TSTP Solution File: SET874+1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET874+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:07:14 EDT 2024

% Result   : Theorem 69.45s 11.21s
% Output   : Refutation 69.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   26 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   60 (  39 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  176 (  17   ~;  18   |;   6   &; 119   @)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   45 (   0   ^  45   !;   0   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_union2_type,type,
    set_union2: $i > $i > $i ).

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

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

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

thf(sk1_type,type,
    sk1: $i ).

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

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( ( set_union2 @ ( singleton @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).

thf(59,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( ( set_union2 @ ( singleton @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(60,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ B )
      | ( ( set_union2 @ ( singleton @ A ) @ B )
        = B ) ),
    inference(cnf,[status(esa)],[59]) ).

thf(61,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_union2 @ ( singleton @ A ) @ B )
        = B )
      | ~ ( in @ A @ B ) ),
    inference(lifteq,[status(thm)],[60]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
      = ( unordered_pair @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
        = ( unordered_pair @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(13,plain,
    ~ ! [A: $i,B: $i] :
        ( ( set_union2 @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
        = ( unordered_pair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,plain,
    ( ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) )
   != ( unordered_pair @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(15,plain,
    ( ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) )
   != ( unordered_pair @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(10297,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ B )
      | ( B
       != ( unordered_pair @ sk1 @ sk2 ) )
      | ( ( set_union2 @ ( singleton @ A ) @ B )
       != ( set_union2 @ ( singleton @ sk1 ) @ ( unordered_pair @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[61,15]) ).

thf(10298,plain,
    ( ~ ( in @ sk1 @ ( unordered_pair @ sk1 @ sk2 ) )
    | ( ( unordered_pair @ sk1 @ sk2 )
     != ( unordered_pair @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[10297:[bind(A,$thf( sk1 )),bind(B,$thf( unordered_pair @ sk1 @ sk2 ))]]) ).

thf(10333,plain,
    ~ ( in @ sk1 @ ( unordered_pair @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[10298]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( unordered_pair @ A @ B ) )
    <=> ! [D: $i] :
          ( ( in @ D @ C )
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

thf(24,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( unordered_pair @ A @ B ) )
       => ! [D: $i] :
            ( ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) )
       => ( C
          = ( unordered_pair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(25,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( C
          = ( unordered_pair @ A @ B ) )
       => ( ! [D: $i] :
              ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
          & ! [D: $i] :
              ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ! [D: $i] :
              ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
          & ! [D: $i] :
              ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) )
       => ( C
          = ( unordered_pair @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[24]) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( unordered_pair @ A @ B ) )
      | ( D != A )
      | ( in @ D @ C ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( unordered_pair @ A @ B ) )
      | ( D != A )
      | ( in @ D @ C ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(47,plain,
    ! [B: $i,A: $i] : ( in @ A @ ( unordered_pair @ A @ B ) ),
    inference(simp,[status(thm)],[46]) ).

thf(10336,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[10333,47]) ).

thf(10337,plain,
    $false,
    inference(simp,[status(thm)],[10336]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET874+1 : TPTP v8.2.0. Released v3.2.0.
% 0.09/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.30  % Computer : n026.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.30  % CPULimit : 300
% 0.15/0.30  % WCLimit  : 300
% 0.15/0.30  % DateTime : Mon May 20 13:22:54 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.84/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/1.02  % [INFO] 	 Parsing done (173ms). 
% 1.22/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.33  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.34  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ... 
% 2.02/1.47  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 2.06/1.50  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.06/1.51  % [INFO] 	 Type checking passed. 
% 2.16/1.51  % [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 ... 
% 69.45/11.20  % [INFO] 	 Killing All external provers ... 
% 69.45/11.21  % Time passed: 10787ms (effective reasoning time: 10162ms)
% 69.45/11.21  % 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)>
% 69.45/11.21  % Axioms used in derivation (2): l23_zfmisc_1, d2_tarski
% 69.45/11.21  % No. of inferences in proof: 20
% 69.45/11.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10787 ms resp. 10162 ms w/o parsing
% 69.45/11.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.45/11.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------