TSTP Solution File: SEU339+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SEU339+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:26:03 EDT 2023

% Result   : Theorem 0.23s 0.53s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   79 (  28 unt;   0 def)
%            Number of atoms       :  218 (  14 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  232 (  93   ~;  88   |;  28   &)
%                                         (   4 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :  113 (  10 sgn;  67   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t25_orders_2,conjecture,
    ! [X1] :
      ( ( antisymmetric_relstr(X1)
        & rel_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( ( related(X1,X2,X3)
                  & related(X1,X3,X2) )
               => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t25_orders_2) ).

fof(dt_u1_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',dt_u1_orders_2) ).

fof(d9_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ! [X3] :
              ( element(X3,the_carrier(X1))
             => ( related(X1,X2,X3)
              <=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',d9_orders_2) ).

fof(dt_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => element(X3,powerset(cartesian_product2(X1,X2))) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',dt_m2_relset_1) ).

fof(cc1_relset_1,axiom,
    ! [X1,X2,X3] :
      ( element(X3,powerset(cartesian_product2(X1,X2)))
     => relation(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',cc1_relset_1) ).

fof(d4_relat_2,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( is_antisymmetric_in(X1,X2)
        <=> ! [X3,X4] :
              ( ( in(X3,X2)
                & in(X4,X2)
                & in(ordered_pair(X3,X4),X1)
                & in(ordered_pair(X4,X3),X1) )
             => X3 = X4 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',d4_relat_2) ).

fof(d6_orders_2,axiom,
    ! [X1] :
      ( rel_str(X1)
     => ( antisymmetric_relstr(X1)
      <=> is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',d6_orders_2) ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t5_subset) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',existence_m1_subset_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t2_subset) ).

fof(t4_subset,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t4_subset) ).

fof(t8_boole,axiom,
    ! [X1,X2] :
      ~ ( empty(X1)
        & X1 != X2
        & empty(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t8_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',rc1_xboole_0) ).

fof(t106_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p',t106_zfmisc_1) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X1] :
        ( ( antisymmetric_relstr(X1)
          & rel_str(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(X1))
           => ! [X3] :
                ( element(X3,the_carrier(X1))
               => ( ( related(X1,X2,X3)
                    & related(X1,X3,X2) )
                 => X2 = X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[t25_orders_2]) ).

fof(c_0_15,plain,
    ! [X27] :
      ( ~ rel_str(X27)
      | relation_of2_as_subset(the_InternalRel(X27),the_carrier(X27),the_carrier(X27)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).

fof(c_0_16,negated_conjecture,
    ( antisymmetric_relstr(esk1_0)
    & rel_str(esk1_0)
    & element(esk2_0,the_carrier(esk1_0))
    & element(esk3_0,the_carrier(esk1_0))
    & related(esk1_0,esk2_0,esk3_0)
    & related(esk1_0,esk3_0,esk2_0)
    & esk2_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).

fof(c_0_17,plain,
    ! [X8,X9,X10] :
      ( ( ~ related(X8,X9,X10)
        | in(ordered_pair(X9,X10),the_InternalRel(X8))
        | ~ element(X10,the_carrier(X8))
        | ~ element(X9,the_carrier(X8))
        | ~ rel_str(X8) )
      & ( ~ in(ordered_pair(X9,X10),the_InternalRel(X8))
        | related(X8,X9,X10)
        | ~ element(X10,the_carrier(X8))
        | ~ element(X9,the_carrier(X8))
        | ~ rel_str(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).

fof(c_0_18,plain,
    ! [X43,X44,X45] :
      ( ~ relation_of2_as_subset(X45,X43,X44)
      | element(X45,powerset(cartesian_product2(X43,X44))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).

cnf(c_0_19,plain,
    ( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    rel_str(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( in(ordered_pair(X2,X3),the_InternalRel(X1))
    | ~ related(X1,X2,X3)
    | ~ element(X3,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    element(esk3_0,the_carrier(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_23,plain,
    ! [X58,X59,X60] :
      ( ~ element(X60,powerset(cartesian_product2(X58,X59)))
      | relation(X60) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).

cnf(c_0_24,plain,
    ( element(X1,powerset(cartesian_product2(X2,X3)))
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    relation_of2_as_subset(the_InternalRel(esk1_0),the_carrier(esk1_0),the_carrier(esk1_0)),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_26,plain,
    ! [X49,X50,X51,X52,X53] :
      ( ( ~ is_antisymmetric_in(X49,X50)
        | ~ in(X51,X50)
        | ~ in(X52,X50)
        | ~ in(ordered_pair(X51,X52),X49)
        | ~ in(ordered_pair(X52,X51),X49)
        | X51 = X52
        | ~ relation(X49) )
      & ( in(esk11_2(X49,X53),X53)
        | is_antisymmetric_in(X49,X53)
        | ~ relation(X49) )
      & ( in(esk12_2(X49,X53),X53)
        | is_antisymmetric_in(X49,X53)
        | ~ relation(X49) )
      & ( in(ordered_pair(esk11_2(X49,X53),esk12_2(X49,X53)),X49)
        | is_antisymmetric_in(X49,X53)
        | ~ relation(X49) )
      & ( in(ordered_pair(esk12_2(X49,X53),esk11_2(X49,X53)),X49)
        | is_antisymmetric_in(X49,X53)
        | ~ relation(X49) )
      & ( esk11_2(X49,X53) != esk12_2(X49,X53)
        | is_antisymmetric_in(X49,X53)
        | ~ relation(X49) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_2])])])])])]) ).

cnf(c_0_27,negated_conjecture,
    ( in(ordered_pair(X1,esk3_0),the_InternalRel(esk1_0))
    | ~ related(esk1_0,X1,esk3_0)
    | ~ element(X1,the_carrier(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20])]) ).

cnf(c_0_28,negated_conjecture,
    related(esk1_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_29,negated_conjecture,
    element(esk2_0,the_carrier(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_30,plain,
    ( relation(X1)
    | ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_31,negated_conjecture,
    element(the_InternalRel(esk1_0),powerset(cartesian_product2(the_carrier(esk1_0),the_carrier(esk1_0)))),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_32,plain,
    ( X3 = X4
    | ~ is_antisymmetric_in(X1,X2)
    | ~ in(X3,X2)
    | ~ in(X4,X2)
    | ~ in(ordered_pair(X3,X4),X1)
    | ~ in(ordered_pair(X4,X3),X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    in(ordered_pair(esk2_0,esk3_0),the_InternalRel(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_34,negated_conjecture,
    relation(the_InternalRel(esk1_0)),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_36,negated_conjecture,
    ( in(ordered_pair(X1,esk2_0),the_InternalRel(esk1_0))
    | ~ related(esk1_0,X1,esk2_0)
    | ~ element(X1,the_carrier(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_29]),c_0_20])]) ).

cnf(c_0_37,negated_conjecture,
    related(esk1_0,esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_38,plain,
    ! [X29] :
      ( ( ~ antisymmetric_relstr(X29)
        | is_antisymmetric_in(the_InternalRel(X29),the_carrier(X29))
        | ~ rel_str(X29) )
      & ( ~ is_antisymmetric_in(the_InternalRel(X29),the_carrier(X29))
        | antisymmetric_relstr(X29)
        | ~ rel_str(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_orders_2])])]) ).

fof(c_0_39,plain,
    ! [X24,X25,X26] :
      ( ~ in(X24,X25)
      | ~ element(X25,powerset(X26))
      | ~ empty(X26) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

fof(c_0_40,plain,
    ! [X11] : element(esk4_1(X11),X11),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_41,plain,
    ! [X19,X20] :
      ( ~ element(X19,X20)
      | empty(X20)
      | in(X19,X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_42,negated_conjecture,
    ( ~ is_antisymmetric_in(the_InternalRel(esk1_0),X1)
    | ~ in(ordered_pair(esk3_0,esk2_0),the_InternalRel(esk1_0))
    | ~ in(esk2_0,X1)
    | ~ in(esk3_0,X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    in(ordered_pair(esk3_0,esk2_0),the_InternalRel(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_22])]) ).

cnf(c_0_44,plain,
    ( is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1))
    | ~ antisymmetric_relstr(X1)
    | ~ rel_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    antisymmetric_relstr(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_46,plain,
    ( ~ in(X1,X2)
    | ~ element(X2,powerset(X3))
    | ~ empty(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,plain,
    element(esk4_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_48,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

fof(c_0_49,plain,
    ! [X21,X22,X23] :
      ( ~ in(X21,X22)
      | ~ element(X22,powerset(X23))
      | element(X21,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).

fof(c_0_50,plain,
    ! [X40,X41] :
      ( ~ empty(X40)
      | X40 = X41
      | ~ empty(X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).

fof(c_0_51,plain,
    empty(esk8_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

cnf(c_0_52,negated_conjecture,
    ( ~ is_antisymmetric_in(the_InternalRel(esk1_0),X1)
    | ~ in(esk2_0,X1)
    | ~ in(esk3_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).

cnf(c_0_53,negated_conjecture,
    is_antisymmetric_in(the_InternalRel(esk1_0),the_carrier(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_20])]) ).

cnf(c_0_54,plain,
    ( ~ empty(X1)
    | ~ in(X2,esk4_1(powerset(X1))) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_55,plain,
    ( empty(X1)
    | in(esk4_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_47]) ).

cnf(c_0_56,plain,
    ( element(X1,X3)
    | ~ in(X1,X2)
    | ~ element(X2,powerset(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_57,plain,
    ( X1 = X2
    | ~ empty(X1)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,plain,
    empty(esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ in(esk2_0,the_carrier(esk1_0))
    | ~ in(esk3_0,the_carrier(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_60,negated_conjecture,
    ( empty(the_carrier(esk1_0))
    | in(esk2_0,the_carrier(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_29]) ).

cnf(c_0_61,negated_conjecture,
    ( empty(the_carrier(esk1_0))
    | in(esk3_0,the_carrier(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_22]) ).

cnf(c_0_62,plain,
    ( empty(esk4_1(powerset(X1)))
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_63,negated_conjecture,
    ( element(X1,cartesian_product2(the_carrier(esk1_0),the_carrier(esk1_0)))
    | ~ in(X1,the_InternalRel(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_56,c_0_31]) ).

cnf(c_0_64,plain,
    ( X1 = esk8_0
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_65,negated_conjecture,
    empty(the_carrier(esk1_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

cnf(c_0_66,plain,
    empty(esk4_1(powerset(esk8_0))),
    inference(spm,[status(thm)],[c_0_62,c_0_58]) ).

fof(c_0_67,plain,
    ! [X34,X35,X36,X37] :
      ( ( in(X34,X36)
        | ~ in(ordered_pair(X34,X35),cartesian_product2(X36,X37)) )
      & ( in(X35,X37)
        | ~ in(ordered_pair(X34,X35),cartesian_product2(X36,X37)) )
      & ( ~ in(X34,X36)
        | ~ in(X35,X37)
        | in(ordered_pair(X34,X35),cartesian_product2(X36,X37)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).

cnf(c_0_68,negated_conjecture,
    element(ordered_pair(esk2_0,esk3_0),cartesian_product2(the_carrier(esk1_0),the_carrier(esk1_0))),
    inference(spm,[status(thm)],[c_0_63,c_0_33]) ).

cnf(c_0_69,negated_conjecture,
    the_carrier(esk1_0) = esk8_0,
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_70,plain,
    esk4_1(powerset(esk8_0)) = esk8_0,
    inference(spm,[status(thm)],[c_0_64,c_0_66]) ).

cnf(c_0_71,negated_conjecture,
    ( ~ empty(cartesian_product2(the_carrier(esk1_0),the_carrier(esk1_0)))
    | ~ in(X1,the_InternalRel(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_46,c_0_31]) ).

cnf(c_0_72,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_73,negated_conjecture,
    ( empty(cartesian_product2(esk8_0,esk8_0))
    | in(ordered_pair(esk2_0,esk3_0),cartesian_product2(esk8_0,esk8_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_68]),c_0_69]),c_0_69]),c_0_69]),c_0_69]) ).

cnf(c_0_74,plain,
    ~ in(X1,esk8_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_70]),c_0_58])]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ empty(cartesian_product2(esk8_0,esk8_0))
    | ~ in(X1,the_InternalRel(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_69]) ).

cnf(c_0_76,negated_conjecture,
    empty(cartesian_product2(esk8_0,esk8_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).

cnf(c_0_77,negated_conjecture,
    ~ in(X1,the_InternalRel(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).

cnf(c_0_78,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_33,c_0_77]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SEU339+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15  % Command    : run_E %s %d THM
% 0.16/0.36  % Computer : n002.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 2400
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon Oct  2 09:27:14 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.23/0.50  Running first-order theorem proving
% 0.23/0.50  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.nXz5xvXYzY/E---3.1_25371.p
% 0.23/0.53  # Version: 3.1pre001
% 0.23/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.23/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.23/0.53  # Starting sh5l with 300s (1) cores
% 0.23/0.53  # new_bool_3 with pid 25451 completed with status 0
% 0.23/0.53  # Result found by new_bool_3
% 0.23/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.23/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.53  # Search class: FGHSM-FFMM21-SFFFFFNN
% 0.23/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.53  # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 163s (1) cores
% 0.23/0.53  # G-E--_200_B02_F1_SE_CS_SP_PI_S0S with pid 25456 completed with status 0
% 0.23/0.53  # Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S0S
% 0.23/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.23/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.53  # Search class: FGHSM-FFMM21-SFFFFFNN
% 0.23/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.53  # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 163s (1) cores
% 0.23/0.53  # Preprocessing time       : 0.002 s
% 0.23/0.53  
% 0.23/0.53  # Proof found!
% 0.23/0.53  # SZS status Theorem
% 0.23/0.53  # SZS output start CNFRefutation
% See solution above
% 0.23/0.53  # Parsed axioms                        : 46
% 0.23/0.53  # Removed by relevancy pruning/SinE    : 22
% 0.23/0.53  # Initial clauses                      : 41
% 0.23/0.53  # Removed in clause preprocessing      : 0
% 0.23/0.53  # Initial clauses in saturation        : 41
% 0.23/0.53  # Processed clauses                    : 152
% 0.23/0.53  # ...of these trivial                  : 5
% 0.23/0.53  # ...subsumed                          : 20
% 0.23/0.53  # ...remaining for further processing  : 127
% 0.23/0.53  # Other redundant clauses eliminated   : 0
% 0.23/0.53  # Clauses deleted for lack of memory   : 0
% 0.23/0.53  # Backward-subsumed                    : 8
% 0.23/0.53  # Backward-rewritten                   : 25
% 0.23/0.53  # Generated clauses                    : 244
% 0.23/0.53  # ...of the previous two non-redundant : 216
% 0.23/0.53  # ...aggressively subsumed             : 0
% 0.23/0.53  # Contextual simplify-reflections      : 1
% 0.23/0.53  # Paramodulations                      : 242
% 0.23/0.53  # Factorizations                       : 0
% 0.23/0.53  # NegExts                              : 0
% 0.23/0.53  # Equation resolutions                 : 0
% 0.23/0.53  # Total rewrite steps                  : 110
% 0.23/0.53  # Propositional unsat checks           : 0
% 0.23/0.53  #    Propositional check models        : 0
% 0.23/0.53  #    Propositional check unsatisfiable : 0
% 0.23/0.53  #    Propositional clauses             : 0
% 0.23/0.53  #    Propositional clauses after purity: 0
% 0.23/0.53  #    Propositional unsat core size     : 0
% 0.23/0.53  #    Propositional preprocessing time  : 0.000
% 0.23/0.53  #    Propositional encoding time       : 0.000
% 0.23/0.53  #    Propositional solver time         : 0.000
% 0.23/0.53  #    Success case prop preproc time    : 0.000
% 0.23/0.53  #    Success case prop encoding time   : 0.000
% 0.23/0.53  #    Success case prop solver time     : 0.000
% 0.23/0.53  # Current number of processed clauses  : 92
% 0.23/0.53  #    Positive orientable unit clauses  : 37
% 0.23/0.53  #    Positive unorientable unit clauses: 0
% 0.23/0.53  #    Negative unit clauses             : 11
% 0.23/0.53  #    Non-unit-clauses                  : 44
% 0.23/0.53  # Current number of unprocessed clauses: 97
% 0.23/0.53  # ...number of literals in the above   : 213
% 0.23/0.53  # Current number of archived formulas  : 0
% 0.23/0.53  # Current number of archived clauses   : 35
% 0.23/0.53  # Clause-clause subsumption calls (NU) : 585
% 0.23/0.53  # Rec. Clause-clause subsumption calls : 437
% 0.23/0.53  # Non-unit clause-clause subsumptions  : 8
% 0.23/0.53  # Unit Clause-clause subsumption calls : 320
% 0.23/0.53  # Rewrite failures with RHS unbound    : 0
% 0.23/0.53  # BW rewrite match attempts            : 9
% 0.23/0.53  # BW rewrite match successes           : 6
% 0.23/0.53  # Condensation attempts                : 0
% 0.23/0.53  # Condensation successes               : 0
% 0.23/0.53  # Termbank termtop insertions          : 5668
% 0.23/0.53  
% 0.23/0.53  # -------------------------------------------------
% 0.23/0.53  # User time                : 0.012 s
% 0.23/0.53  # System time              : 0.006 s
% 0.23/0.53  # Total time               : 0.018 s
% 0.23/0.53  # Maximum resident set size: 1864 pages
% 0.23/0.53  
% 0.23/0.53  # -------------------------------------------------
% 0.23/0.53  # User time                : 0.014 s
% 0.23/0.53  # System time              : 0.008 s
% 0.23/0.53  # Total time               : 0.022 s
% 0.23/0.53  # Maximum resident set size: 1712 pages
% 0.23/0.53  % E---3.1 exiting
% 0.23/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------