TSTP Solution File: SET944+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET944+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n017.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 : Thu Aug 31 15:46:28 EDT 2023

% Result   : Theorem 8.04s 1.51s
% Output   : Refutation 8.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  119 (  33 unt;   0 def)
%            Number of atoms       :  370 (  20 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  395 ( 144   ~; 169   |;  61   &)
%                                         (  14 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :  250 (; 226   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15403,plain,
    $false,
    inference(subsumption_resolution,[],[f15400,f83]) ).

fof(f83,plain,
    ~ subset(sF15,sF18),
    inference(definition_folding,[],[f44,f82,f81,f80,f79,f78]) ).

fof(f78,plain,
    set_intersection2(sK2,sK3) = sF14,
    introduced(function_definition,[]) ).

fof(f79,plain,
    union(sF14) = sF15,
    introduced(function_definition,[]) ).

fof(f80,plain,
    union(sK2) = sF16,
    introduced(function_definition,[]) ).

fof(f81,plain,
    union(sK3) = sF17,
    introduced(function_definition,[]) ).

fof(f82,plain,
    set_intersection2(sF16,sF17) = sF18,
    introduced(function_definition,[]) ).

fof(f44,plain,
    ~ subset(union(set_intersection2(sK2,sK3)),set_intersection2(union(sK2),union(sK3))),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ subset(union(set_intersection2(sK2,sK3)),set_intersection2(union(sK2),union(sK3))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f14,f21]) ).

fof(f21,plain,
    ( ? [X0,X1] : ~ subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1)))
   => ~ subset(union(set_intersection2(sK2,sK3)),set_intersection2(union(sK2),union(sK3))) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1] : ~ subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',t97_zfmisc_1) ).

fof(f15400,plain,
    subset(sF15,sF18),
    inference(duplicate_literal_removal,[],[f15395]) ).

fof(f15395,plain,
    ( subset(sF15,sF18)
    | subset(sF15,sF18) ),
    inference(resolution,[],[f15362,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',d3_tarski) ).

fof(f15362,plain,
    ! [X41] :
      ( ~ in(sK4(X41,sF18),sF15)
      | subset(X41,sF18) ),
    inference(resolution,[],[f15299,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f15299,plain,
    ! [X6] :
      ( in(X6,sF18)
      | ~ in(X6,sF15) ),
    inference(subsumption_resolution,[],[f15296,f11214]) ).

fof(f11214,plain,
    ! [X0] :
      ( in(X0,sF17)
      | ~ in(X0,sF15) ),
    inference(resolution,[],[f11212,f49]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f11212,plain,
    subset(sF15,sF17),
    inference(duplicate_literal_removal,[],[f11199]) ).

fof(f11199,plain,
    ( subset(sF15,sF17)
    | subset(sF15,sF17) ),
    inference(resolution,[],[f11198,f51]) ).

fof(f11198,plain,
    ! [X0] :
      ( in(sK4(sF15,X0),sF17)
      | subset(sF15,X0) ),
    inference(duplicate_literal_removal,[],[f11131]) ).

fof(f11131,plain,
    ! [X0] :
      ( in(sK4(sF15,X0),sF17)
      | subset(sF15,X0)
      | subset(sF15,X0) ),
    inference(resolution,[],[f8206,f1169]) ).

fof(f1169,plain,
    ! [X4] :
      ( in(sK4(sF15,X4),sK7(sF14,sK4(sF15,X4)))
      | subset(sF15,X4) ),
    inference(resolution,[],[f169,f84]) ).

fof(f84,plain,
    sP0(sF14,sF15),
    inference(superposition,[],[f70,f79]) ).

fof(f70,plain,
    ! [X0] : sP0(X0,union(X0)),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f5,f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',d4_tarski) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X2,X0)
      | in(sK4(X0,X1),sK7(X2,sK4(X0,X1)))
      | subset(X0,X1) ),
    inference(resolution,[],[f52,f50]) ).

fof(f52,plain,
    ! [X0,X1,X5] :
      ( ~ in(X5,X1)
      | in(X5,sK7(X0,X5))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK5(X0,X1),X3) )
            | ~ in(sK5(X0,X1),X1) )
          & ( ( in(sK6(X0,X1),X0)
              & in(sK5(X0,X1),sK6(X0,X1)) )
            | in(sK5(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK7(X0,X5),X0)
                & in(X5,sK7(X0,X5)) )
              | ~ in(X5,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f28,f31,f30,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(X2,X3) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( in(X4,X0)
                & in(X2,X4) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ in(X3,X0)
              | ~ in(sK5(X0,X1),X3) )
          | ~ in(sK5(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK5(X0,X1),X4) )
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK5(X0,X1),X4) )
     => ( in(sK6(X0,X1),X0)
        & in(sK5(X0,X1),sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK7(X0,X5),X0)
        & in(X5,sK7(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( in(X4,X0)
                  & in(X2,X4) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ? [X7] :
                  ( in(X7,X0)
                  & in(X5,X7) )
              | ~ in(X5,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) ) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f8206,plain,
    ! [X66,X67] :
      ( ~ in(X66,sK7(sF14,sK4(sF15,X67)))
      | in(X66,sF17)
      | subset(sF15,X67) ),
    inference(resolution,[],[f7972,f1066]) ).

fof(f1066,plain,
    ! [X1] :
      ( in(sK7(sF14,sK4(sF15,X1)),sK3)
      | subset(sF15,X1) ),
    inference(resolution,[],[f965,f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ~ in(X0,sF14)
      | in(X0,sK3) ),
    inference(resolution,[],[f186,f49]) ).

fof(f186,plain,
    subset(sF14,sK3),
    inference(duplicate_literal_removal,[],[f179]) ).

fof(f179,plain,
    ( subset(sF14,sK3)
    | subset(sF14,sK3) ),
    inference(resolution,[],[f176,f51]) ).

fof(f176,plain,
    ! [X9] :
      ( in(sK4(sF14,X9),sK3)
      | subset(sF14,X9) ),
    inference(resolution,[],[f167,f105]) ).

fof(f105,plain,
    sP12(sK3,sF14),
    inference(resolution,[],[f74,f88]) ).

fof(f88,plain,
    sP1(sK3,sK2,sF14),
    inference(superposition,[],[f71,f78]) ).

fof(f71,plain,
    ! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f66]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( sP1(X1,X0,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP1(X1,X0,X2) )
      & ( sP1(X1,X0,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP1(X1,X0,X2) ),
    inference(definition_folding,[],[f4,f19]) ).

fof(f19,plain,
    ! [X1,X0,X2] :
      ( sP1(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',d3_xboole_0) ).

fof(f74,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,X2)
      | sP12(X0,X2) ),
    inference(cnf_transformation,[],[f74_D]) ).

fof(f74_D,plain,
    ! [X2,X0] :
      ( ! [X1] : ~ sP1(X0,X1,X2)
    <=> ~ sP12(X0,X2) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).

fof(f167,plain,
    ! [X2,X0,X1] :
      ( ~ sP12(X2,X0)
      | in(sK4(X0,X1),X2)
      | subset(X0,X1) ),
    inference(resolution,[],[f75,f50]) ).

fof(f75,plain,
    ! [X2,X0,X4] :
      ( ~ in(X4,X2)
      | in(X4,X0)
      | ~ sP12(X0,X2) ),
    inference(general_splitting,[],[f61,f74_D]) ).

fof(f61,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ in(sK8(X0,X1,X2),X0)
            | ~ in(sK8(X0,X1,X2),X1)
            | ~ in(sK8(X0,X1,X2),X2) )
          & ( ( in(sK8(X0,X1,X2),X0)
              & in(sK8(X0,X1,X2),X1) )
            | in(sK8(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X0)
              | ~ in(X4,X1) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f36,f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ~ in(X3,X1)
            | ~ in(X3,X2) )
          & ( ( in(X3,X0)
              & in(X3,X1) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK8(X0,X1,X2),X0)
          | ~ in(sK8(X0,X1,X2),X1)
          | ~ in(sK8(X0,X1,X2),X2) )
        & ( ( in(sK8(X0,X1,X2),X0)
            & in(sK8(X0,X1,X2),X1) )
          | in(sK8(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X0)
              | ~ in(X4,X1) )
            & ( ( in(X4,X0)
                & in(X4,X1) )
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X1,X0,X2] :
      ( ( sP1(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP1(X1,X0,X2) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0,X2] :
      ( ( sP1(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP1(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f965,plain,
    ! [X4] :
      ( in(sK7(sF14,sK4(sF15,X4)),sF14)
      | subset(sF15,X4) ),
    inference(resolution,[],[f170,f84]) ).

fof(f170,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1)
      | in(sK7(X0,sK4(X1,X2)),X0)
      | subset(X1,X2) ),
    inference(resolution,[],[f53,f50]) ).

fof(f53,plain,
    ! [X0,X1,X5] :
      ( ~ in(X5,X1)
      | in(sK7(X0,X5),X0)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f7972,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK3)
      | ~ in(X1,X0)
      | in(X1,sF17) ),
    inference(resolution,[],[f7962,f73]) ).

fof(f73,plain,
    ! [X1,X6,X5] :
      ( ~ sP11(X6,X1)
      | ~ in(X5,X6)
      | in(X5,X1) ),
    inference(general_splitting,[],[f54,f72_D]) ).

fof(f72,plain,
    ! [X0,X1,X6] :
      ( ~ in(X6,X0)
      | ~ sP0(X0,X1)
      | sP11(X6,X1) ),
    inference(cnf_transformation,[],[f72_D]) ).

fof(f72_D,plain,
    ! [X1,X6] :
      ( ! [X0] :
          ( ~ in(X6,X0)
          | ~ sP0(X0,X1) )
    <=> ~ sP11(X6,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).

fof(f54,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(X6,X0)
      | ~ in(X5,X6)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f7962,plain,
    ! [X2] :
      ( sP11(X2,sF17)
      | ~ in(X2,sK3) ),
    inference(superposition,[],[f7946,f81]) ).

fof(f7946,plain,
    ! [X0,X1] :
      ( sP11(X1,union(X0))
      | ~ in(X1,X0) ),
    inference(forward_demodulation,[],[f7931,f46]) ).

fof(f46,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',idempotence_k3_xboole_0) ).

fof(f7931,plain,
    ! [X0,X1] :
      ( sP11(X1,union(set_intersection2(X0,X0)))
      | ~ in(X1,X0) ),
    inference(superposition,[],[f7901,f46]) ).

fof(f7901,plain,
    ! [X2,X0,X1] :
      ( sP11(X0,union(set_intersection2(X2,set_intersection2(X1,X2))))
      | ~ in(X0,set_intersection2(X1,X2)) ),
    inference(resolution,[],[f7746,f70]) ).

fof(f7746,plain,
    ! [X36,X34,X35,X33] :
      ( ~ sP0(set_intersection2(X35,set_intersection2(X34,X35)),X36)
      | ~ in(X33,set_intersection2(X34,X35))
      | sP11(X33,X36) ),
    inference(resolution,[],[f7677,f72]) ).

fof(f7677,plain,
    ! [X2,X0,X1] :
      ( in(X0,set_intersection2(X2,set_intersection2(X1,X2)))
      | ~ in(X0,set_intersection2(X1,X2)) ),
    inference(resolution,[],[f7662,f49]) ).

fof(f7662,plain,
    ! [X14,X15] : subset(set_intersection2(X14,X15),set_intersection2(X15,set_intersection2(X14,X15))),
    inference(duplicate_literal_removal,[],[f7635]) ).

fof(f7635,plain,
    ! [X14,X15] :
      ( subset(set_intersection2(X14,X15),set_intersection2(X15,set_intersection2(X14,X15)))
      | subset(set_intersection2(X14,X15),set_intersection2(X15,set_intersection2(X14,X15))) ),
    inference(resolution,[],[f2460,f51]) ).

fof(f2460,plain,
    ! [X6,X7,X5] :
      ( in(sK4(set_intersection2(X5,X6),X7),set_intersection2(X6,set_intersection2(X5,X6)))
      | subset(set_intersection2(X5,X6),X7) ),
    inference(forward_demodulation,[],[f2455,f47]) ).

fof(f47,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651',commutativity_k3_xboole_0) ).

fof(f2455,plain,
    ! [X6,X7,X5] :
      ( in(sK4(set_intersection2(X5,X6),X7),set_intersection2(set_intersection2(X5,X6),X6))
      | subset(set_intersection2(X5,X6),X7) ),
    inference(duplicate_literal_removal,[],[f2422]) ).

fof(f2422,plain,
    ! [X6,X7,X5] :
      ( in(sK4(set_intersection2(X5,X6),X7),set_intersection2(set_intersection2(X5,X6),X6))
      | subset(set_intersection2(X5,X6),X7)
      | subset(set_intersection2(X5,X6),X7) ),
    inference(resolution,[],[f2154,f173]) ).

fof(f173,plain,
    ! [X2,X3,X4] :
      ( in(sK4(set_intersection2(X2,X3),X4),X3)
      | subset(set_intersection2(X2,X3),X4) ),
    inference(resolution,[],[f167,f101]) ).

fof(f101,plain,
    ! [X0,X1] : sP12(X0,set_intersection2(X1,X0)),
    inference(resolution,[],[f74,f71]) ).

fof(f2154,plain,
    ! [X2,X0,X1] :
      ( ~ in(sK4(X0,X1),X2)
      | in(sK4(X0,X1),set_intersection2(X0,X2))
      | subset(X0,X1) ),
    inference(resolution,[],[f249,f71]) ).

fof(f249,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X2,X0,X3)
      | in(sK4(X0,X1),X3)
      | ~ in(sK4(X0,X1),X2)
      | subset(X0,X1) ),
    inference(resolution,[],[f62,f50]) ).

fof(f62,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,X2)
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f15296,plain,
    ! [X6] :
      ( ~ in(X6,sF17)
      | in(X6,sF18)
      | ~ in(X6,sF15) ),
    inference(resolution,[],[f8943,f89]) ).

fof(f89,plain,
    sP1(sF17,sF16,sF18),
    inference(superposition,[],[f71,f82]) ).

fof(f8943,plain,
    ! [X11,X12,X13] :
      ( ~ sP1(X12,sF16,X13)
      | ~ in(X11,X12)
      | in(X11,X13)
      | ~ in(X11,sF15) ),
    inference(resolution,[],[f8910,f62]) ).

fof(f8910,plain,
    ! [X0] :
      ( in(X0,sF16)
      | ~ in(X0,sF15) ),
    inference(resolution,[],[f8908,f49]) ).

fof(f8908,plain,
    subset(sF15,sF16),
    inference(duplicate_literal_removal,[],[f8895]) ).

fof(f8895,plain,
    ( subset(sF15,sF16)
    | subset(sF15,sF16) ),
    inference(resolution,[],[f8894,f51]) ).

fof(f8894,plain,
    ! [X0] :
      ( in(sK4(sF15,X0),sF16)
      | subset(sF15,X0) ),
    inference(duplicate_literal_removal,[],[f8832]) ).

fof(f8832,plain,
    ! [X0] :
      ( in(sK4(sF15,X0),sF16)
      | subset(sF15,X0)
      | subset(sF15,X0) ),
    inference(resolution,[],[f8098,f1169]) ).

fof(f8098,plain,
    ! [X66,X67] :
      ( ~ in(X66,sK7(sF14,sK4(sF15,X67)))
      | in(X66,sF16)
      | subset(sF15,X67) ),
    inference(resolution,[],[f7964,f1065]) ).

fof(f1065,plain,
    ! [X0] :
      ( in(sK7(sF14,sK4(sF15,X0)),sK2)
      | subset(sF15,X0) ),
    inference(resolution,[],[f965,f223]) ).

fof(f223,plain,
    ! [X0] :
      ( ~ in(X0,sF14)
      | in(X0,sK2) ),
    inference(resolution,[],[f222,f49]) ).

fof(f222,plain,
    subset(sF14,sK2),
    inference(duplicate_literal_removal,[],[f215]) ).

fof(f215,plain,
    ( subset(sF14,sK2)
    | subset(sF14,sK2) ),
    inference(resolution,[],[f175,f51]) ).

fof(f175,plain,
    ! [X8] :
      ( in(sK4(sF14,X8),sK2)
      | subset(sF14,X8) ),
    inference(resolution,[],[f167,f104]) ).

fof(f104,plain,
    sP12(sK2,sF14),
    inference(resolution,[],[f74,f95]) ).

fof(f95,plain,
    sP1(sK2,sK3,sF14),
    inference(superposition,[],[f90,f78]) ).

fof(f90,plain,
    ! [X2,X1] : sP1(X2,X1,set_intersection2(X2,X1)),
    inference(superposition,[],[f71,f47]) ).

fof(f7964,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK2)
      | ~ in(X1,X0)
      | in(X1,sF16) ),
    inference(resolution,[],[f7961,f73]) ).

fof(f7961,plain,
    ! [X1] :
      ( sP11(X1,sF16)
      | ~ in(X1,sK2) ),
    inference(superposition,[],[f7946,f80]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.16  % Problem    : SET944+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.18  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.18/0.37  % Computer : n017.cluster.edu
% 0.18/0.37  % Model    : x86_64 x86_64
% 0.18/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37  % Memory   : 8042.1875MB
% 0.18/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37  % CPULimit   : 300
% 0.18/0.37  % WCLimit    : 300
% 0.18/0.37  % DateTime   : Sat Aug 26 10:08:56 EDT 2023
% 0.18/0.37  % CPUTime    : 
% 0.18/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.18/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.N8IEyc6z2h/Vampire---4.8_8651
% 0.18/0.38  % (8854)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (8859)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.23/0.44  % (8863)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.44  % (8858)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.44  % (8870)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.44  % (8867)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.23/0.44  % (8860)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.44  % (8862)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 8.04/1.51  % (8870)First to succeed.
% 8.04/1.51  % (8870)Refutation found. Thanks to Tanya!
% 8.04/1.51  % SZS status Theorem for Vampire---4
% 8.04/1.51  % SZS output start Proof for Vampire---4
% See solution above
% 8.04/1.51  % (8870)------------------------------
% 8.04/1.51  % (8870)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 8.04/1.51  % (8870)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 8.04/1.51  % (8870)Termination reason: Refutation
% 8.04/1.51  
% 8.04/1.51  % (8870)Memory used [KB]: 24690
% 8.04/1.51  % (8870)Time elapsed: 1.072 s
% 8.04/1.51  % (8870)------------------------------
% 8.04/1.51  % (8870)------------------------------
% 8.04/1.51  % (8854)Success in time 1.121 s
% 8.04/1.51  % Vampire---4.8 exiting
%------------------------------------------------------------------------------