TSTP Solution File: SEU807^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 03:43:53 EDT 2024

% Result   : Theorem 52.26s 8.83s
% Output   : Refutation 52.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   57 (  19 unt;  11 typ;   5 def)
%            Number of atoms       :  142 (  50 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  408 (  50   ~;  36   |;   4   &; 290   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :  115 (   0   ^ 109   !;   6   ?; 115   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

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(setadjoinIL_type,type,
    setadjoinIL: $o ).

thf(setadjoinIL_def,definition,
    ( setadjoinIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).

thf(setadjoinIR_type,type,
    setadjoinIR: $o ).

thf(setadjoinIR_def,definition,
    ( setadjoinIR
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ B )
         => ( in @ C @ ( setadjoin @ A @ B ) ) ) ) ) ).

thf(in__Cong_type,type,
    in__Cong: $o ).

thf(in__Cong_def,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( in @ C @ A )
                = ( in @ D @ B ) ) ) ) ) ) ).

thf(upairset2E_type,type,
    upairset2E: $o ).

thf(upairset2E_def,definition,
    ( upairset2E
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
         => ( ( C = A )
            | ( C = B ) ) ) ) ) ).

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

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

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ( foundationAx
   => ( setadjoinIL
     => ( setadjoinIR
       => ( in__Cong
         => ( upairset2E
           => ! [A: $i,B: $i] :
                ( ( in @ A @ B )
               => ~ ( in @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself2) ).

thf(2,negated_conjecture,
    ~ ( foundationAx
     => ( setadjoinIL
       => ( setadjoinIR
         => ( in__Cong
           => ( upairset2E
             => ! [A: $i,B: $i] :
                  ( ( in @ A @ B )
                 => ~ ( in @ B @ A ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) )
     => ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
       => ( ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ ( setadjoin @ A @ B ) ) )
         => ( ! [A: $i,B: $i] :
                ( ( A = B )
               => ! [C: $i,D: $i] :
                    ( ( C = D )
                   => ( ( in @ C @ A )
                      = ( in @ D @ B ) ) ) )
           => ( ! [A: $i,B: $i,C: $i] :
                  ( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
                 => ( ( C = A )
                    | ( C = B ) ) )
             => ! [A: $i,B: $i] :
                  ( ( in @ A @ B )
                 => ~ ( in @ B @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
    inference(simp,[status(thm)],[10]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( in @ ( sk1 @ A ) @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(24,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ ( sk1 @ C ) @ C )
      | ( ( in @ A @ ( setadjoin @ A @ B ) )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14,11]) ).

thf(25,plain,
    ! [B: $i,A: $i] : ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( setadjoin @ E @ F )),bind(D,$thf( E ))]]) ).

thf(27,plain,
    ! [B: $i,A: $i] : ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) ),
    inference(simp,[status(thm)],[25]) ).

thf(5,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
      | ( C = A )
      | ( C = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( C = B )
      | ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( C = B )
      | ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(417,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = C )
      | ( E = D )
      | ( ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) )
       != ( in @ E @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[27,13]) ).

thf(418,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
        = A )
      | ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
        = B ) ),
    inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( G )),bind(B,$thf( setadjoin @ I @ emptyset )),bind(C,$thf( G )),bind(D,$thf( I )),bind(E,$thf( sk1 @ ( setadjoin @ G @ ( setadjoin @ I @ emptyset ) ) ))]]) ).

thf(453,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
        = A )
      | ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
        = B ) ),
    inference(simp,[status(thm)],[418]) ).

thf(9,plain,
    in @ sk3 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ~ ( in @ C @ ( sk1 @ A ) )
      | ~ ( in @ C @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( sk1 @ A ) )
      | ~ ( in @ C @ A )
      | ( ( in @ B @ A )
       != ( in @ C @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[4]) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( sk1 @ A ) )
      | ~ ( in @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(1613,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ B @ ( sk1 @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,52]) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( sk3 != B )
      | ( ( sk1 @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[1613]) ).

thf(1691,plain,
    ! [A: $i] :
      ( ~ ( in @ sk3 @ A )
      | ( ( sk1 @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[1675]) ).

thf(9137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ C )
       != sk2 )
      | ( ( in @ A @ ( setadjoin @ A @ B ) )
       != ( in @ sk3 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14,1691]) ).

thf(9138,plain,
    ! [A: $i] :
      ( ( sk1 @ ( setadjoin @ sk3 @ A ) )
     != sk2 ),
    inference(pattern_uni,[status(thm)],[9137:[bind(A,$thf( sk3 )),bind(B,$thf( E )),bind(C,$thf( setadjoin @ sk3 @ E ))]]) ).

thf(9220,plain,
    ! [A: $i] :
      ( ( sk1 @ ( setadjoin @ sk3 @ A ) )
     != sk2 ),
    inference(simp,[status(thm)],[9138]) ).

thf(9934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
        = A )
      | ( B != sk2 )
      | ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
       != ( sk1 @ ( setadjoin @ sk3 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[453,9220]) ).

thf(9935,plain,
    ! [A: $i] :
      ( ( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ A @ emptyset ) ) )
        = sk3 )
      | ( A != sk2 ) ),
    inference(pattern_uni,[status(thm)],[9934:[bind(A,$thf( sk3 )),bind(B,$thf( D )),bind(C,$thf( setadjoin @ D @ emptyset ))]]) ).

thf(9968,plain,
    ( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) )
    = sk3 ),
    inference(simp,[status(thm)],[9935]) ).

thf(7,plain,
    in @ sk2 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(1657,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( ( in @ sk2 @ sk3 )
       != ( in @ B @ ( sk1 @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,52]) ).

thf(1683,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( sk2 != B )
      | ( ( sk1 @ A )
       != sk3 ) ),
    inference(simp,[status(thm)],[1657]) ).

thf(1701,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ( ( sk1 @ A )
       != sk3 ) ),
    inference(simp,[status(thm)],[1683]) ).

thf(11771,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ A )
      | ( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9968,1701]) ).

thf(11772,plain,
    ~ ( in @ sk2 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(pattern_uni,[status(thm)],[11771:[bind(A,$thf( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ))]]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ ( setadjoin @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ ( setadjoin @ A @ B ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(657,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ E @ ( setadjoin @ C @ D ) )
      | ( ( in @ A @ ( setadjoin @ A @ B ) )
       != ( in @ E @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[14,15]) ).

thf(658,plain,
    ! [C: $i,B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ C ) ) ),
    inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( setadjoin @ F @ G )),bind(E,$thf( F ))]]) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ C ) ) ),
    inference(simp,[status(thm)],[658]) ).

thf(11867,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[11772,699]) ).

thf(11868,plain,
    $false,
    inference(simp,[status(thm)],[11867]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.13  % Command  : run_Leo-III %s %d
% 0.11/0.33  % Computer : n032.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Sun May 19 17:54:54 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.98/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.12  % [INFO] 	 Parsing done (167ms). 
% 1.28/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.48  % [INFO] 	 nitpick registered as external prover. 
% 1.85/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.16/1.64  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.16/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.64  % [INFO] 	 Type checking passed. 
% 2.16/1.65  % [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 ... 
% 52.26/8.83  % [INFO] 	 Killing All external provers ... 
% 52.26/8.83  % Time passed: 8349ms (effective reasoning time: 7691ms)
% 52.26/8.83  % 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)>
% 52.26/8.83  % Axioms used in derivation (0): 
% 52.26/8.83  % No. of inferences in proof: 41
% 52.26/8.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8349 ms resp. 7691 ms w/o parsing
% 52.26/8.88  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.26/8.88  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------