TSTP Solution File: SET652+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:23:15 EDT 2023

% Result   : Theorem 21.85s 3.19s
% Output   : CNFRefutation 21.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   78 (  17 unt;   0 def)
%            Number of atoms       :  315 (   0 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  388 ( 151   ~; 154   |;  26   &)
%                                         (   8 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-2 aty)
%            Number of variables   :  152 (   5 sgn;  76   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p4,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p4) ).

fof(p26,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p26) ).

fof(prove_relset_1_14,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X3,X1))
                 => ( subset(range_of(X4),X2)
                   => ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',prove_relset_1_14) ).

fof(p3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ( ( subset(X1,X2)
                      & subset(X3,X4) )
                   => subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p3) ).

fof(p6,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ( subset(domain_of(X3),X1)
                & subset(range_of(X3),X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p6) ).

fof(p13,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ilf_type(X1,binary_relation_type)
      <=> ( relation_like(X1)
          & ilf_type(X1,set_type) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p13) ).

fof(p23,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,subset_type(cross_product(X1,X2)))
             => relation_like(X3) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p23) ).

fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( ( subset(X1,X2)
                  & subset(X2,X3) )
               => subset(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p1) ).

fof(p9,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( subset(X1,X2)
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p9) ).

fof(p18,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X1,power_set(X2))
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p18) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,binary_relation_type)
     => subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p2) ).

fof(p24,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p24) ).

fof(p20,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p20) ).

fof(p15,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,subset_type(X1))
          <=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p',p15) ).

fof(c_0_14,plain,
    ! [X10,X11,X12,X13] :
      ( ( ~ ilf_type(X12,subset_type(cross_product(X10,X11)))
        | ilf_type(X12,relation_type(X10,X11))
        | ~ ilf_type(X11,set_type)
        | ~ ilf_type(X10,set_type) )
      & ( ~ ilf_type(X13,relation_type(X10,X11))
        | ilf_type(X13,subset_type(cross_product(X10,X11)))
        | ~ ilf_type(X11,set_type)
        | ~ ilf_type(X10,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).

fof(c_0_15,plain,
    ! [X9] : ilf_type(X9,set_type),
    inference(variable_rename,[status(thm)],[p26]) ).

fof(c_0_16,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,set_type)
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X3,X1))
                   => ( subset(range_of(X4),X2)
                     => ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_14]) ).

fof(c_0_17,plain,
    ! [X23,X24,X25,X26] :
      ( ~ ilf_type(X23,set_type)
      | ~ ilf_type(X24,set_type)
      | ~ ilf_type(X25,set_type)
      | ~ ilf_type(X26,set_type)
      | ~ subset(X23,X24)
      | ~ subset(X25,X26)
      | subset(cross_product(X23,X25),cross_product(X24,X26)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).

fof(c_0_18,plain,
    ! [X17,X18,X19] :
      ( ( subset(domain_of(X19),X17)
        | ~ ilf_type(X19,relation_type(X17,X18))
        | ~ ilf_type(X18,set_type)
        | ~ ilf_type(X17,set_type) )
      & ( subset(range_of(X19),X18)
        | ~ ilf_type(X19,relation_type(X17,X18))
        | ~ ilf_type(X18,set_type)
        | ~ ilf_type(X17,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).

fof(c_0_19,plain,
    ! [X47] :
      ( ( relation_like(X47)
        | ~ ilf_type(X47,binary_relation_type)
        | ~ ilf_type(X47,set_type) )
      & ( ilf_type(X47,set_type)
        | ~ ilf_type(X47,binary_relation_type)
        | ~ ilf_type(X47,set_type) )
      & ( ~ relation_like(X47)
        | ~ ilf_type(X47,set_type)
        | ilf_type(X47,binary_relation_type)
        | ~ ilf_type(X47,set_type) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).

fof(c_0_20,plain,
    ! [X37,X38,X39] :
      ( ~ ilf_type(X37,set_type)
      | ~ ilf_type(X38,set_type)
      | ~ ilf_type(X39,subset_type(cross_product(X37,X38)))
      | relation_like(X39) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).

cnf(c_0_21,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_23,negated_conjecture,
    ( ilf_type(esk1_0,set_type)
    & ilf_type(esk2_0,set_type)
    & ilf_type(esk3_0,set_type)
    & ilf_type(esk4_0,relation_type(esk3_0,esk1_0))
    & subset(range_of(esk4_0),esk2_0)
    & ~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

cnf(c_0_24,plain,
    ( subset(cross_product(X1,X3),cross_product(X2,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | ~ subset(X1,X2)
    | ~ subset(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( subset(domain_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_27,plain,
    ( relation_like(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).

cnf(c_0_29,negated_conjecture,
    ilf_type(esk4_0,relation_type(esk3_0,esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_30,plain,
    ! [X20,X21,X22] :
      ( ~ ilf_type(X20,set_type)
      | ~ ilf_type(X21,set_type)
      | ~ ilf_type(X22,set_type)
      | ~ subset(X20,X21)
      | ~ subset(X21,X22)
      | subset(X20,X22) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).

cnf(c_0_31,plain,
    ( subset(cross_product(X1,X2),cross_product(X3,X4))
    | ~ subset(X2,X4)
    | ~ subset(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).

cnf(c_0_32,negated_conjecture,
    subset(range_of(esk4_0),esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,plain,
    ( subset(domain_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_22])]) ).

cnf(c_0_34,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | ~ ilf_type(X1,set_type) ),
    inference(cn,[status(thm)],[c_0_26]) ).

cnf(c_0_35,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_22]),c_0_22])]) ).

cnf(c_0_36,negated_conjecture,
    ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk1_0))),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_37,plain,
    ! [X27,X28,X29] :
      ( ( ~ subset(X27,X28)
        | ~ ilf_type(X29,set_type)
        | ~ member(X29,X27)
        | member(X29,X28)
        | ~ ilf_type(X28,set_type)
        | ~ ilf_type(X27,set_type) )
      & ( ilf_type(esk6_2(X27,X28),set_type)
        | subset(X27,X28)
        | ~ ilf_type(X28,set_type)
        | ~ ilf_type(X27,set_type) )
      & ( member(esk6_2(X27,X28),X27)
        | subset(X27,X28)
        | ~ ilf_type(X28,set_type)
        | ~ ilf_type(X27,set_type) )
      & ( ~ member(esk6_2(X27,X28),X28)
        | subset(X27,X28)
        | ~ ilf_type(X28,set_type)
        | ~ ilf_type(X27,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])])])]) ).

fof(c_0_38,plain,
    ! [X53,X54,X55] :
      ( ( ~ member(X53,power_set(X54))
        | ~ ilf_type(X55,set_type)
        | ~ member(X55,X53)
        | member(X55,X54)
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,set_type) )
      & ( ilf_type(esk11_2(X53,X54),set_type)
        | member(X53,power_set(X54))
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,set_type) )
      & ( member(esk11_2(X53,X54),X53)
        | member(X53,power_set(X54))
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,set_type) )
      & ( ~ member(esk11_2(X53,X54),X54)
        | member(X53,power_set(X54))
        | ~ ilf_type(X54,set_type)
        | ~ ilf_type(X53,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])]) ).

cnf(c_0_39,plain,
    ( subset(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_40,negated_conjecture,
    ( subset(cross_product(X1,range_of(esk4_0)),cross_product(X2,esk2_0))
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_41,negated_conjecture,
    subset(domain_of(esk4_0),esk3_0),
    inference(spm,[status(thm)],[c_0_33,c_0_29]) ).

fof(c_0_42,plain,
    ! [X42] :
      ( ~ ilf_type(X42,binary_relation_type)
      | subset(X42,cross_product(domain_of(X42),range_of(X42))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).

cnf(c_0_43,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22])]) ).

cnf(c_0_44,negated_conjecture,
    relation_like(esk4_0),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

fof(c_0_45,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[p24]) ).

cnf(c_0_46,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_47,plain,
    ( member(esk11_2(X1,X2),X1)
    | member(X1,power_set(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_22]),c_0_22]),c_0_22])]) ).

cnf(c_0_49,negated_conjecture,
    subset(cross_product(domain_of(esk4_0),range_of(esk4_0)),cross_product(esk3_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_50,plain,
    ( subset(X1,cross_product(domain_of(X1),range_of(X1)))
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_51,negated_conjecture,
    ilf_type(esk4_0,binary_relation_type),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

fof(c_0_52,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[p20]) ).

fof(c_0_53,plain,
    ! [X44,X45] :
      ( ( ~ empty(X44)
        | ~ ilf_type(X45,set_type)
        | ~ member(X45,X44)
        | ~ ilf_type(X44,set_type) )
      & ( ilf_type(esk8_1(X44),set_type)
        | empty(X44)
        | ~ ilf_type(X44,set_type) )
      & ( member(esk8_1(X44),X44)
        | empty(X44)
        | ~ ilf_type(X44,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).

cnf(c_0_54,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_22]),c_0_22]),c_0_22])]) ).

cnf(c_0_55,plain,
    ( member(esk11_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_22]),c_0_22])]) ).

cnf(c_0_56,negated_conjecture,
    ( subset(X1,cross_product(esk3_0,esk2_0))
    | ~ subset(X1,cross_product(domain_of(esk4_0),range_of(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_57,negated_conjecture,
    subset(esk4_0,cross_product(domain_of(esk4_0),range_of(esk4_0))),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

fof(c_0_58,plain,
    ! [X49,X50] :
      ( ( ~ ilf_type(X49,member_type(X50))
        | member(X49,X50)
        | empty(X50)
        | ~ ilf_type(X50,set_type)
        | ~ ilf_type(X49,set_type) )
      & ( ~ member(X49,X50)
        | ilf_type(X49,member_type(X50))
        | empty(X50)
        | ~ ilf_type(X50,set_type)
        | ~ ilf_type(X49,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).

cnf(c_0_59,plain,
    ( ~ empty(X1)
    | ~ ilf_type(X2,set_type)
    | ~ member(X2,X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_60,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk11_2(X1,X2),X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_61,plain,
    ( member(esk11_2(X1,X2),X3)
    | member(X1,power_set(X2))
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    subset(esk4_0,cross_product(esk3_0,esk2_0)),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

fof(c_0_63,plain,
    ! [X33,X34] :
      ( ( ~ ilf_type(X34,subset_type(X33))
        | ilf_type(X34,member_type(power_set(X33)))
        | ~ ilf_type(X34,set_type)
        | ~ ilf_type(X33,set_type) )
      & ( ~ ilf_type(X34,member_type(power_set(X33)))
        | ilf_type(X34,subset_type(X33))
        | ~ ilf_type(X34,set_type)
        | ~ ilf_type(X33,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).

cnf(c_0_64,plain,
    ( ilf_type(X1,member_type(X2))
    | empty(X2)
    | ~ member(X1,X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_65,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_22])]) ).

cnf(c_0_66,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk11_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22]),c_0_22])]) ).

cnf(c_0_67,negated_conjecture,
    ( member(esk11_2(esk4_0,X1),cross_product(esk3_0,esk2_0))
    | member(esk4_0,power_set(X1)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_68,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_69,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_22]),c_0_22])]),c_0_65]) ).

cnf(c_0_70,negated_conjecture,
    member(esk4_0,power_set(cross_product(esk3_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_71,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_72,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,member_type(power_set(X2))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_22]),c_0_22])]) ).

cnf(c_0_73,negated_conjecture,
    ilf_type(esk4_0,member_type(power_set(cross_product(esk3_0,esk2_0)))),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_74,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_22]),c_0_22])]) ).

cnf(c_0_75,negated_conjecture,
    ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_76,negated_conjecture,
    ~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_77,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.09/0.30  % Computer : n023.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 2400
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon Oct  2 17:27:07 EDT 2023
% 0.09/0.30  % CPUTime    : 
% 0.14/0.39  Running first-order model finding
% 0.14/0.39  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.tBxvXpr5Op/E---3.1_21596.p
% 21.85/3.19  # Version: 3.1pre001
% 21.85/3.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 21.85/3.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.85/3.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 21.85/3.19  # Starting new_bool_3 with 300s (1) cores
% 21.85/3.19  # Starting new_bool_1 with 300s (1) cores
% 21.85/3.19  # Starting sh5l with 300s (1) cores
% 21.85/3.19  # new_bool_1 with pid 21675 completed with status 0
% 21.85/3.19  # Result found by new_bool_1
% 21.85/3.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 21.85/3.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.85/3.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 21.85/3.19  # Starting new_bool_3 with 300s (1) cores
% 21.85/3.19  # Starting new_bool_1 with 300s (1) cores
% 21.85/3.19  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 21.85/3.19  # Search class: FGHSF-FFMM21-SFFFFFNN
% 21.85/3.19  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 21.85/3.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 21.85/3.19  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 21678 completed with status 0
% 21.85/3.19  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 21.85/3.19  # Preprocessing class: FSMSSMSSSSSNFFN.
% 21.85/3.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.85/3.19  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 21.85/3.19  # Starting new_bool_3 with 300s (1) cores
% 21.85/3.19  # Starting new_bool_1 with 300s (1) cores
% 21.85/3.19  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 21.85/3.19  # Search class: FGHSF-FFMM21-SFFFFFNN
% 21.85/3.19  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 21.85/3.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 21.85/3.19  # Preprocessing time       : 0.001 s
% 21.85/3.19  # Presaturation interreduction done
% 21.85/3.19  
% 21.85/3.19  # Proof found!
% 21.85/3.19  # SZS status Theorem
% 21.85/3.19  # SZS output start CNFRefutation
% See solution above
% 21.85/3.19  # Parsed axioms                        : 27
% 21.85/3.19  # Removed by relevancy pruning/SinE    : 2
% 21.85/3.19  # Initial clauses                      : 50
% 21.85/3.19  # Removed in clause preprocessing      : 1
% 21.85/3.19  # Initial clauses in saturation        : 49
% 21.85/3.19  # Processed clauses                    : 12927
% 21.85/3.19  # ...of these trivial                  : 125
% 21.85/3.19  # ...subsumed                          : 9270
% 21.85/3.19  # ...remaining for further processing  : 3532
% 21.85/3.19  # Other redundant clauses eliminated   : 0
% 21.85/3.19  # Clauses deleted for lack of memory   : 0
% 21.85/3.19  # Backward-subsumed                    : 163
% 21.85/3.19  # Backward-rewritten                   : 4
% 21.85/3.19  # Generated clauses                    : 209720
% 21.85/3.19  # ...of the previous two non-redundant : 207943
% 21.85/3.19  # ...aggressively subsumed             : 0
% 21.85/3.19  # Contextual simplify-reflections      : 4
% 21.85/3.19  # Paramodulations                      : 209720
% 21.85/3.19  # Factorizations                       : 0
% 21.85/3.19  # NegExts                              : 0
% 21.85/3.19  # Equation resolutions                 : 0
% 21.85/3.19  # Total rewrite steps                  : 2077
% 21.85/3.19  # Propositional unsat checks           : 0
% 21.85/3.19  #    Propositional check models        : 0
% 21.85/3.19  #    Propositional check unsatisfiable : 0
% 21.85/3.19  #    Propositional clauses             : 0
% 21.85/3.19  #    Propositional clauses after purity: 0
% 21.85/3.19  #    Propositional unsat core size     : 0
% 21.85/3.19  #    Propositional preprocessing time  : 0.000
% 21.85/3.19  #    Propositional encoding time       : 0.000
% 21.85/3.19  #    Propositional solver time         : 0.000
% 21.85/3.19  #    Success case prop preproc time    : 0.000
% 21.85/3.19  #    Success case prop encoding time   : 0.000
% 21.85/3.19  #    Success case prop solver time     : 0.000
% 21.85/3.19  # Current number of processed clauses  : 3329
% 21.85/3.19  #    Positive orientable unit clauses  : 937
% 21.85/3.19  #    Positive unorientable unit clauses: 0
% 21.85/3.19  #    Negative unit clauses             : 9
% 21.85/3.19  #    Non-unit-clauses                  : 2383
% 21.85/3.19  # Current number of unprocessed clauses: 195070
% 21.85/3.19  # ...number of literals in the above   : 309197
% 21.85/3.19  # Current number of archived formulas  : 0
% 21.85/3.19  # Current number of archived clauses   : 203
% 21.85/3.19  # Clause-clause subsumption calls (NU) : 492429
% 21.85/3.19  # Rec. Clause-clause subsumption calls : 449665
% 21.85/3.19  # Non-unit clause-clause subsumptions  : 8923
% 21.85/3.19  # Unit Clause-clause subsumption calls : 47063
% 21.85/3.19  # Rewrite failures with RHS unbound    : 0
% 21.85/3.19  # BW rewrite match attempts            : 6629
% 21.85/3.19  # BW rewrite match successes           : 4
% 21.85/3.19  # Condensation attempts                : 0
% 21.85/3.19  # Condensation successes               : 0
% 21.85/3.19  # Termbank termtop insertions          : 3556204
% 21.85/3.19  
% 21.85/3.19  # -------------------------------------------------
% 21.85/3.19  # User time                : 2.590 s
% 21.85/3.19  # System time              : 0.107 s
% 21.85/3.19  # Total time               : 2.697 s
% 21.85/3.19  # Maximum resident set size: 1856 pages
% 21.85/3.19  
% 21.85/3.19  # -------------------------------------------------
% 21.85/3.19  # User time                : 2.592 s
% 21.85/3.19  # System time              : 0.109 s
% 21.85/3.19  # Total time               : 2.701 s
% 21.85/3.19  # Maximum resident set size: 1732 pages
% 21.85/3.19  % E---3.1 exiting
%------------------------------------------------------------------------------