TSTP Solution File: SET974+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n004.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 03:24:59 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  133 (  50 unt;   0 def)
%            Number of atoms       :  242 (  51 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  221 ( 112   ~;  77   |;  23   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-5 aty)
%            Number of variables   :  389 ( 369   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f176,plain,
    $false,
    inference(global_subsumption,[],[f45,f46,f33,f31,f34,f32,f40,f41,f35,f36,f39,f60,f58,f59,f37,f65,f66,f68,f69,f70,f38,f76,f74,f77,f64,f82,f83,f85,f86,f87,f88,f67,f89,f90,f91,f92,f93,f94,f95,f43,f96,f98,f99,f100,f101,f73,f104,f75,f107,f78,f114,f115,f79,f84,f123,f124,f125,f126,f127,f128,f129,f44,f130,f132,f133,f134,f135,f103,f97,f141,f142,f143,f145,f146,f144,f147,f139,f149,f140,f42,f154,f155,f156,f157,f158,f159,f160,f161,f151,f131,f163,f164,f165,f166,f168,f169,f167,f170,f162,f172,f148,f171]) ).

fof(f171,plain,
    ~ disjoint(sK2,sK3),
    inference(resolution,[],[f162,f32]) ).

fof(f148,plain,
    ~ disjoint(sK0,sK1),
    inference(resolution,[],[f139,f32]) ).

fof(f172,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0)) ),
    inference(resolution,[],[f162,f41]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( disjoint(cartesian_product2(X2,X0),cartesian_product2(X3,X1))
      | ~ disjoint(X0,X1) ),
    inference(resolution,[],[f131,f38]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X0)
      | disjoint(cartesian_product2(X1,X0),cartesian_product2(X1,X0)) ),
    inference(resolution,[],[f167,f74]) ).

fof(f167,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,cartesian_product2(X0,X1))
      | ~ disjoint(X1,X1) ),
    inference(superposition,[],[f131,f34]) ).

fof(f169,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ~ disjoint(X1,X3) ),
    inference(superposition,[],[f131,f36]) ).

fof(f168,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ~ disjoint(X1,X3) ),
    inference(superposition,[],[f131,f36]) ).

fof(f166,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(cartesian_product2(X3,cartesian_product2(X4,X0)),cartesian_product2(X5,cartesian_product2(X6,X1)))) ),
    inference(resolution,[],[f131,f44]) ).

fof(f165,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(cartesian_product2(cartesian_product2(X3,X0),X4),cartesian_product2(cartesian_product2(X5,X1),X6))) ),
    inference(resolution,[],[f131,f43]) ).

fof(f164,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X3,X1)),set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X3,X1))) ),
    inference(resolution,[],[f131,f74]) ).

fof(f163,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0)) ),
    inference(resolution,[],[f131,f75]) ).

fof(f131,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X2,X4) ),
    inference(resolution,[],[f44,f39]) ).

fof(f151,plain,
    ~ disjoint(sK1,sK0),
    inference(resolution,[],[f140,f32]) ).

fof(f161,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ordered_pair(sK5(X4,X0,X1,X2,X3),sK6(X4,X0,X1,X2,X3)) = X4 ),
    inference(superposition,[],[f42,f36]) ).

fof(f160,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ordered_pair(sK5(X4,X0,X1,X2,X3),sK6(X4,X0,X1,X2,X3)) = X4 ),
    inference(superposition,[],[f42,f36]) ).

fof(f159,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,cartesian_product2(X0,X1))
      | ordered_pair(sK5(X2,X0,X1,X0,X1),sK6(X2,X0,X1,X0,X1)) = X2 ),
    inference(superposition,[],[f42,f34]) ).

fof(f158,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( sK6(X0,X1,cartesian_product2(X2,X3),X4,cartesian_product2(X5,X6)) = ordered_pair(sK5(sK6(X0,X1,cartesian_product2(X2,X3),X4,cartesian_product2(X5,X6)),X2,X3,X5,X6),sK6(sK6(X0,X1,cartesian_product2(X2,X3),X4,cartesian_product2(X5,X6)),X2,X3,X5,X6))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,cartesian_product2(X5,X6)))) ),
    inference(resolution,[],[f42,f44]) ).

fof(f157,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( sK5(X0,cartesian_product2(X1,X2),X3,cartesian_product2(X4,X5),X6) = ordered_pair(sK5(sK5(X0,cartesian_product2(X1,X2),X3,cartesian_product2(X4,X5),X6),X1,X2,X4,X5),sK6(sK5(X0,cartesian_product2(X1,X2),X3,cartesian_product2(X4,X5),X6),X1,X2,X4,X5))
      | ~ in(X0,set_intersection2(cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(cartesian_product2(X4,X5),X6))) ),
    inference(resolution,[],[f42,f43]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1] :
      ( sK4(set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3))) = ordered_pair(sK5(sK4(set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),X0,X1,X2,X3),sK6(sK4(set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),X0,X1,X2,X3))
      | disjoint(set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3))) ),
    inference(resolution,[],[f42,f74]) ).

fof(f155,plain,
    ! [X2,X3,X0,X1] :
      ( sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sK5(sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),X2,X3,X0,X1),sK6(sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),X2,X3,X0,X1))
      | disjoint(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(resolution,[],[f42,f75]) ).

fof(f154,plain,
    ! [X2,X3,X0,X1] :
      ( sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sK5(sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),X0,X1,X2,X3),sK6(sK4(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),X0,X1,X2,X3))
      | disjoint(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(resolution,[],[f42,f38]) ).

fof(f42,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ordered_pair(sK5(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) = X0 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( in(sK6(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK5(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f20,f25]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
     => ( in(sK6(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK5(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1,X2,X3,X4] :
      ~ ( ! [X5,X6] :
            ~ ( in(X6,set_intersection2(X2,X4))
              & in(X5,set_intersection2(X1,X3))
              & ordered_pair(X5,X6) = X0 )
        & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(f140,plain,
    ! [X2,X3,X0,X1] :
      ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3))
      | ~ disjoint(X0,X1) ),
    inference(resolution,[],[f97,f75]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3)) ),
    inference(resolution,[],[f139,f41]) ).

fof(f139,plain,
    ! [X2,X3,X0,X1] :
      ( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      | ~ disjoint(X0,X1) ),
    inference(resolution,[],[f97,f38]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X0)
      | disjoint(cartesian_product2(X0,X1),cartesian_product2(X0,X1)) ),
    inference(resolution,[],[f144,f74]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,cartesian_product2(X0,X1))
      | ~ disjoint(X0,X0) ),
    inference(superposition,[],[f97,f34]) ).

fof(f146,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ~ disjoint(X0,X2) ),
    inference(superposition,[],[f97,f36]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X0,X1)))
      | ~ disjoint(X0,X2) ),
    inference(superposition,[],[f97,f36]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(cartesian_product2(X3,cartesian_product2(X0,X4)),cartesian_product2(X5,cartesian_product2(X1,X6)))) ),
    inference(resolution,[],[f97,f44]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(cartesian_product2(cartesian_product2(X0,X3),X4),cartesian_product2(cartesian_product2(X1,X5),X6))) ),
    inference(resolution,[],[f97,f43]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3))) ),
    inference(resolution,[],[f97,f74]) ).

fof(f97,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X1,X3) ),
    inference(resolution,[],[f43,f39]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ in(set_intersection2(X1,X0),sK4(X0,X1))
      | disjoint(X0,X1) ),
    inference(superposition,[],[f73,f36]) ).

fof(f135,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK6(X2,X3,X0,X4,X1),set_intersection2(X1,X0))
      | ~ in(X2,set_intersection2(cartesian_product2(X3,X0),cartesian_product2(X4,X1))) ),
    inference(superposition,[],[f44,f36]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK6(X2,X3,X0,X4,X1),set_intersection2(X1,X0))
      | ~ in(X2,set_intersection2(cartesian_product2(X3,X0),cartesian_product2(X4,X1))) ),
    inference(superposition,[],[f44,f36]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( in(sK6(X1,X2,X0,X3,X0),X0)
      | ~ in(X1,set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X3,X0))) ),
    inference(superposition,[],[f44,f34]) ).

fof(f132,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ in(set_intersection2(X2,X4),sK6(X0,X1,X2,X3,X4)) ),
    inference(resolution,[],[f44,f40]) ).

fof(f130,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X4,X2) ),
    inference(resolution,[],[f44,f59]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK6(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f129,plain,
    ! [X0,X1] : unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
    inference(superposition,[],[f37,f84]) ).

fof(f128,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
    inference(superposition,[],[f64,f84]) ).

fof(f127,plain,
    ! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
    inference(superposition,[],[f67,f84]) ).

fof(f126,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
    inference(superposition,[],[f84,f84]) ).

fof(f125,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
    inference(superposition,[],[f84,f67]) ).

fof(f124,plain,
    ! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X0)),
    inference(superposition,[],[f84,f64]) ).

fof(f123,plain,
    ! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
    inference(superposition,[],[f84,f37]) ).

fof(f84,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
    inference(superposition,[],[f64,f35]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( disjoint(set_intersection2(X0,X1),set_intersection2(X0,X1))
      | ~ disjoint(X0,X1) ),
    inference(resolution,[],[f74,f39]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( disjoint(set_intersection2(X1,X0),set_intersection2(X1,X0))
      | ~ disjoint(X1,X0) ),
    inference(superposition,[],[f78,f36]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( disjoint(set_intersection2(X1,X0),set_intersection2(X1,X0))
      | ~ disjoint(X1,X0) ),
    inference(superposition,[],[f78,f36]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( disjoint(set_intersection2(X0,X1),set_intersection2(X0,X1))
      | ~ disjoint(X1,X0) ),
    inference(resolution,[],[f74,f59]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | ~ in(set_intersection2(X1,X0),sK4(X0,X1)) ),
    inference(resolution,[],[f75,f40]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),set_intersection2(X1,X0))
      | disjoint(X0,X1) ),
    inference(superposition,[],[f38,f36]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ~ in(set_intersection2(X1,X0),sK4(X0,X1))
      | disjoint(X0,X1) ),
    inference(superposition,[],[f73,f36]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ in(set_intersection2(X0,X1),sK4(X0,X1))
      | disjoint(X0,X1) ),
    inference(resolution,[],[f38,f40]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK5(X2,X0,X3,X1,X4),set_intersection2(X1,X0))
      | ~ in(X2,set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X4))) ),
    inference(superposition,[],[f43,f36]) ).

fof(f100,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK5(X2,X0,X3,X1,X4),set_intersection2(X1,X0))
      | ~ in(X2,set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X4))) ),
    inference(superposition,[],[f43,f36]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( in(sK5(X1,X0,X2,X0,X3),X0)
      | ~ in(X1,set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X0,X3))) ),
    inference(superposition,[],[f43,f34]) ).

fof(f98,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ in(set_intersection2(X1,X3),sK5(X0,X1,X2,X3,X4)) ),
    inference(resolution,[],[f43,f40]) ).

fof(f96,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X3,X1) ),
    inference(resolution,[],[f43,f59]) ).

fof(f43,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f95,plain,
    ! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
    inference(superposition,[],[f37,f67]) ).

fof(f94,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
    inference(superposition,[],[f64,f67]) ).

fof(f93,plain,
    ! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
    inference(superposition,[],[f67,f67]) ).

fof(f92,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
    inference(superposition,[],[f67,f64]) ).

fof(f91,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
    inference(superposition,[],[f67,f37]) ).

fof(f90,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
    inference(superposition,[],[f67,f35]) ).

fof(f89,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
    inference(superposition,[],[f67,f35]) ).

fof(f67,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
    inference(superposition,[],[f37,f35]) ).

fof(f88,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
    inference(superposition,[],[f35,f64]) ).

fof(f87,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
    inference(superposition,[],[f35,f64]) ).

fof(f86,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
    inference(superposition,[],[f37,f64]) ).

fof(f85,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
    inference(superposition,[],[f64,f35]) ).

fof(f83,plain,
    ! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
    inference(superposition,[],[f64,f64]) ).

fof(f82,plain,
    ! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
    inference(superposition,[],[f64,f37]) ).

fof(f64,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
    inference(superposition,[],[f37,f35]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ in(X0,sK4(X0,X0))
      | disjoint(X0,X0) ),
    inference(resolution,[],[f74,f40]) ).

fof(f74,plain,
    ! [X0] :
      ( in(sK4(X0,X0),X0)
      | disjoint(X0,X0) ),
    inference(superposition,[],[f38,f34]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),set_intersection2(X1,X0))
      | disjoint(X0,X1) ),
    inference(superposition,[],[f38,f36]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),set_intersection2(X0,X1))
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( in(sK4(X0,X1),set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X3] : in(X3,set_intersection2(X0,X1))
     => in(sK4(X0,X1),set_intersection2(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( ? [X3] : in(X3,set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f70,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
    inference(superposition,[],[f35,f37]) ).

fof(f69,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
    inference(superposition,[],[f35,f37]) ).

fof(f68,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
    inference(superposition,[],[f37,f35]) ).

fof(f66,plain,
    ! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
    inference(superposition,[],[f37,f37]) ).

fof(f65,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
    inference(superposition,[],[f37,f35]) ).

fof(f37,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,set_intersection2(X1,X0))
      | ~ disjoint(X0,X1) ),
    inference(superposition,[],[f39,f36]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X0)
      | ~ in(X1,X0) ),
    inference(superposition,[],[f39,f34]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,set_intersection2(X1,X0))
      | ~ disjoint(X0,X1) ),
    inference(superposition,[],[f39,f36]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,set_intersection2(X0,X1))
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f36,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f35,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f32,plain,
    ~ disjoint(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ~ disjoint(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3))
    & ( disjoint(sK2,sK3)
      | disjoint(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
        & ( disjoint(X2,X3)
          | disjoint(X0,X1) ) )
   => ( ~ disjoint(cartesian_product2(sK0,sK2),cartesian_product2(sK1,sK3))
      & ( disjoint(sK2,sK3)
        | disjoint(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      & ( disjoint(X2,X3)
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( disjoint(X2,X3)
          | disjoint(X0,X1) )
       => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( disjoint(X2,X3)
        | disjoint(X0,X1) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(f34,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f31,plain,
    ( disjoint(sK2,sK3)
    | disjoint(sK0,sK1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f33,plain,
    ! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

fof(f46,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    empty(sK8),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f7,f29]) ).

fof(f29,plain,
    ( ? [X0] : empty(X0)
   => empty(sK8) ),
    introduced(choice_axiom,[]) ).

fof(f7,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f45,plain,
    ~ empty(sK7),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ~ empty(sK7),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f8,f27]) ).

fof(f27,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK7) ),
    introduced(choice_axiom,[]) ).

fof(f8,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 12:30:38 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (24312)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36  % (24315)WARNING: value z3 for option sas not known
% 0.21/0.36  % (24313)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.36  % (24316)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.36  % (24314)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.36  % (24315)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.36  % (24319)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.36  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  % (24317)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37  % (24318)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.37  % (24315)First to succeed.
% 0.21/0.37  % (24315)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24312"
% 0.21/0.37  TRYING [3]
% 0.21/0.38  % (24315)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (24315)------------------------------
% 0.21/0.38  % (24315)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (24315)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (24315)Memory used [KB]: 879
% 0.21/0.38  % (24315)Time elapsed: 0.012 s
% 0.21/0.38  % (24315)Instructions burned: 16 (million)
% 0.21/0.38  % (24312)Success in time 0.028 s
%------------------------------------------------------------------------------