TSTP Solution File: SET928+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 03:07:24 EDT 2024

% Result   : Theorem 8.89s 3.54s
% Output   : Refutation 9.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   71 (  13 unt;  11 typ;   0 def)
%            Number of atoms       :  148 (  36 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  494 (  76   ~;  48   |;  19   &; 340   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  78   !;   6   ?;  84   :)

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

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

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

thf(disjoint_type,type,
    disjoint: $i > $i > $o ).

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

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

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i ).

thf(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
        = ( unordered_pair @ A @ B ) )
    <=> ( ~ ( in @ A @ C )
        & ~ ( in @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).

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

thf(11,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
            = ( unordered_pair @ A @ B ) )
         => ( ~ ( in @ A @ C )
            & ~ ( in @ B @ C ) ) )
        & ( ( ~ ( in @ A @ C )
            & ~ ( in @ B @ C ) )
         => ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
            = ( unordered_pair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,plain,
    ~ ( ! [A: $i,B: $i,C: $i] :
          ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
            = ( unordered_pair @ A @ B ) )
         => ( ~ ( in @ A @ C )
            & ~ ( in @ B @ C ) ) )
      & ! [A: $i,B: $i,C: $i] :
          ( ( ~ ( in @ A @ C )
            & ~ ( in @ B @ C ) )
         => ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
            = ( unordered_pair @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[11]) ).

thf(16,plain,
    ( ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
      = ( unordered_pair @ sk2 @ sk3 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[12]) ).

thf(19,plain,
    ( ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
      = ( unordered_pair @ sk2 @ sk3 ) )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[16]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
    <=> ( ( set_difference @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).

thf(38,plain,
    ! [A: $i,B: $i] :
      ( ( ( disjoint @ A @ B )
       => ( ( set_difference @ A @ B )
          = A ) )
      & ( ( ( set_difference @ A @ B )
          = A )
       => ( disjoint @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(39,plain,
    ( ! [A: $i,B: $i] :
        ( ( disjoint @ A @ B )
       => ( ( set_difference @ A @ B )
          = A ) )
    & ! [A: $i,B: $i] :
        ( ( ( set_difference @ A @ B )
          = A )
       => ( disjoint @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[38]) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
       != A )
      | ( disjoint @ A @ B ) ),
    inference(cnf,[status(esa)],[39]) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
       != A )
      | ( disjoint @ A @ B ) ),
    inference(lifteq,[status(thm)],[40]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
       != A )
      | ( disjoint @ A @ B ) ),
    inference(simp,[status(thm)],[42]) ).

thf(81,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ( ( unordered_pair @ sk2 @ sk3 )
       != A )
      | ( disjoint @ A @ B )
      | ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
       != ( set_difference @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,43]) ).

thf(82,plain,
    ( ~ sk1
    | ( ( unordered_pair @ sk2 @ sk3 )
     != ( unordered_pair @ sk2 @ sk3 ) )
    | ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( unordered_pair @ sk2 @ sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(83,plain,
    ( ~ sk1
    | ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
    inference(simp,[status(thm)],[82]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( in @ A @ B )
        & ~ ( in @ C @ B )
        & ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).

thf(35,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( in @ A @ B )
        & ~ ( in @ C @ B )
        & ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(36,plain,
    ~ ? [A: $i,B: $i] :
        ( ~ ( in @ A @ B )
        & ? [C: $i] :
            ( ~ ( in @ C @ B )
            & ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ) ),
    inference(miniscope,[status(thm)],[35]) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( in @ C @ B )
      | ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[36]) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ~ ( disjoint @ A @ B )
      | ( ( set_difference @ A @ B )
        = A ) ),
    inference(cnf,[status(esa)],[39]) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
        = A )
      | ~ ( disjoint @ A @ B ) ),
    inference(lifteq,[status(thm)],[41]) ).

thf(13,plain,
    ( sk1
    | ( ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
     != ( unordered_pair @ sk5 @ sk6 ) ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(18,plain,
    ( ( ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
     != ( unordered_pair @ sk5 @ sk6 ) )
    | sk1 ),
    inference(lifteq,[status(thm)],[13]) ).

thf(146,plain,
    ! [B: $i,A: $i] :
      ( ~ ( disjoint @ A @ B )
      | ( A
       != ( unordered_pair @ sk5 @ sk6 ) )
      | sk1
      | ( ( set_difference @ A @ B )
       != ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[44,18]) ).

thf(147,plain,
    ( ~ ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
    | ( ( unordered_pair @ sk5 @ sk6 )
     != ( unordered_pair @ sk5 @ sk6 ) )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( unordered_pair @ sk5 @ sk6 )),bind(B,$thf( sk7 ))]]) ).

thf(162,plain,
    ( ~ ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
    | sk1 ),
    inference(simp,[status(thm)],[147]) ).

thf(188,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ A @ B )
      | ( in @ C @ B )
      | sk1
      | ( ( disjoint @ ( unordered_pair @ A @ C ) @ B )
       != ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[37,162]) ).

thf(189,plain,
    ( ( in @ sk5 @ sk7 )
    | ( in @ sk6 @ sk7 )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 )),bind(C,$thf( sk6 ))]]) ).

thf(14,plain,
    ( sk1
    | ~ ( in @ sk6 @ sk7 ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(192,plain,
    ( ( in @ sk5 @ sk7 )
    | sk1
    | ( ( in @ sk6 @ sk7 )
     != ( in @ sk6 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[189,14]) ).

thf(193,plain,
    ( ( in @ sk5 @ sk7 )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[192:[]]) ).

thf(17,plain,
    ( sk1
    | ~ ( in @ sk5 @ sk7 ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(224,plain,
    ( sk1
    | ( ( in @ sk5 @ sk7 )
     != ( in @ sk5 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[193,17]) ).

thf(225,plain,
    sk1,
    inference(pattern_uni,[status(thm)],[224:[]]) ).

thf(236,plain,
    ( ~ $true
    | ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
    inference(rewrite,[status(thm)],[83,225]) ).

thf(237,plain,
    disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4,
    inference(simp,[status(thm)],[236]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(15,plain,
    ( ( in @ sk2 @ sk4 )
    | ( in @ sk3 @ sk4 )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[12]) ).

thf(240,plain,
    ( ( in @ sk2 @ sk4 )
    | ( in @ sk3 @ sk4 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[15,225]) ).

thf(241,plain,
    ( ( in @ sk2 @ sk4 )
    | ( in @ sk3 @ sk4 ) ),
    inference(simp,[status(thm)],[240]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
        & ( in @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).

thf(32,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
        & ( in @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(33,plain,
    ~ ? [A: $i,B: $i,C: $i] :
        ( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
        & ( in @ A @ C ) ),
    inference(miniscope,[status(thm)],[32]) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ C )
      | ~ ( in @ A @ C ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ sk1
      | ~ ( in @ A @ C )
      | ( ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
       != ( disjoint @ ( unordered_pair @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[83,34]) ).

thf(171,plain,
    ( ~ sk1
    | ~ ( in @ sk2 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(238,plain,
    ( ~ $true
    | ~ ( in @ sk2 @ sk4 ) ),
    inference(rewrite,[status(thm)],[171,225]) ).

thf(239,plain,
    ~ ( in @ sk2 @ sk4 ),
    inference(simp,[status(thm)],[238]) ).

thf(287,plain,
    ( $false
    | ( in @ sk3 @ sk4 ) ),
    inference(rewrite,[status(thm)],[241,239]) ).

thf(288,plain,
    in @ sk3 @ sk4,
    inference(simp,[status(thm)],[287]) ).

thf(293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ C )
      | ( ( in @ sk3 @ sk4 )
       != ( in @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[288,34]) ).

thf(294,plain,
    ! [A: $i] :
      ~ ( disjoint @ ( unordered_pair @ sk3 @ A ) @ sk4 ),
    inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).

thf(301,plain,
    ! [A: $i] :
      ~ ( disjoint @ ( unordered_pair @ sk3 @ A ) @ sk4 ),
    inference(simp,[status(thm)],[294]) ).

thf(328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ sk4 )
      | ( ( unordered_pair @ B @ A )
       != ( unordered_pair @ sk3 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,301]) ).

thf(329,plain,
    ! [A: $i] :
      ~ ( disjoint @ ( unordered_pair @ A @ sk3 ) @ sk4 ),
    inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).

thf(369,plain,
    $false,
    inference(rewrite,[status(thm)],[237,329]) ).

thf(370,plain,
    $false,
    inference(simp,[status(thm)],[369]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May 20 12:40:54 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.09/1.05  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.44/1.23  % [INFO] 	 Parsing done (179ms). 
% 1.49/1.24  % [INFO] 	 Running in sequential loop mode. 
% 2.06/1.65  % [INFO] 	 nitpick registered as external prover. 
% 2.06/1.66  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.77  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.40/1.82  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.40/1.84  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.40/1.85  % [INFO] 	 Type checking passed. 
% 2.40/1.85  % [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 ... 
% 8.89/3.52  % [INFO] 	 Killing All external provers ... 
% 8.89/3.54  % Time passed: 3037ms (effective reasoning time: 2286ms)
% 8.89/3.54  % 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)>
% 8.89/3.54  % Axioms used in derivation (4): t83_xboole_1, t57_zfmisc_1, commutativity_k2_tarski, t55_zfmisc_1
% 8.89/3.54  % No. of inferences in proof: 60
% 8.89/3.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3037 ms resp. 2286 ms w/o parsing
% 9.04/3.62  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------