TSTP Solution File: SET624^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET624^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 03:06:33 EDT 2024

% Result   : Theorem 7.01s 2.55s
% Output   : Refutation 7.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   77 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  240 (  22 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  449 (  77   ~; 126   |;  21   &; 225   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  33   !;  21   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

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

thf(sk3_type,type,
    sk3: a > $o ).

thf(sk4_type,type,
    sk4: a ).

thf(sk5_type,type,
    sk5: a ).

thf(sk6_type,type,
    sk6: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ( ? [D: a] :
            ( ( A @ D )
            & ( ( B @ D )
              | ( C @ D ) ) ) )
      = ( ? [D: a] :
            ( ( A @ D )
            & ( B @ D ) )
        | ? [D: a] :
            ( ( A @ D )
            & ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_100_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ? [D: a] :
              ( ( A @ D )
              & ( ( B @ D )
                | ( C @ D ) ) ) )
        = ( ? [D: a] :
              ( ( A @ D )
              & ( B @ D ) )
          | ? [D: a] :
              ( ( A @ D )
              & ( C @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( ? [A: a] :
          ( ( sk1 @ A )
          & ( ( sk2 @ A )
            | ( sk3 @ A ) ) ) )
   != ( ? [A: a] :
          ( ( sk1 @ A )
          & ( sk2 @ A ) )
      | ? [A: a] :
          ( ( sk1 @ A )
          & ( sk3 @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [A: a] :
          ( ( sk1 @ A )
          & ( ( sk2 @ A )
            | ( sk3 @ A ) ) ) )
   != ( ? [A: a] :
          ( ( sk1 @ A )
          & ( sk2 @ A ) )
      | ? [A: a] :
          ( ( sk1 @ A )
          & ( sk3 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ? [A: a] :
        ( ( sk1 @ A )
        & ( ( sk2 @ A )
          | ( sk3 @ A ) ) )
    | ? [A: a] :
        ( ( sk1 @ A )
        & ( sk2 @ A ) )
    | ? [A: a] :
        ( ( sk1 @ A )
        & ( sk3 @ A ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(20,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(16,plain,
    ( ( sk2 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(15,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(17,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(6,plain,
    ( ~ ? [A: a] :
          ( ( sk1 @ A )
          & ( ( sk2 @ A )
            | ( sk3 @ A ) ) )
    | ~ ( ? [A: a] :
            ( ( sk1 @ A )
            & ( sk2 @ A ) )
        | ? [A: a] :
            ( ( sk1 @ A )
            & ( sk3 @ A ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ B )
      | ~ ( sk3 @ B )
      | ~ ( sk1 @ A )
      | ~ ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(12,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ B )
      | ~ ( sk3 @ B )
      | ~ ( sk1 @ A )
      | ~ ( sk3 @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(100,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ B )
      | ~ ( sk3 @ B )
      | ~ ( sk1 @ A )
      | ( ( sk3 @ A )
       != ( sk3 @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[12]) ).

thf(101,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ~ ( sk3 @ A )
      | ~ ( sk1 @ A ) ),
    inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(104,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ~ ( sk3 @ A ) ),
    inference(simp,[status(thm)],[101]) ).

thf(118,plain,
    ! [A: a] :
      ( ( sk1 @ sk5 )
      | ( sk1 @ sk4 )
      | ~ ( sk3 @ A )
      | ( ( sk1 @ sk6 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[17,104]) ).

thf(119,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk4 )
    | ~ ( sk3 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk6 ))]]) ).

thf(181,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk4 )
    | ( ( sk3 @ sk6 )
     != ( sk3 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[15,119]) ).

thf(182,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[181:[]]) ).

thf(19,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(11,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ B )
      | ~ ( sk2 @ B )
      | ~ ( sk1 @ A )
      | ~ ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(43,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ B )
      | ~ ( sk2 @ B )
      | ~ ( sk1 @ A )
      | ( ( sk2 @ A )
       != ( sk2 @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[11]) ).

thf(44,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A )
      | ~ ( sk1 @ A ) ),
    inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(46,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ A ) ),
    inference(simp,[status(thm)],[44]) ).

thf(114,plain,
    ! [A: a] :
      ( ( sk1 @ sk6 )
      | ( sk1 @ sk4 )
      | ~ ( sk1 @ A )
      | ( ( sk2 @ sk5 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[19,46]) ).

thf(115,plain,
    ( ( sk1 @ sk6 )
    | ( sk1 @ sk4 )
    | ~ ( sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( sk5 ))]]) ).

thf(201,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk6 )
    | ( ( sk1 @ sk5 )
     != ( sk1 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[182,115]) ).

thf(202,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[201:[]]) ).

thf(226,plain,
    ! [A: a] :
      ( ( sk1 @ sk4 )
      | ~ ( sk3 @ A )
      | ( ( sk1 @ sk6 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[202,104]) ).

thf(227,plain,
    ( ( sk1 @ sk4 )
    | ~ ( sk3 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( sk6 ))]]) ).

thf(244,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk4 )
    | ( ( sk3 @ sk6 )
     != ( sk3 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[16,227]) ).

thf(245,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[244:[]]) ).

thf(197,plain,
    ! [A: a] :
      ( ( sk1 @ sk4 )
      | ~ ( sk2 @ A )
      | ( ( sk1 @ sk5 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[182,46]) ).

thf(198,plain,
    ( ( sk1 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( sk5 ))]]) ).

thf(260,plain,
    ( ( sk1 @ sk4 )
    | ( ( sk2 @ sk5 )
     != ( sk2 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[245,198]) ).

thf(261,plain,
    sk1 @ sk4,
    inference(pattern_uni,[status(thm)],[260:[]]) ).

thf(268,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[261,104]) ).

thf(269,plain,
    ~ ( sk3 @ sk4 ),
    inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( sk4 ))]]) ).

thf(276,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[20,269]) ).

thf(277,plain,
    ( ( sk1 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 ) ),
    inference(simp,[status(thm)],[276]) ).

thf(18,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk2 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(274,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk2 @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[18,269]) ).

thf(275,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk2 @ sk4 ) ),
    inference(simp,[status(thm)],[274]) ).

thf(270,plain,
    ! [A: a] :
      ( ~ ( sk2 @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[261,46]) ).

thf(271,plain,
    ~ ( sk2 @ sk4 ),
    inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( sk4 ))]]) ).

thf(342,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[275,271]) ).

thf(343,plain,
    ( ( sk1 @ sk5 )
    | ( sk3 @ sk6 ) ),
    inference(simp,[status(thm)],[342]) ).

thf(14,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(272,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[14,269]) ).

thf(273,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 )
    | ( sk2 @ sk4 ) ),
    inference(simp,[status(thm)],[272]) ).

thf(280,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[273,271]) ).

thf(281,plain,
    ( ( sk2 @ sk5 )
    | ( sk1 @ sk6 ) ),
    inference(simp,[status(thm)],[280]) ).

thf(283,plain,
    ! [A: a] :
      ( ( sk1 @ sk6 )
      | ~ ( sk1 @ A )
      | ( ( sk2 @ sk5 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[281,46]) ).

thf(284,plain,
    ( ( sk1 @ sk6 )
    | ~ ( sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( sk5 ))]]) ).

thf(21,plain,
    ( ( sk2 @ sk5 )
    | ( sk3 @ sk6 )
    | ( sk2 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(288,plain,
    ( ( sk2 @ sk5 )
    | ( sk3 @ sk6 )
    | $false
    | $false ),
    inference(rewrite,[status(thm)],[21,269,271]) ).

thf(289,plain,
    ( ( sk2 @ sk5 )
    | ( sk3 @ sk6 ) ),
    inference(simp,[status(thm)],[288]) ).

thf(290,plain,
    ! [A: a] :
      ( ( sk2 @ sk5 )
      | ~ ( sk1 @ A )
      | ( ( sk3 @ sk6 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[289,104]) ).

thf(291,plain,
    ( ( sk2 @ sk5 )
    | ~ ( sk1 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( sk6 ))]]) ).

thf(311,plain,
    ! [A: a] :
      ( ~ ( sk1 @ sk6 )
      | ~ ( sk1 @ A )
      | ( ( sk2 @ sk5 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[291,46]) ).

thf(312,plain,
    ( ~ ( sk1 @ sk6 )
    | ~ ( sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( sk5 ))]]) ).

thf(370,plain,
    ( ~ ( sk1 @ sk5 )
    | ( ( sk1 @ sk6 )
     != ( sk1 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[284,312]) ).

thf(371,plain,
    ~ ( sk1 @ sk5 ),
    inference(pattern_uni,[status(thm)],[370:[]]) ).

thf(381,plain,
    ( $false
    | ( sk3 @ sk6 ) ),
    inference(rewrite,[status(thm)],[343,371]) ).

thf(382,plain,
    sk3 @ sk6,
    inference(simp,[status(thm)],[381]) ).

thf(385,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( ( sk3 @ sk6 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[382,104]) ).

thf(386,plain,
    ~ ( sk1 @ sk6 ),
    inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( sk6 ))]]) ).

thf(402,plain,
    ( $false
    | $false
    | $false ),
    inference(rewrite,[status(thm)],[277,386,371,271]) ).

thf(403,plain,
    $false,
    inference(simp,[status(thm)],[402]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET624^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n024.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May 20 11:30:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 1.00/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.99  % [INFO] 	 Parsing done (106ms). 
% 1.18/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.60/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.91/1.31  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.91/1.31  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.91/1.31  % [INFO] 	 Type checking passed. 
% 1.91/1.31  % [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 ... 
% 7.01/2.54  % [INFO] 	 Killing All external provers ... 
% 7.01/2.54  % Time passed: 2011ms (effective reasoning time: 1541ms)
% 7.01/2.54  % 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)>
% 7.01/2.55  % Axioms used in derivation (0): 
% 7.01/2.55  % No. of inferences in proof: 70
% 7.01/2.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2011 ms resp. 1541 ms w/o parsing
% 7.01/2.61  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.01/2.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------