TSTP Solution File: SET924+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 4.24s 2.05s
% Output   : Refutation 4.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   40 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   75 (  35 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  279 (  37   ~;  23   |;   4   &; 204   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 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(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(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = ( singleton @ A ) )
    <=> ~ ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( set_difference @ ( singleton @ A ) @ B )
          = ( singleton @ A ) )
       => ~ ( in @ A @ B ) )
      & ( ~ ( in @ A @ B )
       => ( ( set_difference @ ( singleton @ A ) @ B )
          = ( singleton @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(24,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( set_difference @ ( singleton @ A ) @ B )
          = ( singleton @ A ) )
       => ~ ( in @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ~ ( in @ A @ B )
       => ( ( set_difference @ ( singleton @ A ) @ B )
          = ( singleton @ A ) ) ) ),
    inference(miniscope,[status(thm)],[23]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( ( set_difference @ ( singleton @ A ) @ B )
        = ( singleton @ A ) ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = ( singleton @ A ) )
      | ( in @ A @ B ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = ( singleton @ A ) )
      | ( in @ A @ B ) ),
    inference(simp,[status(thm)],[27]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = ( singleton @ A ) )
    <=> ~ ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).

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

thf(7,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( ( set_difference @ ( singleton @ A ) @ B )
            = ( singleton @ A ) )
         => ~ ( in @ A @ B ) )
        & ( ~ ( in @ A @ B )
         => ( ( set_difference @ ( singleton @ A ) @ B )
            = ( singleton @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ B )
            = ( singleton @ A ) )
         => ~ ( in @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
         => ( ( set_difference @ ( singleton @ A ) @ B )
            = ( singleton @ A ) ) ) ),
    inference(miniscope,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = ( singleton @ sk1 ) )
    | ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != ( singleton @ sk3 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

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

thf(12,plain,
    ( ( in @ sk1 @ sk2 )
    | ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != ( singleton @ sk3 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
     != ( singleton @ sk3 ) )
    | ( in @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(50,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( ( singleton @ A )
       != ( singleton @ sk3 ) )
      | ( in @ sk1 @ sk2 )
      | ( ( set_difference @ ( singleton @ A ) @ B )
       != ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[28,15]) ).

thf(51,plain,
    ( ( in @ sk3 @ sk4 )
    | ( ( singleton @ sk3 )
     != ( singleton @ sk3 ) )
    | ( in @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(67,plain,
    ( ( in @ sk3 @ sk4 )
    | ( in @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[51]) ).

thf(11,plain,
    ( ( in @ sk1 @ sk2 )
    | ~ ( in @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(143,plain,
    ( ( in @ sk1 @ sk2 )
    | ( ( in @ sk3 @ sk4 )
     != ( in @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[67,11]) ).

thf(144,plain,
    in @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[143:[]]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
       != ( singleton @ A ) )
      | ~ ( in @ A @ B ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
       != ( singleton @ A ) )
      | ~ ( in @ A @ B ) ),
    inference(lifteq,[status(thm)],[26]) ).

thf(169,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
       != ( singleton @ A ) )
      | ( ( in @ sk1 @ sk2 )
       != ( in @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[144,29]) ).

thf(170,plain,
    ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
   != ( singleton @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(181,plain,
    ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
   != ( singleton @ sk3 ) ),
    inference(simplifyReflect,[status(thm)],[14,170]) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( ( singleton @ A )
       != ( singleton @ sk3 ) )
      | ( ( set_difference @ ( singleton @ A ) @ B )
       != ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[28,181]) ).

thf(221,plain,
    ( ( in @ sk3 @ sk4 )
    | ( ( singleton @ sk3 )
     != ( singleton @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(234,plain,
    in @ sk3 @ sk4,
    inference(simp,[status(thm)],[221]) ).

thf(9,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = ( singleton @ sk1 ) )
    | ~ ( in @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(13,plain,
    ( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
      = ( singleton @ sk1 ) )
    | ~ ( in @ sk3 @ sk4 ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(182,plain,
    ~ ( in @ sk3 @ sk4 ),
    inference(simplifyReflect,[status(thm)],[13,170]) ).

thf(235,plain,
    $false,
    inference(rewrite,[status(thm)],[234,182]) ).

thf(236,plain,
    $false,
    inference(simp,[status(thm)],[235]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n006.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 12:29:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.93/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.94  % [INFO] 	 Parsing done (99ms). 
% 1.18/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.54/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.80/1.25  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.80/1.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.80/1.25  % [INFO] 	 Type checking passed. 
% 1.80/1.26  % [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 ... 
% 4.24/2.04  % [INFO] 	 Killing All external provers ... 
% 4.24/2.05  % Time passed: 1544ms (effective reasoning time: 1097ms)
% 4.24/2.05  % 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)>
% 4.24/2.05  % Axioms used in derivation (1): l34_zfmisc_1
% 4.24/2.05  % No. of inferences in proof: 33
% 4.24/2.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1544 ms resp. 1097 ms w/o parsing
% 4.32/2.10  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.32/2.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------