TSTP Solution File: SET651+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET651+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n019.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  : 600s
% DateTime : Tue Jul 19 00:52:54 EDT 2022

% Result   : Theorem 0.51s 51.68s
% Output   : CNFRefutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   76 (  18 unt;   0 def)
%            Number of atoms       :  297 (   0 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  364 ( 143   ~; 147   |;  25   &)
%                                         (   5 <=>;  44  =>;   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    :   15 (  15 usr;   6 con; 0-2 aty)
%            Number of variables   :  144 (   5 sgn  70   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox/solver/bin/../tmp/theBenchmark.p',p6) ).

fof(p26,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p26) ).

fof(prove_relset_1_13,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(X1,X3))
                 => ( subset(domain_of(X4),X2)
                   => ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',prove_relset_1_13) ).

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/sandbox/solver/bin/../tmp/theBenchmark.p',p4) ).

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/sandbox/solver/bin/../tmp/theBenchmark.p',p3) ).

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/sandbox/solver/bin/../tmp/theBenchmark.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/sandbox/solver/bin/../tmp/theBenchmark.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/sandbox/solver/bin/../tmp/theBenchmark.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/sandbox/solver/bin/../tmp/theBenchmark.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/sandbox/solver/bin/../tmp/theBenchmark.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/sandbox/solver/bin/../tmp/theBenchmark.p',p2) ).

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/sandbox/solver/bin/../tmp/theBenchmark.p',p20) ).

fof(p19,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ~ empty(power_set(X1))
        & ilf_type(power_set(X1),set_type) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p19) ).

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/sandbox/solver/bin/../tmp/theBenchmark.p',p15) ).

fof(c_0_14,plain,
    ! [X4,X5,X6] :
      ( ( subset(domain_of(X6),X4)
        | ~ ilf_type(X6,relation_type(X4,X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( subset(range_of(X6),X5)
        | ~ ilf_type(X6,relation_type(X4,X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])])]) ).

fof(c_0_15,plain,
    ! [X2] : ilf_type(X2,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(X1,X3))
                   => ( subset(domain_of(X4),X2)
                     => ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_13]) ).

fof(c_0_17,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
        | ilf_type(X7,relation_type(X5,X6))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ~ ilf_type(X8,relation_type(X5,X6))
        | ilf_type(X8,subset_type(cross_product(X5,X6)))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])])]) ).

fof(c_0_18,plain,
    ! [X5,X6,X7,X8] :
      ( ~ ilf_type(X5,set_type)
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X7,set_type)
      | ~ ilf_type(X8,set_type)
      | ~ subset(X5,X6)
      | ~ subset(X7,X8)
      | subset(cross_product(X5,X7),cross_product(X6,X8)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).

cnf(c_0_19,plain,
    ( subset(range_of(X3),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_21,negated_conjecture,
    ( ilf_type(esk12_0,set_type)
    & ilf_type(esk13_0,set_type)
    & ilf_type(esk14_0,set_type)
    & ilf_type(esk15_0,relation_type(esk12_0,esk14_0))
    & subset(domain_of(esk15_0),esk13_0)
    & ~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).

fof(c_0_22,plain,
    ! [X2] :
      ( ( relation_like(X2)
        | ~ ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) )
      & ( ilf_type(X2,set_type)
        | ~ ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) )
      & ( ~ relation_like(X2)
        | ~ ilf_type(X2,set_type)
        | ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).

fof(c_0_23,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X4,set_type)
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
      | relation_like(X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])])])]) ).

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

cnf(c_0_25,plain,
    ( subset(cross_product(X1,X2),cross_product(X3,X4))
    | ~ subset(X2,X4)
    | ~ subset(X1,X3)
    | ~ ilf_type(X4,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( subset(range_of(X1),X2)
    | ~ ilf_type(X1,relation_type(X3,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).

cnf(c_0_27,negated_conjecture,
    ilf_type(esk15_0,relation_type(esk12_0,esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ relation_like(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( relation_like(X1)
    | ~ 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_23]) ).

cnf(c_0_30,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_24,c_0_20]),c_0_20])]) ).

fof(c_0_31,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X4,set_type)
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X6,set_type)
      | ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).

cnf(c_0_32,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_25,c_0_20]),c_0_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_33,negated_conjecture,
    subset(range_of(esk15_0),esk14_0),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

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_28]) ).

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_29,c_0_20]),c_0_20])]) ).

cnf(c_0_36,negated_conjecture,
    ilf_type(esk15_0,subset_type(cross_product(esk12_0,esk14_0))),
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

fof(c_0_37,plain,
    ! [X4,X5,X6] :
      ( ( ~ subset(X4,X5)
        | ~ ilf_type(X6,set_type)
        | ~ member(X6,X4)
        | member(X6,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ilf_type(esk3_2(X4,X5),set_type)
        | subset(X4,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( member(esk3_2(X4,X5),X4)
        | subset(X4,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ~ member(esk3_2(X4,X5),X5)
        | subset(X4,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])])])])])]) ).

fof(c_0_38,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,power_set(X5))
        | ~ ilf_type(X6,set_type)
        | ~ member(X6,X4)
        | member(X6,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ilf_type(esk6_2(X4,X5),set_type)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( member(esk6_2(X4,X5),X4)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ~ member(esk6_2(X4,X5),X5)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])])])]) ).

cnf(c_0_39,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,negated_conjecture,
    ( subset(cross_product(X1,range_of(esk15_0)),cross_product(X2,esk14_0))
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    subset(domain_of(esk15_0),esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_42,plain,
    ! [X2] :
      ( ~ ilf_type(X2,binary_relation_type)
      | subset(X2,cross_product(domain_of(X2),range_of(X2))) ),
    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_20])]) ).

cnf(c_0_44,negated_conjecture,
    relation_like(esk15_0),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_45,plain,
    ( member(X3,X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(X3,X1)
    | ~ ilf_type(X3,set_type)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,plain,
    ( member(X1,power_set(X2))
    | member(esk6_2(X1,X2),X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,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_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_48,negated_conjecture,
    subset(cross_product(domain_of(esk15_0),range_of(esk15_0)),cross_product(esk13_0,esk14_0)),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_49,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_50,negated_conjecture,
    ilf_type(esk15_0,binary_relation_type),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_51,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_45,c_0_20]),c_0_20]),c_0_20])]) ).

cnf(c_0_52,plain,
    ( member(esk6_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_20]),c_0_20])]) ).

cnf(c_0_53,negated_conjecture,
    ( subset(X1,cross_product(esk13_0,esk14_0))
    | ~ subset(X1,cross_product(domain_of(esk15_0),range_of(esk15_0))) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_54,negated_conjecture,
    subset(esk15_0,cross_product(domain_of(esk15_0),range_of(esk15_0))),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

fof(c_0_55,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X3,member_type(X4))
        | member(X3,X4)
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ member(X3,X4)
        | ilf_type(X3,member_type(X4))
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p20])])])])])])]) ).

cnf(c_0_56,plain,
    ( member(X1,power_set(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(esk6_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_57,plain,
    ( member(esk6_2(X1,X2),X3)
    | member(X1,power_set(X2))
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    subset(esk15_0,cross_product(esk13_0,esk14_0)),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

fof(c_0_59,plain,
    ! [X2] :
      ( ( ~ empty(power_set(X2))
        | ~ ilf_type(X2,set_type) )
      & ( ilf_type(power_set(X2),set_type)
        | ~ ilf_type(X2,set_type) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p19])])])]) ).

fof(c_0_60,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X4,subset_type(X3))
        | ilf_type(X4,member_type(power_set(X3)))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ ilf_type(X4,member_type(power_set(X3)))
        | ilf_type(X4,subset_type(X3))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])])])]) ).

cnf(c_0_61,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_62,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk6_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_20]),c_0_20])]) ).

cnf(c_0_63,negated_conjecture,
    ( member(esk6_2(esk15_0,X1),cross_product(esk13_0,esk14_0))
    | member(esk15_0,power_set(X1)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_64,plain,
    ( ~ ilf_type(X1,set_type)
    | ~ empty(power_set(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_65,plain,
    ( ilf_type(X2,subset_type(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X2,member_type(power_set(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_66,plain,
    ( empty(X1)
    | ilf_type(X2,member_type(X1))
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_20]),c_0_20])]) ).

cnf(c_0_67,negated_conjecture,
    member(esk15_0,power_set(cross_product(esk13_0,esk14_0))),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_68,plain,
    ~ empty(power_set(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_20])]) ).

cnf(c_0_69,plain,
    ( ilf_type(X3,relation_type(X1,X2))
    | ~ 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_17]) ).

cnf(c_0_70,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_65,c_0_20]),c_0_20])]) ).

cnf(c_0_71,negated_conjecture,
    ilf_type(esk15_0,member_type(power_set(cross_product(esk13_0,esk14_0)))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_72,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_69,c_0_20]),c_0_20])]) ).

cnf(c_0_73,negated_conjecture,
    ilf_type(esk15_0,subset_type(cross_product(esk13_0,esk14_0))),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_74,negated_conjecture,
    ~ ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_75,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET651+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 08:09:53 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.35/23.41  eprover: CPU time limit exceeded, terminating
% 0.35/23.42  eprover: CPU time limit exceeded, terminating
% 0.35/23.42  eprover: CPU time limit exceeded, terminating
% 0.35/23.42  eprover: CPU time limit exceeded, terminating
% 0.48/46.43  eprover: CPU time limit exceeded, terminating
% 0.48/46.44  eprover: CPU time limit exceeded, terminating
% 0.48/46.44  eprover: CPU time limit exceeded, terminating
% 0.48/46.46  eprover: CPU time limit exceeded, terminating
% 0.51/51.68  # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.51/51.68  
% 0.51/51.68  # Failure: Resource limit exceeded (time)
% 0.51/51.68  # OLD status Res
% 0.51/51.68  # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.51/51.68  # Preprocessing time       : 0.016 s
% 0.51/51.68  # Running protocol protocol_eprover_230b6c199cce1dcf6700db59e75a93feb83d1bd9 for 23 seconds:
% 0.51/51.68  # SinE strategy is GSinE(CountFormulas,hypos,1.1,,01,20000,1.0)
% 0.51/51.68  # Preprocessing time       : 0.015 s
% 0.51/51.68  
% 0.51/51.68  # Failure: Out of unprocessed clauses!
% 0.51/51.68  # OLD status GaveUp
% 0.51/51.68  # Parsed axioms                        : 27
% 0.51/51.68  # Removed by relevancy pruning/SinE    : 20
% 0.51/51.68  # Initial clauses                      : 13
% 0.51/51.68  # Removed in clause preprocessing      : 0
% 0.51/51.68  # Initial clauses in saturation        : 13
% 0.51/51.68  # Processed clauses                    : 14
% 0.51/51.68  # ...of these trivial                  : 1
% 0.51/51.68  # ...subsumed                          : 0
% 0.51/51.68  # ...remaining for further processing  : 13
% 0.51/51.68  # Other redundant clauses eliminated   : 0
% 0.51/51.68  # Clauses deleted for lack of memory   : 0
% 0.51/51.68  # Backward-subsumed                    : 0
% 0.51/51.68  # Backward-rewritten                   : 3
% 0.51/51.68  # Generated clauses                    : 4
% 0.51/51.68  # ...of the previous two non-trivial   : 1
% 0.51/51.68  # Contextual simplify-reflections      : 0
% 0.51/51.68  # Paramodulations                      : 4
% 0.51/51.68  # Factorizations                       : 0
% 0.51/51.68  # Equation resolutions                 : 0
% 0.51/51.68  # Current number of processed clauses  : 10
% 0.51/51.68  #    Positive orientable unit clauses  : 5
% 0.51/51.68  #    Positive unorientable unit clauses: 0
% 0.51/51.68  #    Negative unit clauses             : 1
% 0.51/51.68  #    Non-unit-clauses                  : 4
% 0.51/51.68  # Current number of unprocessed clauses: 0
% 0.51/51.68  # ...number of literals in the above   : 0
% 0.51/51.68  # Current number of archived formulas  : 0
% 0.51/51.68  # Current number of archived clauses   : 3
% 0.51/51.68  # Clause-clause subsumption calls (NU) : 0
% 0.51/51.68  # Rec. Clause-clause subsumption calls : 0
% 0.51/51.68  # Non-unit clause-clause subsumptions  : 0
% 0.51/51.68  # Unit Clause-clause subsumption calls : 0
% 0.51/51.68  # Rewrite failures with RHS unbound    : 0
% 0.51/51.68  # BW rewrite match attempts            : 4
% 0.51/51.68  # BW rewrite match successes           : 3
% 0.51/51.68  # Condensation attempts                : 0
% 0.51/51.68  # Condensation successes               : 0
% 0.51/51.68  # Termbank termtop insertions          : 1258
% 0.51/51.68  
% 0.51/51.68  # -------------------------------------------------
% 0.51/51.68  # User time                : 0.013 s
% 0.51/51.68  # System time              : 0.003 s
% 0.51/51.68  # Total time               : 0.016 s
% 0.51/51.68  # Maximum resident set size: 2720 pages
% 0.51/51.68  # Running protocol protocol_eprover_48e494e00e0717ec2eabf59b73b2d711334607de for 23 seconds:
% 0.51/51.68  
% 0.51/51.68  # Failure: Resource limit exceeded (time)
% 0.51/51.68  # OLD status Res
% 0.51/51.68  # SinE strategy is GSinE(CountFormulas,hypos,1.1,,03,20000,1.0)
% 0.51/51.68  # Preprocessing time       : 0.016 s
% 0.51/51.68  # Running protocol protocol_eprover_33aa8a325940064c53b389b41203bb48a5cb5006 for 23 seconds:
% 0.51/51.68  # Preprocessing time       : 0.010 s
% 0.51/51.68  
% 0.51/51.68  # Proof found!
% 0.51/51.68  # SZS status Theorem
% 0.51/51.68  # SZS output start CNFRefutation
% See solution above
% 0.51/51.68  # Proof object total steps             : 76
% 0.51/51.68  # Proof object clause steps            : 47
% 0.51/51.68  # Proof object formula steps           : 29
% 0.51/51.68  # Proof object conjectures             : 20
% 0.51/51.68  # Proof object clause conjectures      : 17
% 0.51/51.68  # Proof object formula conjectures     : 3
% 0.51/51.68  # Proof object initial clauses used    : 18
% 0.51/51.68  # Proof object initial formulas used   : 14
% 0.51/51.68  # Proof object generating inferences   : 15
% 0.51/51.68  # Proof object simplifying inferences  : 44
% 0.51/51.68  # Training examples: 0 positive, 0 negative
% 0.51/51.68  # Parsed axioms                        : 27
% 0.51/51.68  # Removed by relevancy pruning/SinE    : 0
% 0.51/51.68  # Initial clauses                      : 54
% 0.51/51.68  # Removed in clause preprocessing      : 1
% 0.51/51.68  # Initial clauses in saturation        : 53
% 0.51/51.68  # Processed clauses                    : 87825
% 0.51/51.68  # ...of these trivial                  : 158
% 0.51/51.68  # ...subsumed                          : 80891
% 0.51/51.68  # ...remaining for further processing  : 6776
% 0.51/51.68  # Other redundant clauses eliminated   : 0
% 0.51/51.68  # Clauses deleted for lack of memory   : 168054
% 0.51/51.68  # Backward-subsumed                    : 71
% 0.51/51.68  # Backward-rewritten                   : 3
% 0.51/51.68  # Generated clauses                    : 369625
% 0.51/51.68  # ...of the previous two non-trivial   : 364349
% 0.51/51.68  # Contextual simplify-reflections      : 0
% 0.51/51.68  # Paramodulations                      : 369625
% 0.51/51.68  # Factorizations                       : 0
% 0.51/51.68  # Equation resolutions                 : 0
% 0.51/51.68  # Current number of processed clauses  : 6702
% 0.51/51.68  #    Positive orientable unit clauses  : 3524
% 0.51/51.68  #    Positive unorientable unit clauses: 0
% 0.51/51.68  #    Negative unit clauses             : 9
% 0.51/51.68  #    Non-unit-clauses                  : 3169
% 0.51/51.68  # Current number of unprocessed clauses: 108292
% 0.51/51.68  # ...number of literals in the above   : 192362
% 0.51/51.68  # Current number of archived formulas  : 0
% 0.51/51.68  # Current number of archived clauses   : 74
% 0.51/51.68  # Clause-clause subsumption calls (NU) : 3397392
% 0.51/51.68  # Rec. Clause-clause subsumption calls : 3182129
% 0.51/51.68  # Non-unit clause-clause subsumptions  : 80019
% 0.51/51.68  # Unit Clause-clause subsumption calls : 13177
% 0.51/51.68  # Rewrite failures with RHS unbound    : 0
% 0.51/51.68  # BW rewrite match attempts            : 226582
% 0.51/51.68  # BW rewrite match successes           : 3
% 0.51/51.68  # Condensation attempts                : 0
% 0.51/51.68  # Condensation successes               : 0
% 0.51/51.68  # Termbank termtop insertions          : 7798543
% 0.51/51.68  
% 0.51/51.68  # -------------------------------------------------
% 0.51/51.68  # User time                : 4.784 s
% 0.51/51.68  # System time              : 0.107 s
% 0.51/51.68  # Total time               : 4.891 s
% 0.51/51.68  # Maximum resident set size: 137748 pages
% 0.51/69.44  eprover: CPU time limit exceeded, terminating
% 0.51/69.45  eprover: CPU time limit exceeded, terminating
% 0.51/69.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46  eprover: No such file or directory
% 0.51/69.46  eprover: CPU time limit exceeded, terminating
% 0.51/69.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47  eprover: No such file or directory
% 0.51/69.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47  eprover: No such file or directory
% 0.51/69.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47  eprover: No such file or directory
% 0.51/69.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.48  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49  eprover: No such file or directory
% 0.51/69.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50  eprover: No such file or directory
% 0.51/69.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.50  eprover: No such file or directory
% 0.51/69.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.50  eprover: No such file or directory
% 0.51/69.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50  eprover: No such file or directory
% 0.51/69.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.50  eprover: No such file or directory
% 0.51/69.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.51  eprover: No such file or directory
% 0.51/69.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51  eprover: No such file or directory
% 0.51/69.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51  eprover: No such file or directory
% 0.51/69.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.51  eprover: No such file or directory
% 0.51/69.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51  eprover: No such file or directory
%------------------------------------------------------------------------------