TSTP Solution File: SEV464^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV464^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 04:10:36 EDT 2024

% Result   : Theorem 10.97s 3.83s
% Output   : Refutation 10.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :   63 (  24 equ;   0 cnn)
%            Maximal formula atoms :    1 (   4 avg)
%            Number of connectives :  173 (   5   ~;   0   |;   2   &; 166   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-6 aty)
%            Number of variables   :   64 (   0   ^  56   !;   2   ?;  64   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

thf(skt3_type,type,
    skt3: $tType ).

thf(sk1_type,type,
    sk1: skt2 > skt1 ).

thf(sk2_type,type,
    sk2: skt3 > skt2 ).

thf(sk3_type,type,
    sk3: skt3 > $o ).

thf(sk4_type,type,
    sk4: skt1 ).

thf(1,conjecture,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
      ( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
      = ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IMAGE_o_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
        ( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
        = ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
        ( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
        = ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
      ( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
      = ( ? [D: TA] :
            ( ( A
              = ( C @ D ) )
            & ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_') ).

thf(9,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
      ( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
      = ( ? [D: TA] :
            ( ( A
              = ( C @ D ) )
            & ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).

thf(15,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,plain,
    ! [TA: $tType,B: TA > $o,A: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(17,plain,
    ! [TA: $tType,B: TA > $o,A: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(4,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA] :
      ( ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B @ C )
      = ( A @ ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/trivia/o_THM_') ).

thf(12,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA] :
      ( ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B @ C )
      = ( A @ ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,plain,
    ( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 )
   != ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 )
   != ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(18,plain,
    ( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 @ sk4 )
   != ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) @ sk4 ) ),
    inference(func_ext,[status(esa)],[8]) ).

thf(122,plain,
    $false,
    inference(cvc4,[status(thm)],[6,9,17,12,18,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEV464^1 : TPTP v8.2.0. Released v7.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.33  % Computer : n003.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 18:35:09 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.11  % [INFO] 	 Parsing done (162ms). 
% 1.27/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.48  % [INFO] 	 eprover registered as external prover. 
% 1.86/1.49  % [INFO] 	 cvc4 registered as external prover. 
% 1.86/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.03/1.62  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.24/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.24/1.65  % [INFO] 	 Type checking passed. 
% 2.24/1.65  % [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 ... 
% 10.97/3.82  % External prover 'cvc4' found a proof!
% 10.97/3.82  % [INFO] 	 Killing All external provers ... 
% 10.97/3.82  % Time passed: 3345ms (effective reasoning time: 2692ms)
% 10.97/3.82  % 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)>
% 10.97/3.83  % Axioms used in derivation (3): thm/sets/IN_IMAGE_, thm/sets/EXTENSION_, thm/trivia/o_THM_
% 10.97/3.83  % No. of inferences in proof: 15
% 10.97/3.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3345 ms resp. 2692 ms w/o parsing
% 10.97/3.86  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.97/3.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------