) ) ) ) ).

thf(setunionAx_type,type,
    setunionAx: $o ).

thf(setunionAx_def,definition,
    ( setunionAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          = ( ? [C: $i] :
                ( ( in @ B @ C )
                & ( in @ C @ A ) ) ) ) ) ) ).

thf(omega0Ax_type,type,
    omega0Ax: $o ).

thf(omega0Ax_def,definition,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ) ).

thf(omegaSAx_type,type,
    omegaSAx: $o ).

thf(omegaSAx_def,definition,
    ( omegaSAx
    = ( ! [A: $i] :
          ( ( in @ A @ omega )
         => ( in @ ( setadjoin @ A @ A ) @ omega ) ) ) ) ).

thf(omegaIndAx_type,type,
    omegaIndAx: $o ).

thf(omegaIndAx_def,definition,
    ( omegaIndAx
    = ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [B: $i] :
                ( ( ( in @ B @ omega )
                  & ( in @ B @ A ) )
               => ( in @ ( setadjoin @ B @ B ) @ A ) ) )
         => ! [B: $i] :
              ( ( in @ B @ omega )
             => ( in @ B @ A ) ) ) ) ) ).

thf(replAx_type,type,
    replAx: $o ).

thf(replAx_def,definition,
    ( replAx
    = ( ! [A: $i > $i > $o,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( exu @ ( A @ C ) ) )
         => ? [C: $i] :
            ! [D: $i] :
              ( ( in @ D @ C )
              = ( ? [E: $i] :
                    ( ( in @ E @ B )
                    & ( A @ E @ D ) ) ) ) ) ) ) ).

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(foundationAx_def,definition,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) ) ) ) ).

thf(wellorderingAx_type,type,
    wellorderingAx: $o ).

thf(wellorderingAx_def,definition,
    ( wellorderingAx
    = ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ! [D: $i] :
                  ( ( in @ D @ C )
                 => ( in @ D @ A ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ A )
                & ( in @ D @ A ) )
             => ( ! [E: $i] :
                    ( ( in @ E @ B )
                   => ( ( in @ C @ E )
                      = ( in @ D @ E ) ) )
               => ( C = D ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( in @ E @ D ) )
                | ! [E: $i] :
                    ( ( in @ E @ D )
                   => ( in @ E @ C ) ) ) )
          & ! [C: $i] :
              ( ( ! [D: $i] :
                    ( ( in @ D @ C )
                   => ( in @ D @ A ) )
                & ? [D: $i] : ( in @ D @ C ) )
             => ? [D: $i,E: $i] :
                  ( ( in @ D @ B )
                  & ( in @ E @ C )
                  & ~ ? [F: $i] :
                        ( ( in @ F @ D )
                        & ( in @ F @ C ) )
                  & ! [F: $i] :
                      ( ( in @ F @ B )
                     => ( ! [G: $i] :
                            ( ( in @ G @ F )
                           => ( in @ G @ D ) )
                        | ( in @ E @ F ) ) ) ) ) ) ) ) ).

thf(descrp_type,type,
    descrp: $o ).

thf(descrp_def,definition,
    ( descrp
    = ( ! [A: $i > $o] :
          ( ( exu @ A )
         => ( A @ ( descr @ A ) ) ) ) ) ).

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

thf(dsetconstrI_def,definition,
    ( dsetconstrI
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

thf(dsetconstrEL_def,definition,
    ( dsetconstrEL
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( in @ C @ A ) ) ) ) ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

thf(exuE1_type,type,
    exuE1: $o ).

thf(exuE1_def,definition,
    ( exuE1
    = ( ! [A: $i > $o] :
          ( ( exu @ A )
         => ? [B: $i] :
              ( ( A @ B )
              & ! [C: $i] :
                  ( ( A @ C )
                 => ( B = C ) ) ) ) ) ) ).

thf(prop2setE_type,type,
    prop2setE: $o ).

thf(prop2setE_def,definition,
    ( prop2setE
    = ( ! [A: $o,B: $i] :
          ( ( in @ B @ ( prop2set @ A ) )
         => A ) ) ) ).

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(emptysetE_def,definition,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ) ).

thf(emptysetimpfalse_type,type,
    emptysetimpfalse: $o ).

thf(emptysetimpfalse_def,definition,
    ( emptysetimpfalse
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => $false ) ) ) ).

thf(1,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ! [A: $i] :
                                            ~ ( in @ A @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).

thf(2,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ! [A: $i] :
                                              ~ ( in @ A @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    $false,
    inference(simp,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU503^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n029.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 : Sun May 19 16:30:53 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.96/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.01  % [INFO] 	 Parsing done (145ms). 
% 1.34/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.78/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.78/1.23  % [INFO] 	 Scanning for conjecture ... 
% 2.28/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.36/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.36/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.36/1.37  % [INFO] 	 Type checking passed. 
% 2.36/1.38  % [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 ... 
% 2.62/1.50  % [INFO] 	 Killing All external provers ... 
% 2.62/1.51  % Time passed: 981ms (effective reasoning time: 480ms)
% 2.62/1.51  % 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)>
% 2.62/1.51  % Axioms used in derivation (0): 
% 2.62/1.51  % No. of inferences in proof: 4
% 2.62/1.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 981 ms resp. 480 ms w/o parsing
% 2.78/1.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.78/1.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------