TSTP Solution File: SET611^3 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET611^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 03:03:10 EDT 2024

% Result   : Theorem 8.13s 3.06s
% Output   : Refutation 8.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   51 (  13 unt;   7 typ;   3 def)
%            Number of atoms       :  178 (  36 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  262 (  61   ~;  45   |;  28   &; 128   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   49 (  28   ^  21   !;   0   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(emptyset_type,type,
    emptyset: $i > $o ).

thf(emptyset_def,definition,
    ( emptyset
    = ( ^ [A: $i] : $false ) ) ).

thf(intersection_type,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(intersection_def,definition,
    ( intersection
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(setminus_type,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(setminus_def,definition,
    ( setminus
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          & ~ ( B @ C ) ) ) ) ).

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i ).

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o] :
      ( ( ( intersection @ A @ B )
        = emptyset )
      = ( ( setminus @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $o,B: $i > $o] :
        ( ( ( intersection @ A @ B )
          = emptyset )
        = ( ( setminus @ A @ B )
          = A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i > $o,B: $i > $o] :
        ( ( ( ^ [C: $i] :
                ( ( A @ C )
                & ( B @ C ) ) )
          = ( ^ [C: $i] : $false ) )
        = ( ( ^ [C: $i] :
                ( ( A @ C )
                & ~ ( B @ C ) ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
      = ( ^ [A: $i] : $false ) )
   != ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = sk1 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = sk1 )
   != ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
      = ( ^ [A: $i] : $false ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != sk1 )
    | ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
     != ( ^ [A: $i] : $false ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != sk1 )
    | ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
     != ( ^ [A: $i] : $false ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ( ( sk1 @ sk5 )
        & ~ ( sk2 @ sk5 ) )
     != ( sk1 @ sk5 ) )
    | ( ( sk1 @ sk6 )
      & ( sk2 @ sk6 ) ) ),
    inference(func_ext,[status(esa)],[9]) ).

thf(15,plain,
    ( ( sk1 @ sk6 )
    | ( ( ( sk1 @ sk5 )
        & ~ ( sk2 @ sk5 ) )
     != ( sk1 @ sk5 ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(109,plain,
    ( ( sk1 @ sk6 )
    | ( ( sk1 @ sk5 )
      & ~ ( sk2 @ sk5 ) )
    | ( sk1 @ sk5 ) ),
    inference(bool_ext,[status(thm)],[15]) ).

thf(121,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk5 )
    | ( sk1 @ sk6 ) ),
    inference(cnf,[status(esa)],[109]) ).

thf(122,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk6 ) ),
    inference(simp,[status(thm)],[121]) ).

thf(14,plain,
    ( ( sk2 @ sk6 )
    | ( ( ( sk1 @ sk5 )
        & ~ ( sk2 @ sk5 ) )
     != ( sk1 @ sk5 ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(47,plain,
    ( ( sk2 @ sk6 )
    | ( ( sk1 @ sk5 )
      & ~ ( sk2 @ sk5 ) )
    | ( sk1 @ sk5 ) ),
    inference(bool_ext,[status(thm)],[14]) ).

thf(53,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk5 )
    | ( sk2 @ sk6 ) ),
    inference(cnf,[status(esa)],[47]) ).

thf(54,plain,
    ( ( sk1 @ sk5 )
    | ( sk2 @ sk6 ) ),
    inference(simp,[status(thm)],[53]) ).

thf(8,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = sk1 )
    | ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
      = ( ^ [A: $i] : $false ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = sk1 )
    | ( ( ^ [A: $i] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) ) )
      = ( ^ [A: $i] : $false ) ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( sk1 @ A )
          & ~ ( sk2 @ A ) )
        = ( sk1 @ A ) )
      | ~ ( ( sk1 @ B )
          & ( sk2 @ B ) ) ),
    inference(func_ext,[status(esa)],[10]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ B )
      | ~ ( sk2 @ B )
      | ( ( ( sk1 @ A )
          & ~ ( sk2 @ A ) )
        = ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(230,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ B )
      | ~ ( sk2 @ B )
      | ( ( sk1 @ A )
        & ~ ( sk2 @ A ) )
      | ~ ( sk1 @ A ) ),
    inference(bool_ext,[status(thm)],[26]) ).

thf(272,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A )
      | ~ ( sk2 @ B )
      | ~ ( sk1 @ B ) ),
    inference(cnf,[status(esa)],[230]) ).

thf(318,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A )
      | ~ ( sk1 @ B )
      | ( ( sk2 @ B )
       != ( sk2 @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[272]) ).

thf(319,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A )
      | ~ ( sk1 @ A ) ),
    inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( B ))]]) ).

thf(326,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A ) ),
    inference(simp,[status(thm)],[319]) ).

thf(331,plain,
    ! [A: $i] :
      ( ( sk1 @ sk5 )
      | ~ ( sk1 @ A )
      | ( ( sk2 @ sk6 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[54,326]) ).

thf(332,plain,
    ( ( sk1 @ sk5 )
    | ~ ( sk1 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( sk6 ))]]) ).

thf(366,plain,
    ( ( sk1 @ sk5 )
    | ( ( sk1 @ sk6 )
     != ( sk1 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[122,332]) ).

thf(367,plain,
    sk1 @ sk5,
    inference(pattern_uni,[status(thm)],[366:[]]) ).

thf(376,plain,
    ( ( sk1 @ sk6 )
    | ~ ( $true
        & ~ ( sk2 @ sk5 ) ) ),
    inference(rewrite,[status(thm)],[15,367]) ).

thf(377,plain,
    ( ( sk1 @ sk6 )
    | ( sk2 @ sk5 ) ),
    inference(simp,[status(thm)],[376]) ).

thf(372,plain,
    ( ( sk2 @ sk6 )
    | ~ ( $true
        & ~ ( sk2 @ sk5 ) ) ),
    inference(rewrite,[status(thm)],[14,367]) ).

thf(373,plain,
    ( ( sk2 @ sk6 )
    | ( sk2 @ sk5 ) ),
    inference(simp,[status(thm)],[372]) ).

thf(380,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ A )
      | ( ( sk1 @ sk5 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[367,326]) ).

thf(381,plain,
    ~ ( sk2 @ sk5 ),
    inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( sk5 ))]]) ).

thf(385,plain,
    ( ( sk2 @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[373,381]) ).

thf(386,plain,
    sk2 @ sk6,
    inference(simp,[status(thm)],[385]) ).

thf(389,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ( ( sk2 @ sk6 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[386,326]) ).

thf(390,plain,
    ~ ( sk1 @ sk6 ),
    inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( sk6 ))]]) ).

thf(409,plain,
    ( $false
    | $false ),
    inference(rewrite,[status(thm)],[377,390,381]) ).

thf(410,plain,
    $false,
    inference(simp,[status(thm)],[409]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET611^3 : TPTP v8.2.0. Released v3.6.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n008.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 11:17:09 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.96/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.11  % [INFO] 	 Parsing done (180ms). 
% 1.33/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.96/1.47  % [INFO] 	 eprover registered as external prover. 
% 1.96/1.48  % [INFO] 	 cvc4 registered as external prover. 
% 1.96/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.23/1.63  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.23/1.63  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.23/1.63  % [INFO] 	 Type checking passed. 
% 2.23/1.63  % [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 ... 
% 8.13/3.05  % [INFO] 	 Killing All external provers ... 
% 8.13/3.06  % Time passed: 2591ms (effective reasoning time: 1928ms)
% 8.13/3.06  % 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)>
% 8.13/3.06  % Axioms used in derivation (0): 
% 8.13/3.06  % No. of inferences in proof: 41
% 8.13/3.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2591 ms resp. 1928 ms w/o parsing
% 8.13/3.10  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.13/3.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------