TSTP Solution File: SET655+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 15:08:57 EDT 2023

% Result   : Theorem 7.69s 1.67s
% Output   : CNFRefutation 7.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  150 (  15 unt;   0 def)
%            Number of atoms       :  641 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  816 ( 325   ~; 313   |; 116   &)
%                                         (  13 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  363 (   2 sgn; 137   !;  44   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => ( ( subset(X2,X3)
                      & subset(X0,X1) )
                   => subset(cross_product(X0,X2),cross_product(X1,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

fof(f5,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).

fof(f7,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => subset(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).

fof(f10,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).

fof(f11,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).

fof(f12,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => ! [X4] :
                      ( ilf_type(X4,relation_type(X0,X2))
                     => ( ( subset(X2,X3)
                          & subset(X0,X1) )
                       => ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_17) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,set_type)
                   => ! [X4] :
                        ( ilf_type(X4,relation_type(X0,X2))
                       => ( ( subset(X2,X3)
                            & subset(X0,X1) )
                         => ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f22,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
    inference(rectify,[],[f3]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(cross_product(X0,X2),cross_product(X1,X3))
                  | ~ subset(X2,X3)
                  | ~ subset(X0,X1)
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f26,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( subset(cross_product(X0,X2),cross_product(X1,X3))
                  | ~ subset(X2,X3)
                  | ~ subset(X0,X1)
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f25]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ~ ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
                | ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f29,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,X1)
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f29]) ).

fof(f32,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f34,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f35]) ).

fof(f37,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f38]) ).

fof(f42,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f49,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ ilf_type(X4,relation_type(X1,X3))
                      & subset(X2,X3)
                      & subset(X0,X1)
                      & ilf_type(X4,relation_type(X0,X2)) )
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f50,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ ilf_type(X4,relation_type(X1,X3))
                      & subset(X2,X3)
                      & subset(X0,X1)
                      & ilf_type(X4,relation_type(X0,X2)) )
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f49]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f53]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0)
        & ilf_type(sK1(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK1(X0,X1),X1)
                & member(sK1(X0,X1),X0)
                & ilf_type(sK1(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f54,f55]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) )
            & ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f60,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f60]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0)
        & ilf_type(sK3(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK3(X0,X1),X1)
                & member(sK3(X0,X1),X0)
                & ilf_type(sK3(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f61,f62]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f67,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f68,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f67]) ).

fof(f69,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( member(sK5(X0),X0)
        & ilf_type(sK5(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ( member(sK5(X0),X0)
            & ilf_type(sK5(X0),set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f68,f69]) ).

fof(f77,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ~ ilf_type(X4,relation_type(X1,X3))
                        & subset(X2,X3)
                        & subset(X0,X1)
                        & ilf_type(X4,relation_type(X0,X2)) )
                    & ilf_type(X3,set_type) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ ilf_type(X4,relation_type(X1,X3))
                      & subset(X2,X3)
                      & subset(sK9,X1)
                      & ilf_type(X4,relation_type(sK9,X2)) )
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK9,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ~ ilf_type(X4,relation_type(X1,X3))
                    & subset(X2,X3)
                    & subset(sK9,X1)
                    & ilf_type(X4,relation_type(sK9,X2)) )
                & ilf_type(X3,set_type) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ~ ilf_type(X4,relation_type(sK10,X3))
                  & subset(X2,X3)
                  & subset(sK9,sK10)
                  & ilf_type(X4,relation_type(sK9,X2)) )
              & ilf_type(X3,set_type) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK10,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ~ ilf_type(X4,relation_type(sK10,X3))
                & subset(X2,X3)
                & subset(sK9,sK10)
                & ilf_type(X4,relation_type(sK9,X2)) )
            & ilf_type(X3,set_type) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ~ ilf_type(X4,relation_type(sK10,X3))
              & subset(sK11,X3)
              & subset(sK9,sK10)
              & ilf_type(X4,relation_type(sK9,sK11)) )
          & ilf_type(X3,set_type) )
      & ilf_type(sK11,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ~ ilf_type(X4,relation_type(sK10,X3))
            & subset(sK11,X3)
            & subset(sK9,sK10)
            & ilf_type(X4,relation_type(sK9,sK11)) )
        & ilf_type(X3,set_type) )
   => ( ? [X4] :
          ( ~ ilf_type(X4,relation_type(sK10,sK12))
          & subset(sK11,sK12)
          & subset(sK9,sK10)
          & ilf_type(X4,relation_type(sK9,sK11)) )
      & ilf_type(sK12,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ( ? [X4] :
        ( ~ ilf_type(X4,relation_type(sK10,sK12))
        & subset(sK11,sK12)
        & subset(sK9,sK10)
        & ilf_type(X4,relation_type(sK9,sK11)) )
   => ( ~ ilf_type(sK13,relation_type(sK10,sK12))
      & subset(sK11,sK12)
      & subset(sK9,sK10)
      & ilf_type(sK13,relation_type(sK9,sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ( ~ ilf_type(sK13,relation_type(sK10,sK12))
    & subset(sK11,sK12)
    & subset(sK9,sK10)
    & ilf_type(sK13,relation_type(sK9,sK11))
    & ilf_type(sK12,set_type)
    & ilf_type(sK11,set_type)
    & ilf_type(sK10,set_type)
    & ilf_type(sK9,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f50,f81,f80,f79,f78,f77]) ).

fof(f84,plain,
    ! [X2,X3,X0,X1] :
      ( subset(cross_product(X0,X2),cross_product(X1,X3))
      | ~ subset(X2,X3)
      | ~ subset(X0,X1)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f85,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f86,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f88,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f96,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f97,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ ilf_type(X3,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK3(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK3(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f106,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ empty(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f118,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f123,plain,
    ilf_type(sK13,relation_type(sK9,sK11)),
    inference(cnf_transformation,[],[f82]) ).

fof(f124,plain,
    subset(sK9,sK10),
    inference(cnf_transformation,[],[f82]) ).

fof(f125,plain,
    subset(sK11,sK12),
    inference(cnf_transformation,[],[f82]) ).

fof(f126,plain,
    ~ ilf_type(sK13,relation_type(sK10,sK12)),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_50,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X3)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(cross_product(X0,X2),cross_product(X1,X3)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_51,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_52,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_57,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_59,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,subset_type(X1)) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_60,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_62,plain,
    ( ~ ilf_type(X0,set_type)
    | subset(X0,X0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_63,plain,
    ( ~ member(sK3(X0,X1),X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_64,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(sK3(X0,X1),X0)
    | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_66,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_68,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_69,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(X1))
    | empty(X1) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_70,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_74,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_84,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_85,negated_conjecture,
    ~ ilf_type(sK13,relation_type(sK10,sK12)),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_86,negated_conjecture,
    subset(sK11,sK12),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_87,negated_conjecture,
    subset(sK9,sK10),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_88,negated_conjecture,
    ilf_type(sK13,relation_type(sK9,sK11)),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_123,plain,
    subset(X0,X0),
    inference(global_subsumption_just,[status(thm)],[c_62,c_84,c_62]) ).

cnf(c_126,plain,
    ~ empty(power_set(X0)),
    inference(global_subsumption_just,[status(thm)],[c_68,c_84,c_68]) ).

cnf(c_183,plain,
    ( ~ ilf_type(X1,set_type)
    | member(sK3(X0,X1),X0)
    | member(X0,power_set(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_64,c_84,c_64]) ).

cnf(c_184,plain,
    ( ~ ilf_type(X0,set_type)
    | member(sK3(X1,X0),X1)
    | member(X1,power_set(X0)) ),
    inference(renaming,[status(thm)],[c_183]) ).

cnf(c_185,plain,
    ( member(sK3(X1,X0),X1)
    | member(X1,power_set(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_184,c_84,c_184]) ).

cnf(c_186,plain,
    ( member(sK3(X0,X1),X0)
    | member(X0,power_set(X1)) ),
    inference(renaming,[status(thm)],[c_185]) ).

cnf(c_190,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | member(X0,X1)
    | empty(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_70,c_84,c_70]) ).

cnf(c_192,plain,
    ( ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | ~ member(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_69,c_84,c_74,c_69]) ).

cnf(c_193,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(X1)) ),
    inference(renaming,[status(thm)],[c_192]) ).

cnf(c_195,plain,
    ( ~ member(sK3(X0,X1),X1)
    | ~ ilf_type(X1,set_type)
    | member(X0,power_set(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_63,c_84,c_63]) ).

cnf(c_197,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(global_subsumption_just,[status(thm)],[c_60,c_84,c_60]) ).

cnf(c_199,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,subset_type(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_59,c_84,c_59]) ).

cnf(c_209,plain,
    ( ~ member(X2,X0)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_57,c_84,c_57]) ).

cnf(c_210,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(renaming,[status(thm)],[c_209]) ).

cnf(c_213,plain,
    ( ~ member(X2,X0)
    | ~ member(X0,power_set(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_66,c_84,c_66]) ).

cnf(c_214,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(renaming,[status(thm)],[c_213]) ).

cnf(c_215,plain,
    ( ~ subset(X2,X3)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(cross_product(X0,X2),cross_product(X1,X3)) ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).

cnf(c_216,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(cross_product(X0,X2),cross_product(X1,X3)) ),
    inference(renaming,[status(thm)],[c_215]) ).

cnf(c_219,plain,
    ( ~ member(sK3(X0,X1),X1)
    | member(X0,power_set(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_195,c_84]) ).

cnf(c_221,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_210,c_84]) ).

cnf(c_222,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_197,c_84]) ).

cnf(c_223,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ilf_type(X0,subset_type(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_199,c_84]) ).

cnf(c_225,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_51,c_84]) ).

cnf(c_228,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_52,c_84]) ).

cnf(c_229,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X3)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | subset(cross_product(X0,X2),cross_product(X1,X3)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_216,c_84]) ).

cnf(c_231,plain,
    ( ~ member(X0,X1)
    | ilf_type(X0,member_type(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_193,c_84]) ).

cnf(c_232,plain,
    ( ~ ilf_type(X0,member_type(X1))
    | member(X0,X1)
    | empty(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_190,c_84]) ).

cnf(c_233,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | member(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_214,c_84]) ).

cnf(c_343,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_225,c_84]) ).

cnf(c_354,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_228,c_84]) ).

cnf(c_366,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_221,c_84]) ).

cnf(c_394,plain,
    ( ~ member(X0,power_set(X1))
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_233,c_84]) ).

cnf(c_409,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X3)
    | subset(cross_product(X0,X2),cross_product(X1,X3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_229,c_84,c_84]) ).

cnf(c_674,plain,
    ( ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(prop_impl_just,[status(thm)],[c_354]) ).

cnf(c_675,plain,
    ( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(renaming,[status(thm)],[c_674]) ).

cnf(c_676,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(prop_impl_just,[status(thm)],[c_343]) ).

cnf(c_678,plain,
    ( ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X0,member_type(power_set(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_223]) ).

cnf(c_679,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ilf_type(X0,subset_type(X1)) ),
    inference(renaming,[status(thm)],[c_678]) ).

cnf(c_680,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_222]) ).

cnf(c_690,plain,
    ( ~ member(sK3(X0,X1),X1)
    | member(X0,power_set(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_219]) ).

cnf(c_694,plain,
    ( member(X0,power_set(X1))
    | member(sK3(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_186]) ).

cnf(c_695,plain,
    ( member(sK3(X0,X1),X0)
    | member(X0,power_set(X1)) ),
    inference(renaming,[status(thm)],[c_694]) ).

cnf(c_696,plain,
    ( ~ member(X0,X1)
    | ilf_type(X0,member_type(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_231]) ).

cnf(c_2090,plain,
    ( ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2))))
    | ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(instantiation,[status(thm)],[c_679]) ).

cnf(c_2189,plain,
    ( ~ member(X0,power_set(X1))
    | ilf_type(X0,member_type(power_set(X1))) ),
    inference(instantiation,[status(thm)],[c_696]) ).

cnf(c_2299,plain,
    ( ~ member(X0,power_set(cross_product(X1,X2)))
    | ilf_type(X0,member_type(power_set(cross_product(X1,X2)))) ),
    inference(instantiation,[status(thm)],[c_2189]) ).

cnf(c_3687,plain,
    ( ~ ilf_type(sK13,subset_type(cross_product(sK10,sK12)))
    | ilf_type(sK13,relation_type(sK10,sK12)) ),
    inference(instantiation,[status(thm)],[c_675]) ).

cnf(c_4869,plain,
    ( ~ ilf_type(sK13,member_type(power_set(cross_product(sK10,sK12))))
    | ilf_type(sK13,subset_type(cross_product(sK10,sK12))) ),
    inference(instantiation,[status(thm)],[c_2090]) ).

cnf(c_7165,plain,
    ( ~ member(sK13,power_set(cross_product(sK10,sK12)))
    | ilf_type(sK13,member_type(power_set(cross_product(sK10,sK12)))) ),
    inference(instantiation,[status(thm)],[c_2299]) ).

cnf(c_20081,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1))
    | empty(power_set(X1)) ),
    inference(superposition,[status(thm)],[c_680,c_232]) ).

cnf(c_20082,plain,
    ( ~ ilf_type(X0,subset_type(X1))
    | member(X0,power_set(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_20081,c_126]) ).

cnf(c_20188,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | member(X0,power_set(cross_product(X1,X2))) ),
    inference(superposition,[status(thm)],[c_676,c_20082]) ).

cnf(c_20909,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ member(X3,X0)
    | member(X3,cross_product(X1,X2)) ),
    inference(superposition,[status(thm)],[c_20188,c_394]) ).

cnf(c_21086,plain,
    ( ~ member(X0,cross_product(X1,X2))
    | ~ subset(X1,X3)
    | ~ subset(X2,X4)
    | member(X0,cross_product(X3,X4)) ),
    inference(superposition,[status(thm)],[c_409,c_366]) ).

cnf(c_21214,plain,
    ( ~ member(X0,sK13)
    | member(X0,cross_product(sK9,sK11)) ),
    inference(superposition,[status(thm)],[c_88,c_20909]) ).

cnf(c_21449,plain,
    ( ~ subset(sK11,X0)
    | ~ subset(sK9,X1)
    | ~ member(X2,sK13)
    | member(X2,cross_product(X1,X0)) ),
    inference(superposition,[status(thm)],[c_21214,c_21086]) ).

cnf(c_21503,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X3)
    | ~ subset(sK11,X0)
    | ~ subset(sK9,X2)
    | ~ member(X4,sK13)
    | member(X4,cross_product(X3,X1)) ),
    inference(superposition,[status(thm)],[c_21449,c_21086]) ).

cnf(c_21795,plain,
    ( ~ subset(X0,X1)
    | ~ subset(sK9,X0)
    | ~ member(X2,sK13)
    | ~ subset(sK11,sK11)
    | member(X2,cross_product(X1,sK12)) ),
    inference(superposition,[status(thm)],[c_86,c_21503]) ).

cnf(c_21811,plain,
    ( ~ subset(X0,X1)
    | ~ subset(sK9,X0)
    | ~ member(X2,sK13)
    | member(X2,cross_product(X1,sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_21795,c_123]) ).

cnf(c_22194,plain,
    ( ~ member(X0,sK13)
    | ~ subset(sK9,sK9)
    | member(X0,cross_product(sK10,sK12)) ),
    inference(superposition,[status(thm)],[c_87,c_21811]) ).

cnf(c_22204,plain,
    ( ~ member(X0,sK13)
    | member(X0,cross_product(sK10,sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22194,c_123]) ).

cnf(c_22320,plain,
    ( ~ member(sK3(X0,cross_product(sK10,sK12)),sK13)
    | member(X0,power_set(cross_product(sK10,sK12))) ),
    inference(superposition,[status(thm)],[c_22204,c_690]) ).

cnf(c_22469,plain,
    member(sK13,power_set(cross_product(sK10,sK12))),
    inference(superposition,[status(thm)],[c_695,c_22320]) ).

cnf(c_22470,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_22469,c_7165,c_4869,c_3687,c_85]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n020.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 : Sat Aug 26 11:06:15 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.69/1.67  % SZS status Started for theBenchmark.p
% 7.69/1.67  % SZS status Theorem for theBenchmark.p
% 7.69/1.67  
% 7.69/1.67  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.69/1.67  
% 7.69/1.67  ------  iProver source info
% 7.69/1.67  
% 7.69/1.67  git: date: 2023-05-31 18:12:56 +0000
% 7.69/1.67  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.69/1.67  git: non_committed_changes: false
% 7.69/1.67  git: last_make_outside_of_git: false
% 7.69/1.67  
% 7.69/1.67  ------ Parsing...
% 7.69/1.67  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.69/1.67  
% 7.69/1.67  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.69/1.67  
% 7.69/1.67  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.69/1.67  
% 7.69/1.67  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.69/1.67  ------ Proving...
% 7.69/1.67  ------ Problem Properties 
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  clauses                                 31
% 7.69/1.67  conjectures                             4
% 7.69/1.67  EPR                                     8
% 7.69/1.67  Horn                                    25
% 7.69/1.67  unary                                   9
% 7.69/1.67  binary                                  16
% 7.69/1.67  lits                                    59
% 7.69/1.67  lits eq                                 2
% 7.69/1.67  fd_pure                                 0
% 7.69/1.67  fd_pseudo                               0
% 7.69/1.67  fd_cond                                 0
% 7.69/1.67  fd_pseudo_cond                          0
% 7.69/1.67  AC symbols                              0
% 7.69/1.67  
% 7.69/1.67  ------ Schedule dynamic 5 is on 
% 7.69/1.67  
% 7.69/1.67  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  ------ 
% 7.69/1.67  Current options:
% 7.69/1.67  ------ 
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  ------ Proving...
% 7.69/1.67  
% 7.69/1.67  
% 7.69/1.67  % SZS status Theorem for theBenchmark.p
% 7.69/1.67  
% 7.69/1.67  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.69/1.67  
% 7.69/1.67  
%------------------------------------------------------------------------------