TSTP Solution File: SET951+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.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 03:02:06 EDT 2024

% Result   : Theorem 3.76s 1.16s
% Output   : CNFRefutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   85 (  20 unt;   0 def)
%            Number of atoms       :  315 (  97 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  390 ( 160   ~; 146   |;  74   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  256 (   7 sgn 172   !;  35   ?)

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

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

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(f5,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(f6,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f11,conjecture,
    ! [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/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(f12,negated_conjecture,
    ~ ! [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(negated_conjecture,[],[f11]) ).

fof(f13,axiom,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
     => ( X1 = X3
        & X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).

fof(f16,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,[],[f12]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X1)
                  & in(X6,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X1)
                  & in(X11,X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(rectify,[],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X1)
                & in(X6,X0) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
              | ~ in(X5,X1)
              | ~ in(X4,X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
              & in(X7,X1)
              & in(X6,X0) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
          & in(X7,X1)
          & in(X6,X0) )
     => ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
        & in(sK2(X0,X1,X2),X1)
        & in(sK1(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X1)
          & in(X11,X0) )
     => ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
        & in(sK4(X0,X1,X8),X1)
        & in(sK3(X0,X1,X8),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
              & in(sK2(X0,X1,X2),X1)
              & in(sK1(X0,X1,X2),X0) )
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
                & in(sK4(X0,X1,X8),X1)
                & in(sK3(X0,X1,X8),X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f22,f21,f20]) ).

fof(f24,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,[],[f5]) ).

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(flattening,[],[f24]) ).

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) ) ) )
      & ( ! [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,[],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK5(X0,X1,X2),X1)
          | ~ in(sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( ( in(sK5(X0,X1,X2),X1)
            & in(sK5(X0,X1,X2),X0) )
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK5(X0,X1,X2),X1)
            | ~ in(sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( ( in(sK5(X0,X1,X2),X1)
              & in(sK5(X0,X1,X2),X0) )
            | in(sK5(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,[sK5])],[f26,f27]) ).

fof(f33,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))) )
   => ( ! [X6,X5] :
          ( ~ in(X6,set_intersection2(sK10,sK12))
          | ~ in(X5,set_intersection2(sK9,sK11))
          | ordered_pair(X5,X6) != sK8 )
      & in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ( ! [X5,X6] :
        ( ~ in(X6,set_intersection2(sK10,sK12))
        | ~ in(X5,set_intersection2(sK9,sK11))
        | ordered_pair(X5,X6) != sK8 )
    & in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f16,f33]) ).

fof(f36,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f37,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f38,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f39,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f40,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f46,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f47,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f48,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f52,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f57,plain,
    in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))),
    inference(cnf_transformation,[],[f34]) ).

fof(f58,plain,
    ! [X6,X5] :
      ( ~ in(X6,set_intersection2(sK10,sK12))
      | ~ in(X5,set_intersection2(sK9,sK11))
      | ordered_pair(X5,X6) != sK8 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f64,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f40,f52]) ).

fof(f66,plain,
    ! [X6,X5] :
      ( ~ in(X6,set_intersection2(sK10,sK12))
      | ~ in(X5,set_intersection2(sK9,sK11))
      | sK8 != unordered_pair(unordered_pair(X5,X6),singleton(X5)) ),
    inference(definition_unfolding,[],[f58,f52]) ).

fof(f67,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
    inference(definition_unfolding,[],[f60,f52,f52]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
    inference(definition_unfolding,[],[f59,f52,f52]) ).

fof(f71,plain,
    ! [X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f64]) ).

fof(f72,plain,
    ! [X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f39]) ).

fof(f73,plain,
    ! [X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f38]) ).

fof(f74,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f48]) ).

fof(f75,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f47]) ).

fof(f76,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f46]) ).

cnf(c_50,plain,
    unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_51,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_57,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_58,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | in(sK4(X1,X2,X0),X2) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_59,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | in(sK3(X1,X2,X0),X1) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_63,plain,
    ( ~ in(X0,X1)
    | ~ in(X0,X2)
    | in(X0,set_intersection2(X2,X1)) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_64,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_65,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_70,negated_conjecture,
    ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK8
    | ~ in(X0,set_intersection2(sK9,sK11))
    | ~ in(X1,set_intersection2(sK10,sK12)) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_71,negated_conjecture,
    in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_72,plain,
    ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
    | X1 = X3 ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_73,plain,
    ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
    | X0 = X2 ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_547,plain,
    in(sK8,set_intersection2(cartesian_product2(sK11,sK12),cartesian_product2(sK9,sK10))),
    inference(demodulation,[status(thm)],[c_71,c_51]) ).

cnf(c_549,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK8
    | ~ in(X0,set_intersection2(sK11,sK9))
    | ~ in(X1,set_intersection2(sK12,sK10)) ),
    inference(demodulation,[status(thm)],[c_70,c_50,c_51]) ).

cnf(c_600,plain,
    ( ~ in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12)))
    | in(sK8,cartesian_product2(sK11,sK12)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_602,plain,
    in(sK8,cartesian_product2(sK9,sK10)),
    inference(superposition,[status(thm)],[c_547,c_64]) ).

cnf(c_610,plain,
    in(sK8,cartesian_product2(sK11,sK12)),
    inference(superposition,[status(thm)],[c_547,c_65]) ).

cnf(c_630,plain,
    ( ~ in(sK8,cartesian_product2(sK11,sK12))
    | in(sK3(sK11,sK12,sK8),sK11) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_631,plain,
    ( ~ in(sK8,cartesian_product2(sK11,sK12))
    | in(sK4(sK11,sK12,sK8),sK12) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_635,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
    | X1 = X3 ),
    inference(demodulation,[status(thm)],[c_72,c_50]) ).

cnf(c_645,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X3))
    | X0 = X2 ),
    inference(demodulation,[status(thm)],[c_73,c_50]) ).

cnf(c_690,plain,
    ( ~ in(sK8,cartesian_product2(sK9,sK10))
    | in(sK3(sK9,sK10,sK8),sK9) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_691,plain,
    ( ~ in(sK8,cartesian_product2(sK9,sK10))
    | in(sK4(sK9,sK10,sK8),sK10) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_745,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 ),
    inference(demodulation,[status(thm)],[c_57,c_50]) ).

cnf(c_750,plain,
    unordered_pair(singleton(sK3(sK11,sK12,sK8)),unordered_pair(sK3(sK11,sK12,sK8),sK4(sK11,sK12,sK8))) = sK8,
    inference(superposition,[status(thm)],[c_610,c_745]) ).

cnf(c_751,plain,
    unordered_pair(singleton(sK3(sK9,sK10,sK8)),unordered_pair(sK3(sK9,sK10,sK8),sK4(sK9,sK10,sK8))) = sK8,
    inference(superposition,[status(thm)],[c_602,c_745]) ).

cnf(c_821,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK8
    | sK3(sK11,sK12,sK8) = X0 ),
    inference(superposition,[status(thm)],[c_750,c_645]) ).

cnf(c_822,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK8
    | sK4(sK11,sK12,sK8) = X1 ),
    inference(superposition,[status(thm)],[c_750,c_635]) ).

cnf(c_1115,plain,
    ( ~ in(sK3(sK9,sK10,sK8),set_intersection2(sK11,sK9))
    | ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK12,sK10)) ),
    inference(superposition,[status(thm)],[c_751,c_549]) ).

cnf(c_1467,plain,
    ( ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK12,sK10))
    | ~ in(sK3(sK9,sK10,sK8),sK9)
    | ~ in(sK3(sK9,sK10,sK8),sK11) ),
    inference(superposition,[status(thm)],[c_63,c_1115]) ).

cnf(c_1468,plain,
    ( ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK12,sK10))
    | ~ in(sK3(sK9,sK10,sK8),sK11) ),
    inference(global_subsumption_just,[status(thm)],[c_1467,c_602,c_690,c_1467]) ).

cnf(c_1495,plain,
    ( ~ in(sK3(sK9,sK10,sK8),sK11)
    | ~ in(sK4(sK9,sK10,sK8),sK10)
    | ~ in(sK4(sK9,sK10,sK8),sK12) ),
    inference(superposition,[status(thm)],[c_63,c_1468]) ).

cnf(c_1496,plain,
    ( ~ in(sK3(sK9,sK10,sK8),sK11)
    | ~ in(sK4(sK9,sK10,sK8),sK12) ),
    inference(global_subsumption_just,[status(thm)],[c_1495,c_602,c_691,c_1495]) ).

cnf(c_2197,plain,
    sK3(sK9,sK10,sK8) = sK3(sK11,sK12,sK8),
    inference(superposition,[status(thm)],[c_751,c_821]) ).

cnf(c_2295,plain,
    sK4(sK9,sK10,sK8) = sK4(sK11,sK12,sK8),
    inference(superposition,[status(thm)],[c_751,c_822]) ).

cnf(c_2392,plain,
    ( ~ in(sK3(sK11,sK12,sK8),sK11)
    | ~ in(sK4(sK9,sK10,sK8),sK12) ),
    inference(superposition,[status(thm)],[c_2197,c_1496]) ).

cnf(c_2397,plain,
    ~ in(sK4(sK9,sK10,sK8),sK12),
    inference(global_subsumption_just,[status(thm)],[c_2392,c_71,c_600,c_630,c_2392]) ).

cnf(c_2399,plain,
    ~ in(sK4(sK11,sK12,sK8),sK12),
    inference(demodulation,[status(thm)],[c_2397,c_2295]) ).

cnf(c_2471,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2399,c_631,c_600,c_71]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May  2 20:10:35 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  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
% 3.76/1.16  % SZS status Started for theBenchmark.p
% 3.76/1.16  % SZS status Theorem for theBenchmark.p
% 3.76/1.16  
% 3.76/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.76/1.16  
% 3.76/1.16  ------  iProver source info
% 3.76/1.16  
% 3.76/1.16  git: date: 2024-05-02 19:28:25 +0000
% 3.76/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.76/1.16  git: non_committed_changes: false
% 3.76/1.16  
% 3.76/1.16  ------ Parsing...
% 3.76/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.76/1.16  
% 3.76/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.76/1.16  
% 3.76/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.76/1.16  
% 3.76/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.76/1.16  ------ Proving...
% 3.76/1.16  ------ Problem Properties 
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  clauses                                 25
% 3.76/1.16  conjectures                             2
% 3.76/1.16  EPR                                     3
% 3.76/1.16  Horn                                    20
% 3.76/1.16  unary                                   7
% 3.76/1.16  binary                                  8
% 3.76/1.16  lits                                    56
% 3.76/1.16  lits eq                                 18
% 3.76/1.16  fd_pure                                 0
% 3.76/1.16  fd_pseudo                               0
% 3.76/1.16  fd_cond                                 0
% 3.76/1.16  fd_pseudo_cond                          9
% 3.76/1.16  AC symbols                              0
% 3.76/1.16  
% 3.76/1.16  ------ Input Options Time Limit: Unbounded
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  ------ 
% 3.76/1.16  Current options:
% 3.76/1.16  ------ 
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  ------ Proving...
% 3.76/1.16  
% 3.76/1.16  
% 3.76/1.16  % SZS status Theorem for theBenchmark.p
% 3.76/1.16  
% 3.76/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.17  
% 3.76/1.17  
%------------------------------------------------------------------------------