TSTP Solution File: SEV481^1 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV481^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n028.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 16:00:21 EDT 2024

% Result   : Theorem 4.03s 2.45s
% Output   : Refutation 4.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   13 (   1 unt;   0 typ;   0 def)
%            Number of atoms       :   94 (   1 equ;   0 cnn)
%            Maximal formula atoms :   10 (   7 avg)
%            Number of connectives :  295 (  12   ~;   6   |;  14   &; 256   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  12 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   4 con; 0-4 aty)
%            Number of variables   :   65 (   9   ^  38   !;  18   ?;  65   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'const/sets/SETSPEC\'_type',type,
    '\'const/sets/SETSPEC\'': 
      !>[TA: $tType] : ( TA > $o > TA > $o ) ).

thf('\'const/sets/IN\'_type',type,
    '\'const/sets/IN\'': 
      !>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).

thf('\'const/sets/GSPEC\'_type',type,
    '\'const/sets/GSPEC\'': 
      !>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).

thf('\'const/sets/FINITE\'_type',type,
    '\'const/sets/FINITE\'': 
      !>[TA: $tType] : ( ( TA > $o ) > $o ) ).

thf('\'const/pair/,\'_type',type,
    '\'const/pair/,\'': 
      !>[TA: $tType,TB: $tType] : ( TB > TA > ( '\'type/pair/prod\'' @ TB @ TA ) ) ).

thf(skt1_type,type,
    skt1: $tType ).

thf(skt2_type,type,
    skt2: $tType ).

thf(sk1_type,type,
    sk1: skt1 > $o ).

thf(sk2_type,type,
    sk2: skt2 > $o ).

thf(3,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TB @ B )
        & ! [D: TB] :
            ( ( '\'const/sets/IN\'' @ TB @ D @ B )
           => ( '\'const/sets/FINITE\'' @ TA @ ( C @ D ) ) ) )
     => ( '\'const/sets/FINITE\'' @ TC
        @ ( '\'const/sets/GSPEC\'' @ TC
          @ ^ [D: TC] :
            ? [E: TB,F: TA] :
              ( '\'const/sets/SETSPEC\'' @ TC @ D
              @ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
                & ( '\'const/sets/IN\'' @ TA @ F @ ( C @ E ) ) )
              @ ( A @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_DEPENDENT_') ).

thf(8,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TB @ B )
        & ! [D: TB] :
            ( ( '\'const/sets/IN\'' @ TB @ D @ B )
           => ( '\'const/sets/FINITE\'' @ TA @ ( C @ D ) ) ) )
     => ( '\'const/sets/FINITE\'' @ TC
        @ ( '\'const/sets/GSPEC\'' @ TC
          @ ^ [D: TC] :
            ? [E: TB,F: TA] :
              ( '\'const/sets/SETSPEC\'' @ TC @ D
              @ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
                & ( '\'const/sets/IN\'' @ TA @ F @ ( C @ E ) ) )
              @ ( A @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
      ( ~ ( '\'const/sets/FINITE\'' @ TB @ B )
      | ~ ( '\'const/sets/FINITE\'' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
      | ( '\'const/sets/FINITE\'' @ TA
        @ ( '\'const/sets/GSPEC\'' @ TA
          @ ^ [D: TA] :
            ? [E: TB,F: TC] :
              ( '\'const/sets/SETSPEC\'' @ TA @ D
              @ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
                & ( '\'const/sets/IN\'' @ TC @ F @ ( C @ E ) ) )
              @ ( A @ E @ F ) ) ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(1,conjecture,
    ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
        & ( '\'const/sets/FINITE\'' @ TA @ B ) )
     => ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
        @ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
          @ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
            ? [D: TB,E: TA] :
              ( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
              @ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
                & ( '\'const/sets/IN\'' @ TA @ E @ B ) )
              @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
        ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
          & ( '\'const/sets/FINITE\'' @ TA @ B ) )
       => ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
          @ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
            @ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
              ? [D: TB,E: TA] :
                ( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
                @ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
                  & ( '\'const/sets/IN\'' @ TA @ E @ B ) )
                @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
        ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
          & ( '\'const/sets/FINITE\'' @ TA @ B ) )
       => ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
          @ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
            @ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
              ? [D: TB,E: TA] :
                ( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
                @ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
                  & ( '\'const/sets/IN\'' @ TA @ E @ B ) )
                @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ~ ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
      @ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
        @ ^ [A: '\'type/pair/prod\'' @ skt1 @ skt2] :
          ? [B: skt1,C: skt2] :
            ( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ A
            @ ( ( '\'const/sets/IN\'' @ skt1 @ B @ sk1 )
              & ( '\'const/sets/IN\'' @ skt2 @ C @ sk2 ) )
            @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(13,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
      ( ~ ( '\'const/sets/FINITE\'' @ TB @ B )
      | ~ ( '\'const/sets/FINITE\'' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
      | ( ( '\'const/sets/FINITE\'' @ TA
          @ ( '\'const/sets/GSPEC\'' @ TA
            @ ^ [D: TA] :
              ? [E: TB,F: TC] :
                ( '\'const/sets/SETSPEC\'' @ TA @ D
                @ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
                  & ( '\'const/sets/IN\'' @ TC @ F @ ( C @ E ) ) )
                @ ( A @ E @ F ) ) ) )
       != ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
          @ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
            @ ^ [D: '\'type/pair/prod\'' @ skt1 @ skt2] :
              ? [E: skt1,F: skt2] :
                ( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ D
                @ ( ( '\'const/sets/IN\'' @ skt1 @ E @ sk1 )
                  & ( '\'const/sets/IN\'' @ skt2 @ F @ sk2 ) )
                @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ E @ F ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,5]) ).

thf(14,plain,
    ( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
    | ~ ( '\'const/sets/FINITE\'' @ skt2 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( '\'const/pair/,\'' @ skt1 @ skt2 )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [D: skt1] : sk2 )),bind_type(TA,$thf( '\'type/pair/prod\'' @ skt1 @ skt2 )),bind_type(TB,$thf( skt1 )),bind_type(TC,$thf( skt2 ))]]) ).

thf(6,plain,
    '\'const/sets/FINITE\'' @ skt2 @ sk2,
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    '\'const/sets/FINITE\'' @ skt1 @ sk1,
    inference(cnf,[status(esa)],[4]) ).

thf(32,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[14,6,7]) ).

thf(33,plain,
    $false,
    inference(simp,[status(thm)],[32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEV481^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.09  % Command  : run_Leo-III %s %d SAT
% 0.09/0.29  % Computer : n028.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Fri Jun 21 19:09:55 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.93/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.11  % [INFO] 	 Parsing done (178ms). 
% 1.22/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.47  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.12/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 2.12/1.63  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 2.12/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.12/1.65  % [INFO] 	 Type checking passed. 
% 2.12/1.65  % [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 ... 
% 4.03/2.44  % [INFO] 	 Killing All external provers ... 
% 4.03/2.45  % Time passed: 1987ms (effective reasoning time: 1318ms)
% 4.03/2.45  % 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)>
% 4.03/2.45  % Axioms used in derivation (1): thm/sets/FINITE_PRODUCT_DEPENDENT_
% 4.03/2.45  % No. of inferences in proof: 13
% 4.03/2.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1987 ms resp. 1318 ms w/o parsing
% 4.42/2.52  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.42/2.52  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------