TSTP Solution File: SET919+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 : Fri May  3 03:02:00 EDT 2024

% Result   : Theorem 17.72s 3.19s
% Output   : CNFRefutation 17.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   85 (  17 unt;   0 def)
%            Number of atoms       :  357 ( 165 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  436 ( 164   ~; 188   |;  72   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  163 (   1 sgn 102   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f10,conjecture,
    ! [X0,X1,X2] :
      ( in(X0,X1)
     => ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
        | ( X0 != X2
          & in(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( in(X0,X1)
       => ( singleton(X0) = set_intersection2(unordered_pair(X0,X2),X1)
          | ( X0 != X2
            & in(X2,X1) ) ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
      & ( X0 = X2
        | ~ in(X2,X1) )
      & in(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
      & ( X0 = X2
        | ~ in(X2,X1) )
      & in(X0,X1) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f16]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(flattening,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(rectify,[],[f21]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X1 != X3
              & X0 != X3 )
            | ~ in(X3,X2) )
          & ( X1 = X3
            | X0 = X3
            | in(X3,X2) ) )
     => ( ( ( sK1(X0,X1,X2) != X1
            & sK1(X0,X1,X2) != X0 )
          | ~ in(sK1(X0,X1,X2),X2) )
        & ( sK1(X0,X1,X2) = X1
          | sK1(X0,X1,X2) = X0
          | in(sK1(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ( ( ( sK1(X0,X1,X2) != X1
              & sK1(X0,X1,X2) != X0 )
            | ~ in(sK1(X0,X1,X2),X2) )
          & ( sK1(X0,X1,X2) = X1
            | sK1(X0,X1,X2) = X0
            | in(sK1(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = 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) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = 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) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f26]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK2(X0,X1,X2),X1)
          | ~ in(sK2(X0,X1,X2),X0)
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( ( in(sK2(X0,X1,X2),X1)
            & in(sK2(X0,X1,X2),X0) )
          | in(sK2(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK2(X0,X1,X2),X1)
            | ~ in(sK2(X0,X1,X2),X0)
            | ~ in(sK2(X0,X1,X2),X2) )
          & ( ( in(sK2(X0,X1,X2),X1)
              & in(sK2(X0,X1,X2),X0) )
            | in(sK2(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).

fof(f34,plain,
    ( ? [X0,X1,X2] :
        ( singleton(X0) != set_intersection2(unordered_pair(X0,X2),X1)
        & ( X0 = X2
          | ~ in(X2,X1) )
        & in(X0,X1) )
   => ( singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
      & ( sK5 = sK7
        | ~ in(sK7,sK6) )
      & in(sK5,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ( singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6)
    & ( sK5 = sK7
      | ~ in(sK7,sK6) )
    & in(sK5,sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f34]) ).

fof(f39,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f40,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f43,plain,
    ! [X2,X0,X1,X4] :
      ( X1 = X4
      | X0 = X4
      | ~ in(X4,X2)
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f44,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | X0 != X4
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | in(sK2(X0,X1,X2),X0)
      | in(sK2(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | in(sK2(X0,X1,X2),X1)
      | in(sK2(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X0,X1) = X2
      | ~ in(sK2(X0,X1,X2),X1)
      | ~ in(sK2(X0,X1,X2),X0)
      | ~ in(sK2(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f58,plain,
    in(sK5,sK6),
    inference(cnf_transformation,[],[f35]) ).

fof(f59,plain,
    ( sK5 = sK7
    | ~ in(sK7,sK6) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f60,plain,
    singleton(sK5) != set_intersection2(unordered_pair(sK5,sK7),sK6),
    inference(cnf_transformation,[],[f35]) ).

fof(f61,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f40]) ).

fof(f62,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f61]) ).

fof(f63,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f39]) ).

fof(f66,plain,
    ! [X2,X1,X4] :
      ( in(X4,X2)
      | unordered_pair(X4,X1) != X2 ),
    inference(equality_resolution,[],[f44]) ).

fof(f67,plain,
    ! [X1,X4] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f66]) ).

fof(f68,plain,
    ! [X0,X1,X4] :
      ( X1 = X4
      | X0 = X4
      | ~ in(X4,unordered_pair(X0,X1)) ),
    inference(equality_resolution,[],[f43]) ).

cnf(c_54,plain,
    in(X0,singleton(X0)),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_55,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_60,plain,
    in(X0,unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_61,plain,
    ( ~ in(X0,unordered_pair(X1,X2))
    | X0 = X1
    | X0 = X2 ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_62,plain,
    ( ~ in(sK2(X0,X1,X2),X0)
    | ~ in(sK2(X0,X1,X2),X1)
    | ~ in(sK2(X0,X1,X2),X2)
    | set_intersection2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_63,plain,
    ( set_intersection2(X0,X1) = X2
    | in(sK2(X0,X1,X2),X1)
    | in(sK2(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_64,plain,
    ( set_intersection2(X0,X1) = X2
    | in(sK2(X0,X1,X2),X0)
    | in(sK2(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_71,negated_conjecture,
    set_intersection2(unordered_pair(sK5,sK7),sK6) != singleton(sK5),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_72,negated_conjecture,
    ( ~ in(sK7,sK6)
    | sK5 = sK7 ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_73,negated_conjecture,
    in(sK5,sK6),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_74,plain,
    in(sK5,singleton(sK5)),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_313,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_315,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_316,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_594,plain,
    ( set_intersection2(unordered_pair(sK5,sK7),sK6) = singleton(sK5)
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),unordered_pair(sK5,sK7))
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_597,plain,
    ( X0 != sK5
    | X1 != sK6
    | ~ in(sK5,sK6)
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_316]) ).

cnf(c_602,plain,
    ( ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5))
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5 ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_621,plain,
    ( X0 != sK5
    | sK6 != sK6
    | ~ in(sK5,sK6)
    | in(X0,sK6) ),
    inference(instantiation,[status(thm)],[c_597]) ).

cnf(c_622,plain,
    ( X0 != sK5
    | ~ in(sK5,sK6)
    | in(X0,sK6) ),
    inference(equality_resolution_simp,[status(thm)],[c_621]) ).

cnf(c_879,plain,
    ( sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) != sK5
    | ~ in(sK5,sK6)
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6) ),
    inference(instantiation,[status(thm)],[c_622]) ).

cnf(c_1621,plain,
    ( X0 != X1
    | X1 = X0 ),
    inference(resolution,[status(thm)],[c_315,c_313]) ).

cnf(c_2332,plain,
    ( X0 != X1
    | ~ in(X1,X2)
    | in(X0,X2) ),
    inference(resolution,[status(thm)],[c_316,c_313]) ).

cnf(c_2616,plain,
    ( X0 != sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5))
    | X1 != sK6
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_316]) ).

cnf(c_2668,plain,
    ( X0 != sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5))
    | sK6 != sK6
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | in(X0,sK6) ),
    inference(instantiation,[status(thm)],[c_2616]) ).

cnf(c_2669,plain,
    ( X0 != sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5))
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | in(X0,sK6) ),
    inference(equality_resolution_simp,[status(thm)],[c_2668]) ).

cnf(c_3079,plain,
    ( sK7 != sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5))
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | in(sK7,sK6) ),
    inference(instantiation,[status(thm)],[c_2669]) ).

cnf(c_3693,plain,
    ( in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5))
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6) ),
    inference(resolution,[status(thm)],[c_63,c_71]) ).

cnf(c_4117,plain,
    ( in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),unordered_pair(sK5,sK7))
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5)) ),
    inference(resolution,[status(thm)],[c_64,c_71]) ).

cnf(c_4694,plain,
    in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6),
    inference(global_subsumption_just,[status(thm)],[c_3693,c_73,c_602,c_879,c_3693]) ).

cnf(c_4790,plain,
    ( sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK7
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5)) ),
    inference(resolution,[status(thm)],[c_4117,c_61]) ).

cnf(c_4839,plain,
    ( sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK7
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5 ),
    inference(global_subsumption_just,[status(thm)],[c_4790,c_602,c_4790]) ).

cnf(c_4840,plain,
    ( sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK7 ),
    inference(renaming,[status(thm)],[c_4839]) ).

cnf(c_4849,plain,
    ( sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5
    | sK7 = sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) ),
    inference(resolution,[status(thm)],[c_4840,c_1621]) ).

cnf(c_4850,plain,
    ( X0 != sK7
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = X0
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5 ),
    inference(resolution,[status(thm)],[c_4840,c_315]) ).

cnf(c_4851,plain,
    ( sK5 != sK7
    | sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5 ),
    inference(instantiation,[status(thm)],[c_4850]) ).

cnf(c_4872,plain,
    sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)) = sK5,
    inference(global_subsumption_just,[status(thm)],[c_4849,c_72,c_3079,c_4694,c_4849,c_4851]) ).

cnf(c_4878,plain,
    sK5 = sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),
    inference(resolution,[status(thm)],[c_4872,c_1621]) ).

cnf(c_7430,plain,
    ( ~ in(sK5,X0)
    | in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),X0) ),
    inference(resolution,[status(thm)],[c_2332,c_4872]) ).

cnf(c_7433,plain,
    ( ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),X0)
    | in(sK5,X0) ),
    inference(resolution,[status(thm)],[c_2332,c_4878]) ).

cnf(c_10001,plain,
    ( ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),unordered_pair(sK5,sK7))
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | ~ in(sK5,singleton(sK5))
    | set_intersection2(unordered_pair(sK5,sK7),sK6) = singleton(sK5) ),
    inference(resolution,[status(thm)],[c_7430,c_62]) ).

cnf(c_10130,plain,
    ( in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5))
    | in(sK5,unordered_pair(sK5,sK7)) ),
    inference(resolution,[status(thm)],[c_7433,c_4117]) ).

cnf(c_10352,plain,
    in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),singleton(sK5)),
    inference(global_subsumption_just,[status(thm)],[c_10130,c_74,c_71,c_594,c_4694,c_10001]) ).

cnf(c_10369,plain,
    ( ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),unordered_pair(sK5,sK7))
    | ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),sK6)
    | set_intersection2(unordered_pair(sK5,sK7),sK6) = singleton(sK5) ),
    inference(resolution,[status(thm)],[c_10352,c_62]) ).

cnf(c_10374,plain,
    ~ in(sK2(unordered_pair(sK5,sK7),sK6,singleton(sK5)),unordered_pair(sK5,sK7)),
    inference(global_subsumption_just,[status(thm)],[c_10369,c_74,c_71,c_4694,c_10001]) ).

cnf(c_10382,plain,
    ~ in(sK5,unordered_pair(sK5,sK7)),
    inference(resolution,[status(thm)],[c_10374,c_7430]) ).

cnf(c_10384,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_10382,c_60]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 20:34:42 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.72/3.19  % SZS status Started for theBenchmark.p
% 17.72/3.19  % SZS status Theorem for theBenchmark.p
% 17.72/3.19  
% 17.72/3.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.72/3.19  
% 17.72/3.19  ------  iProver source info
% 17.72/3.19  
% 17.72/3.19  git: date: 2024-05-02 19:28:25 +0000
% 17.72/3.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.72/3.19  git: non_committed_changes: false
% 17.72/3.19  
% 17.72/3.19  ------ Parsing...
% 17.72/3.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.72/3.19  
% 17.72/3.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 17.72/3.19  
% 17.72/3.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.72/3.19  
% 17.72/3.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.72/3.19  ------ Proving...
% 17.72/3.19  ------ Problem Properties 
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  clauses                                 24
% 17.72/3.19  conjectures                             3
% 17.72/3.19  EPR                                     4
% 17.72/3.19  Horn                                    19
% 17.72/3.19  unary                                   9
% 17.72/3.19  binary                                  5
% 17.72/3.19  lits                                    51
% 17.72/3.19  lits eq                                 23
% 17.72/3.19  fd_pure                                 0
% 17.72/3.19  fd_pseudo                               0
% 17.72/3.19  fd_cond                                 0
% 17.72/3.19  fd_pseudo_cond                          8
% 17.72/3.19  AC symbols                              0
% 17.72/3.19  
% 17.72/3.19  ------ Input Options Time Limit: Unbounded
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  ------ 
% 17.72/3.19  Current options:
% 17.72/3.19  ------ 
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  ------ Proving...
% 17.72/3.19  
% 17.72/3.19  
% 17.72/3.19  % SZS status Theorem for theBenchmark.p
% 17.72/3.19  
% 17.72/3.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.72/3.19  
% 17.72/3.19  
%------------------------------------------------------------------------------