TSTP Solution File: SET925+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 03:07:22 EDT 2024

% Result   : Theorem 6.89s 3.14s
% Output   : Refutation 6.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   71 (  33 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  238 (  28   ~;  21   |;   4   &; 174   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (   0   ^  34   !;   0   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(empty_set_type,type,
    empty_set: $i ).

thf(in_type,type,
    in: $i > $i > $o ).

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

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

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set )
    <=> ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( ( set_difference @ ( singleton @ A ) @ B )
          = empty_set )
      <=> ( in @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set )
         => ( in @ A @ B ) )
        & ( ( in @ A @ B )
         => ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set )
         => ( in @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set ) ) ),
    inference(miniscope,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set )
    | ( in @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(14,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set )
    | ( in @ sk3 @ sk4 ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set )
    <=> ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).

thf(25,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( set_difference @ ( singleton @ A ) @ B )
          = empty_set )
       => ( in @ A @ B ) )
      & ( ( in @ A @ B )
       => ( ( set_difference @ ( singleton @ A ) @ B )
          = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(26,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( set_difference @ ( singleton @ A ) @ B )
          = empty_set )
       => ( in @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( in @ A @ B )
       => ( ( set_difference @ ( singleton @ A ) @ B )
          = empty_set ) ) ),
    inference(miniscope,[status(thm)],[25]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ B )
      | ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set )
      | ~ ( in @ A @ B ) ),
    inference(lifteq,[status(thm)],[27]) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set )
      | ~ ( in @ A @ B ) ),
    inference(simp,[status(thm)],[29]) ).

thf(11,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set )
    | ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != empty_set ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(15,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set )
    | ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != empty_set ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(120,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ B )
      | ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
        = empty_set )
      | ( ( set_difference @ ( singleton @ A ) @ B )
       != ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[30,15]) ).

thf(121,plain,
    ( ~ ( in @ sk3 @ sk4 )
    | ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set ) ),
    inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(149,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = empty_set )
    | ( ( in @ sk3 @ sk4 )
     != ( in @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,121]) ).

thf(150,plain,
    ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
    = empty_set ),
    inference(pattern_uni,[status(thm)],[149:[]]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
       != empty_set )
      | ( in @ A @ B ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
       != empty_set )
      | ( in @ A @ B ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(184,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
       != ( set_difference @ ( singleton @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[150,31]) ).

thf(185,plain,
    in @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(12,plain,
    ( ~ ( in @ sk1 @ sk2 )
    | ( in @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(13,plain,
    ( ~ ( in @ sk1 @ sk2 )
    | ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != empty_set ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != empty_set )
    | ~ ( in @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(118,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ B )
      | ~ ( in @ sk1 @ sk2 )
      | ( ( set_difference @ ( singleton @ A ) @ B )
       != ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[30,16]) ).

thf(119,plain,
    ( ~ ( in @ sk3 @ sk4 )
    | ~ ( in @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(135,plain,
    ( ~ ( in @ sk1 @ sk2 )
    | ( ( in @ sk3 @ sk4 )
     != ( in @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,119]) ).

thf(136,plain,
    ~ ( in @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[135:[]]) ).

thf(191,plain,
    $false,
    inference(rewrite,[status(thm)],[185,136]) ).

thf(192,plain,
    $false,
    inference(simp,[status(thm)],[191]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 13:13:54 EDT 2024
% 0.20/0.35  % CPUTime  : 
% 1.18/1.09  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.49/1.26  % [INFO] 	 Parsing done (170ms). 
% 1.49/1.28  % [INFO] 	 Running in sequential loop mode. 
% 2.15/1.70  % [INFO] 	 nitpick registered as external prover. 
% 2.15/1.71  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.81  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 2.40/1.85  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.40/1.86  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.40/1.86  % [INFO] 	 Type checking passed. 
% 2.40/1.87  % [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 ... 
% 6.70/3.13  % [INFO] 	 Killing All external provers ... 
% 6.89/3.14  % Time passed: 2612ms (effective reasoning time: 1848ms)
% 6.89/3.14  % 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)>
% 6.89/3.14  % Axioms used in derivation (1): l36_zfmisc_1
% 6.89/3.14  % No. of inferences in proof: 31
% 6.89/3.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2612 ms resp. 1848 ms w/o parsing
% 6.89/3.19  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.89/3.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------