TSTP Solution File: SEU708^2 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEU708^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n022.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 : Mon Jun 24 15:28:06 EDT 2024

% Result   : Theorem 2.99s 1.74s
% Output   : Refutation 3.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   5 unt;   0 typ;   4 def)
%            Number of atoms       :   53 (  21 equ;   0 cnn)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  127 (  13   ~;   6   |;  12   &;  64   @)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-4 aty)
%            Number of variables   :   42 (  10   ^  32   !;   0   ?;  42   :)

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

thf(setunion_type,type,
    setunion: $i > $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(singleton_type,type,
    singleton: $i > $o ).

thf(iffalseProp1_type,type,
    iffalseProp1: $o ).

thf(iffalseProp1_def,definition,
    ( iffalseProp1
    = ( ! [A: $i,B: $o,C: $i] :
          ( ( in @ C @ A )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( ~ B
               => ( in @ D
                  @ ( dsetconstr @ A
                    @ ^ [E: $i] :
                        ( ( B
                          & ( E = C ) )
                        | ( ~ B
                          & ( E = D ) ) ) ) ) ) ) ) ) ) ).

thf(ifSingleton_type,type,
    ifSingleton: $o ).

thf(ifSingleton_def,definition,
    ( ifSingleton
    = ( ! [A: $i,B: $o,C: $i] :
          ( ( in @ C @ A )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( singleton
                @ ( dsetconstr @ A
                  @ ^ [E: $i] :
                      ( ( B
                        & ( E = C ) )
                      | ( ~ B
                        & ( E = D ) ) ) ) ) ) ) ) ) ).

thf(if_type,type,
    if: $i > $o > $i > $i > $i ).

thf(if_def,definition,
    ( if
    = ( ^ [A: $i,B: $o,C: $i,D: $i] :
          ( setunion
          @ ( dsetconstr @ A
            @ ^ [E: $i] :
                ( ( B
                  & ( E = C ) )
                | ( ~ B
                  & ( E = D ) ) ) ) ) ) ) ).

thf(theeq_type,type,
    theeq: $o ).

thf(theeq_def,definition,
    ( theeq
    = ( ! [A: $i] :
          ( ( singleton @ A )
         => ! [B: $i] :
              ( ( in @ B @ A )
             => ( ( setunion @ A )
                = B ) ) ) ) ) ).

thf(1,conjecture,
    ( iffalseProp1
   => ( ifSingleton
     => ( theeq
       => ! [A: $i,B: $o,C: $i] :
            ( ( in @ C @ A )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ( ~ B
                 => ( ( if @ A @ B @ C @ D )
                    = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).

thf(2,negated_conjecture,
    ~ ( iffalseProp1
     => ( ifSingleton
       => ( theeq
         => ! [A: $i,B: $o,C: $i] :
              ( ( in @ C @ A )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ~ B
                   => ( ( if @ A @ B @ C @ D )
                      = D ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $o,C: $i] :
          ( ( in @ C @ A )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( ~ B
               => ( in @ D
                  @ ( dsetconstr @ A
                    @ ^ [E: $i] :
                        ( ( B
                          & ( E = C ) )
                        | ( ~ B
                          & ( E = D ) ) ) ) ) ) ) )
     => ( ! [A: $i,B: $o,C: $i] :
            ( ( in @ C @ A )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ( singleton
                  @ ( dsetconstr @ A
                    @ ^ [E: $i] :
                        ( ( B
                          & ( E = C ) )
                        | ( ~ B
                          & ( E = D ) ) ) ) ) ) )
       => ( ! [A: $i] :
              ( ( singleton @ A )
             => ! [B: $i] :
                  ( ( in @ B @ A )
                 => ( ( setunion @ A )
                    = B ) ) )
         => ! [A: $i,B: $o,C: $i] :
              ( ( in @ C @ A )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ~ B
                   => ( ( setunion
                        @ ( dsetconstr @ A
                          @ ^ [E: $i] :
                              ( ( B
                                & ( E = C ) )
                              | ( ~ B
                                & ( E = D ) ) ) ) )
                      = D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU708^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jun 21 14:31:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.93/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/1.03  % [INFO] 	 Parsing done (122ms). 
% 1.21/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.06/1.34  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.06/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.34  % [INFO] 	 Type checking passed. 
% 2.06/1.34  % [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 ... 
% 2.99/1.74  % External prover 'e' found a proof!
% 2.99/1.74  % [INFO] 	 Killing All external provers ... 
% 2.99/1.74  % Time passed: 1205ms (effective reasoning time: 698ms)
% 2.99/1.74  % 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)>
% 2.99/1.74  % Axioms used in derivation (0): 
% 2.99/1.74  % No. of inferences in proof: 4
% 2.99/1.74  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1205 ms resp. 698 ms w/o parsing
% 3.30/1.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.30/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------