TSTP Solution File: SEV486^1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n026.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 16:00:22 EDT 2024

% Result   : Theorem 3.12s 1.71s
% Output   : Refutation 3.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   18 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :   74 (  11 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  190 (  10   ~;   3   |;   5   &; 172   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-4 aty)
%            Number of variables   :   55 (  12   ^  31   !;  12   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
    '\'type/nums/num\'': $tType ).

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

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

thf('\'const/arith/<\'_type',type,
    '\'const/arith/<\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).

thf(sk1_type,type,
    sk1: '\'type/nums/num\'' ).

thf(3,axiom,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
      @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).

thf(7,plain,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,plain,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
      @ A ),
    inference(cnf,[status(esa)],[7]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
      ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      = ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).

thf(9,plain,
    ! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
      ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      = ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,plain,
    ! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
      ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      = ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(11,plain,
    ! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) )
      = ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(13,plain,
    ! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) )
      | ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B ) ),
    inference(bool_ext,[status(thm)],[11]) ).

thf(18,plain,
    ! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
      ( ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      | ( '\'const/sets/FINITE\'' @ TA @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(1,conjecture,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).

thf(2,negated_conjecture,
    ~ ! [A: '\'type/nums/num\''] :
        ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: '\'type/nums/num\''] :
        ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [A: '\'type/nums/num\''] :
          ? [B: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ A @ ( '\'const/arith/<\'' @ B @ sk1 ) @ B ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(20,plain,
    ! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
      ( ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      | ( ( '\'const/sets/FINITE\'' @ TA @ A )
       != ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
          @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
            @ ^ [C: '\'type/nums/num\''] :
              ? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18,6]) ).

thf(21,plain,
    ! [A: '\'type/nums/num\''] :
      ~ ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ sk1 ) @ C ) )
        @ A ),
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( '\'const/sets/GSPEC\'' @ '\'type/nums/num\'' @ ^ [C: '\'type/nums/num\''] : ? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) )),bind(B,$thf( B )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).

thf(26,plain,
    ! [A: '\'type/nums/num\''] :
      ~ ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ sk1 ) @ C ) )
        @ A ),
    inference(simp,[status(thm)],[21]) ).

thf(28,plain,
    ! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
      ( ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [C: '\'type/nums/num\''] :
            ? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ A ) @ D ) )
        @ A )
     != ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [C: '\'type/nums/num\''] :
            ? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) )
        @ B ) ),
    inference(paramod_ordered,[status(thm)],[8,26]) ).

thf(29,plain,
    $false,
    inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.11  % Command  : run_Leo-III %s %d SAT
% 0.12/0.32  % Computer : n026.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Fri Jun 21 18:49:55 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.97  % [INFO] 	 Parsing done (109ms). 
% 1.21/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.59/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.83/1.26  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.83/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.27  % [INFO] 	 Type checking passed. 
% 1.83/1.28  % [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 ... 
% 3.12/1.70  % [INFO] 	 Killing All external provers ... 
% 3.12/1.70  % Time passed: 1185ms (effective reasoning time: 721ms)
% 3.12/1.70  % 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)>
% 3.12/1.71  % Axioms used in derivation (2): thm/sets/HAS_SIZE_NUMSEG_LT_, thm/sets/HAS_SIZE_
% 3.12/1.71  % No. of inferences in proof: 18
% 3.12/1.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1185 ms resp. 721 ms w/o parsing
% 3.12/1.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------