TSTP Solution File: SEU078+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n003.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 09:16:43 EDT 2022

% Result   : Theorem 0.27s 9.46s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  119 (  25 unt;   0 def)
%            Number of atoms       :  393 (  86 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  469 ( 195   ~; 204   |;  43   &)
%                                         (  11 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   3 con; 0-3 aty)
%            Number of variables   :  217 (  28 sgn 103   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t7_boole) ).

fof(d5_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,relation_dom(X1))
                  & X3 = apply(X1,X4) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d5_funct_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t6_boole) ).

fof(fc7_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => ( empty(relation_dom(X1))
        & relation(relation_dom(X1)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc7_relat_1) ).

fof(cc1_funct_1,axiom,
    ! [X1] :
      ( empty(X1)
     => function(X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',cc1_funct_1) ).

fof(cc1_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => relation(X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',cc1_relat_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t2_subset) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',existence_m1_subset_1) ).

fof(t159_funct_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
      <=> ! [X2] :
          ? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t159_funct_1) ).

fof(fc12_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set)
    & relation_empty_yielding(empty_set) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc12_relat_1) ).

fof(fc8_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => ( empty(relation_rng(X1))
        & relation(relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc8_relat_1) ).

fof(symmetry_r1_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(t56_zfmisc_1,axiom,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t56_zfmisc_1) ).

fof(t144_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( ! [X2] :
            ~ ( in(X2,relation_rng(X1))
              & ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
      <=> one_to_one(X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t144_funct_1) ).

fof(t173_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X2)
     => ( relation_inverse_image(X2,X1) = empty_set
      <=> disjoint(relation_rng(X2),X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t173_relat_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',reflexivity_r1_tarski) ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t5_subset) ).

fof(rc2_subset_1,axiom,
    ! [X1] :
    ? [X2] :
      ( element(X2,powerset(X1))
      & empty(X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',rc2_subset_1) ).

fof(t39_zfmisc_1,axiom,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t39_zfmisc_1) ).

fof(t2_xboole_1,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t2_xboole_1) ).

fof(fc2_subset_1,axiom,
    ! [X1] : ~ empty(singleton(X1)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc2_subset_1) ).

fof(t4_subset,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t4_subset) ).

fof(rc1_subset_1,axiom,
    ! [X1] :
      ( ~ empty(X1)
     => ? [X2] :
          ( element(X2,powerset(X1))
          & ~ empty(X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',rc1_subset_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d1_tarski) ).

fof(d13_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_inverse_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ( in(X4,relation_dom(X1))
                & in(apply(X1,X4),X2) ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d13_funct_1) ).

fof(c_0_25,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(c_0_26,plain,
    ! [X5,X6,X7,X7,X9,X6,X11] :
      ( ( in(esk3_3(X5,X6,X7),relation_dom(X5))
        | ~ in(X7,X6)
        | X6 != relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( X7 = apply(X5,esk3_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(X9,relation_dom(X5))
        | X7 != apply(X5,X9)
        | in(X7,X6)
        | X6 != relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(esk4_2(X5,X6),X6)
        | ~ in(X11,relation_dom(X5))
        | esk4_2(X5,X6) != apply(X5,X11)
        | X6 = relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(esk5_2(X5,X6),relation_dom(X5))
        | in(esk4_2(X5,X6),X6)
        | X6 = relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( esk4_2(X5,X6) = apply(X5,esk5_2(X5,X6))
        | in(esk4_2(X5,X6),X6)
        | X6 = relation_rng(X5)
        | ~ relation(X5)
        | ~ function(X5) ) ),
    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)],[d5_funct_1])])])])])])]) ).

fof(c_0_27,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_28,plain,
    ! [X2] :
      ( ( empty(relation_dom(X2))
        | ~ empty(X2) )
      & ( relation(relation_dom(X2))
        | ~ empty(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).

cnf(c_0_29,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,plain,
    ( in(esk3_3(X1,X2,X3),relation_dom(X1))
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_rng(X1)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,plain,
    ( empty(relation_dom(X1))
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_33,plain,
    ! [X2] :
      ( ~ empty(X2)
      | function(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).

fof(c_0_34,plain,
    ! [X2] :
      ( ~ empty(X2)
      | relation(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).

fof(c_0_35,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_36,plain,
    ! [X3] : element(esk6_1(X3),X3),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_37,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( one_to_one(X1)
        <=> ! [X2] :
            ? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
    inference(assume_negation,[status(cth)],[t159_funct_1]) ).

cnf(c_0_38,plain,
    ( X1 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ empty(relation_dom(X2))
    | ~ in(X3,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_39,plain,
    ( relation_dom(X1) = empty_set
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).

cnf(c_0_41,plain,
    ( function(X1)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    ( relation(X1)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_44,plain,
    element(esk6_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

fof(c_0_45,plain,
    ! [X2] :
      ( ( empty(relation_rng(X2))
        | ~ empty(X2) )
      & ( relation(relation_rng(X2))
        | ~ empty(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).

fof(c_0_46,plain,
    ! [X3,X4] :
      ( ~ disjoint(X3,X4)
      | disjoint(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).

fof(c_0_47,plain,
    ! [X3,X4] :
      ( in(X3,X4)
      | disjoint(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t56_zfmisc_1])])]) ).

fof(c_0_48,negated_conjecture,
    ! [X6,X7] :
      ( relation(esk19_0)
      & function(esk19_0)
      & ( ~ one_to_one(esk19_0)
        | ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X6)) )
      & ( one_to_one(esk19_0)
        | subset(relation_inverse_image(esk19_0,singleton(X7)),singleton(esk21_1(X7))) ) ),
    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)],[c_0_37])])])])])]) ).

fof(c_0_49,plain,
    ! [X4,X6,X7] :
      ( ( in(esk17_1(X4),relation_rng(X4))
        | one_to_one(X4)
        | ~ relation(X4)
        | ~ function(X4) )
      & ( relation_inverse_image(X4,singleton(esk17_1(X4))) != singleton(X6)
        | one_to_one(X4)
        | ~ relation(X4)
        | ~ function(X4) )
      & ( ~ one_to_one(X4)
        | ~ in(X7,relation_rng(X4))
        | relation_inverse_image(X4,singleton(X7)) = singleton(esk18_2(X4,X7))
        | ~ relation(X4)
        | ~ function(X4) ) ),
    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)],[t144_funct_1])])])])])])]) ).

cnf(c_0_50,plain,
    ( X1 != relation_rng(X2)
    | ~ empty(X2)
    | ~ in(X3,X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]),c_0_42]) ).

cnf(c_0_51,plain,
    ( empty(X1)
    | in(esk6_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_52,plain,
    ( empty(relation_rng(X1))
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_53,plain,
    ! [X3,X4] :
      ( ( relation_inverse_image(X4,X3) != empty_set
        | disjoint(relation_rng(X4),X3)
        | ~ relation(X4) )
      & ( ~ disjoint(relation_rng(X4),X3)
        | relation_inverse_image(X4,X3) = empty_set
        | ~ relation(X4) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])]) ).

cnf(c_0_54,plain,
    ( disjoint(X1,X2)
    | ~ disjoint(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_55,plain,
    ( disjoint(singleton(X1),X2)
    | in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1))
    | ~ one_to_one(esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_57,plain,
    ( relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2))
    | ~ function(X1)
    | ~ relation(X1)
    | ~ in(X2,relation_rng(X1))
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

fof(c_0_58,plain,
    ! [X3] : subset(X3,X3),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_59,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | ~ empty(X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

fof(c_0_60,plain,
    ! [X3] :
      ( element(esk13_1(X3),powerset(X3))
      & empty(esk13_1(X3)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).

cnf(c_0_61,plain,
    ( empty(X1)
    | X1 != relation_rng(X2)
    | ~ empty(X2) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_62,plain,
    ( relation_rng(X1) = empty_set
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_52]) ).

fof(c_0_63,plain,
    ! [X3,X4,X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( X3 != empty_set
        | subset(X3,singleton(X4)) )
      & ( X3 != singleton(X4)
        | subset(X3,singleton(X4)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])])])]) ).

cnf(c_0_64,plain,
    ( relation_inverse_image(X1,X2) = empty_set
    | ~ relation(X1)
    | ~ disjoint(relation_rng(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_65,plain,
    ( disjoint(X1,singleton(X2))
    | in(X2,X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

fof(c_0_66,plain,
    ! [X2] : subset(empty_set,X2),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

cnf(c_0_67,negated_conjecture,
    ( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),relation_inverse_image(X1,singleton(X2)))
    | ~ one_to_one(esk19_0)
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_68,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_69,negated_conjecture,
    relation(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_70,negated_conjecture,
    function(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_71,plain,
    ( ~ empty(X1)
    | ~ element(X2,powerset(X1))
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_72,plain,
    element(esk13_1(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_73,plain,
    empty(esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

fof(c_0_74,plain,
    ! [X2] : ~ empty(singleton(X2)),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_subset_1])]) ).

cnf(c_0_75,plain,
    ( empty(X1)
    | X1 != empty_set
    | ~ empty(X2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_76,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | element(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).

fof(c_0_77,plain,
    ! [X3] :
      ( ( element(esk9_1(X3),powerset(X3))
        | empty(X3) )
      & ( ~ empty(esk9_1(X3))
        | empty(X3) ) ),
    inference(distribute,[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)],[inference(fof_simplification,[status(thm)],[rc1_subset_1])])])])])])]) ).

cnf(c_0_78,plain,
    ( X1 = singleton(X2)
    | X1 = empty_set
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_79,negated_conjecture,
    ( subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1)))
    | one_to_one(esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_80,plain,
    ( relation_inverse_image(X1,singleton(X2)) = empty_set
    | in(X2,relation_rng(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_81,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_82,negated_conjecture,
    ( ~ one_to_one(esk19_0)
    | ~ in(esk20_0,relation_rng(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70])]) ).

cnf(c_0_83,plain,
    ( ~ empty(X1)
    | ~ in(X2,esk13_1(X1)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_84,plain,
    esk13_1(X1) = empty_set,
    inference(spm,[status(thm)],[c_0_31,c_0_73]) ).

fof(c_0_85,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk2_2(X4,X5),X5)
        | esk2_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk2_2(X4,X5),X5)
        | esk2_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    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)],[d1_tarski])])])])])])]) ).

cnf(c_0_86,plain,
    ~ empty(singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_87,plain,
    ( empty(X1)
    | X1 != empty_set ),
    inference(spm,[status(thm)],[c_0_75,c_0_40]) ).

cnf(c_0_88,plain,
    ( element(X1,X2)
    | ~ element(X3,powerset(X2))
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_89,plain,
    ( empty(X1)
    | element(esk9_1(X1),powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

fof(c_0_90,plain,
    ! [X5,X6,X7,X8,X8,X6,X7] :
      ( ( in(X8,relation_dom(X5))
        | ~ in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(apply(X5,X8),X6)
        | ~ in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(X8,relation_dom(X5))
        | ~ in(apply(X5,X8),X6)
        | in(X8,X7)
        | X7 != relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( ~ in(esk1_3(X5,X6,X7),X7)
        | ~ in(esk1_3(X5,X6,X7),relation_dom(X5))
        | ~ in(apply(X5,esk1_3(X5,X6,X7)),X6)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(esk1_3(X5,X6,X7),relation_dom(X5))
        | in(esk1_3(X5,X6,X7),X7)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) )
      & ( in(apply(X5,esk1_3(X5,X6,X7)),X6)
        | in(esk1_3(X5,X6,X7),X7)
        | X7 = relation_inverse_image(X5,X6)
        | ~ relation(X5)
        | ~ function(X5) ) ),
    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)],[d13_funct_1])])])])])])]) ).

cnf(c_0_91,negated_conjecture,
    ( singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1))
    | relation_inverse_image(esk19_0,singleton(X1)) = empty_set
    | one_to_one(esk19_0) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_92,negated_conjecture,
    ~ one_to_one(esk19_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_81]),c_0_69])]),c_0_82]) ).

cnf(c_0_93,plain,
    ( ~ empty(X1)
    | ~ in(X2,empty_set) ),
    inference(rw,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_94,plain,
    ( X1 = singleton(X2)
    | esk2_2(X2,X1) = X2
    | in(esk2_2(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_95,plain,
    singleton(X1) != empty_set,
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_96,plain,
    ( element(X1,X2)
    | empty(X2)
    | ~ in(X1,esk9_1(X2)) ),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_97,plain,
    ( empty(X1)
    | ~ empty(esk9_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_98,plain,
    ( in(X4,X2)
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_inverse_image(X1,X3)
    | ~ in(apply(X1,X4),X3)
    | ~ in(X4,relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_90]) ).

cnf(c_0_99,plain,
    ( X3 = apply(X1,esk3_3(X1,X2,X3))
    | ~ function(X1)
    | ~ relation(X1)
    | X2 != relation_rng(X1)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_100,plain,
    ( one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1)
    | relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_101,negated_conjecture,
    ( singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1))
    | relation_inverse_image(esk19_0,singleton(X1)) = empty_set ),
    inference(sr,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_102,plain,
    ( esk2_2(X1,empty_set) = X1
    | ~ empty(X2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).

cnf(c_0_103,plain,
    ( element(esk6_1(esk9_1(X1)),X1)
    | empty(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_51]),c_0_97]) ).

cnf(c_0_104,plain,
    ( in(esk3_3(X1,X2,X3),X4)
    | X4 != relation_inverse_image(X1,X5)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,X5)
    | ~ in(X3,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_30]) ).

cnf(c_0_105,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
    | one_to_one(X2)
    | relation_inverse_image(X2,singleton(esk17_1(X2))) != relation_inverse_image(esk19_0,singleton(X1))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_106,plain,
    ( X1 = singleton(X2)
    | esk2_2(X2,X1) != X2
    | ~ in(esk2_2(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_107,plain,
    esk2_2(X1,empty_set) = X1,
    inference(spm,[status(thm)],[c_0_102,c_0_40]) ).

cnf(c_0_108,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_109,plain,
    ( empty(X1)
    | in(esk6_1(esk9_1(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_103]) ).

cnf(c_0_110,plain,
    ( in(esk3_3(X1,X2,X3),relation_inverse_image(X1,X4))
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X3,X4)
    | ~ in(X3,X2) ),
    inference(er,[status(thm)],[c_0_104]) ).

cnf(c_0_111,negated_conjecture,
    relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_105]),c_0_69]),c_0_70])]),c_0_92]) ).

cnf(c_0_112,plain,
    ~ in(X1,empty_set),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_95]) ).

cnf(c_0_113,plain,
    ( X1 = esk6_1(esk9_1(X2))
    | empty(X2)
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_114,negated_conjecture,
    ( X1 != relation_rng(esk19_0)
    | ~ in(X2,singleton(esk17_1(esk19_0)))
    | ~ in(X2,X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_69]),c_0_70])]),c_0_112]) ).

cnf(c_0_115,plain,
    esk6_1(esk9_1(singleton(X1))) = X1,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_113]),c_0_86]) ).

cnf(c_0_116,negated_conjecture,
    ( X1 != relation_rng(esk19_0)
    | ~ in(esk17_1(esk19_0),X1) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_109]),c_0_115]),c_0_86]) ).

cnf(c_0_117,plain,
    ( one_to_one(X1)
    | in(esk17_1(X1),relation_rng(X1))
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_118,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_69]),c_0_70])]),c_0_92]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n003.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 : Sun Jun 19 14:59:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.27/9.46  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.27/9.46  # Preprocessing time       : 0.018 s
% 0.27/9.46  
% 0.27/9.46  # Proof found!
% 0.27/9.46  # SZS status Theorem
% 0.27/9.46  # SZS output start CNFRefutation
% See solution above
% 0.27/9.46  # Proof object total steps             : 119
% 0.27/9.46  # Proof object clause steps            : 69
% 0.27/9.46  # Proof object formula steps           : 50
% 0.27/9.46  # Proof object conjectures             : 17
% 0.27/9.46  # Proof object clause conjectures      : 14
% 0.27/9.46  # Proof object formula conjectures     : 3
% 0.27/9.46  # Proof object initial clauses used    : 35
% 0.27/9.46  # Proof object initial formulas used   : 25
% 0.27/9.46  # Proof object generating inferences   : 32
% 0.27/9.46  # Proof object simplifying inferences  : 32
% 0.27/9.46  # Training examples: 0 positive, 0 negative
% 0.27/9.46  # Parsed axioms                        : 43
% 0.27/9.46  # Removed by relevancy pruning/SinE    : 0
% 0.27/9.46  # Initial clauses                      : 82
% 0.27/9.46  # Removed in clause preprocessing      : 2
% 0.27/9.46  # Initial clauses in saturation        : 80
% 0.27/9.46  # Processed clauses                    : 24424
% 0.27/9.46  # ...of these trivial                  : 82
% 0.27/9.46  # ...subsumed                          : 20302
% 0.27/9.46  # ...remaining for further processing  : 4040
% 0.27/9.46  # Other redundant clauses eliminated   : 6
% 0.27/9.46  # Clauses deleted for lack of memory   : 205542
% 0.27/9.46  # Backward-subsumed                    : 309
% 0.27/9.46  # Backward-rewritten                   : 47
% 0.27/9.46  # Generated clauses                    : 361027
% 0.27/9.46  # ...of the previous two non-trivial   : 346331
% 0.27/9.46  # Contextual simplify-reflections      : 28803
% 0.27/9.46  # Paramodulations                      : 360362
% 0.27/9.46  # Factorizations                       : 36
% 0.27/9.46  # Equation resolutions                 : 627
% 0.27/9.46  # Current number of processed clauses  : 3681
% 0.27/9.46  #    Positive orientable unit clauses  : 46
% 0.27/9.46  #    Positive unorientable unit clauses: 0
% 0.27/9.46  #    Negative unit clauses             : 30
% 0.27/9.46  #    Non-unit-clauses                  : 3605
% 0.27/9.46  # Current number of unprocessed clauses: 101543
% 0.27/9.46  # ...number of literals in the above   : 658066
% 0.27/9.46  # Current number of archived formulas  : 0
% 0.27/9.46  # Current number of archived clauses   : 358
% 0.27/9.46  # Clause-clause subsumption calls (NU) : 10084592
% 0.27/9.46  # Rec. Clause-clause subsumption calls : 3093399
% 0.27/9.46  # Non-unit clause-clause subsumptions  : 45052
% 0.27/9.46  # Unit Clause-clause subsumption calls : 2348
% 0.27/9.46  # Rewrite failures with RHS unbound    : 0
% 0.27/9.46  # BW rewrite match attempts            : 31
% 0.27/9.46  # BW rewrite match successes           : 23
% 0.27/9.46  # Condensation attempts                : 0
% 0.27/9.46  # Condensation successes               : 0
% 0.27/9.46  # Termbank termtop insertions          : 8329753
% 0.27/9.46  
% 0.27/9.46  # -------------------------------------------------
% 0.27/9.46  # User time                : 8.144 s
% 0.27/9.46  # System time              : 0.086 s
% 0.27/9.46  # Total time               : 8.230 s
% 0.27/9.46  # Maximum resident set size: 137324 pages
% 0.27/23.41  eprover: CPU time limit exceeded, terminating
% 0.27/23.41  eprover: CPU time limit exceeded, terminating
% 0.27/23.42  eprover: CPU time limit exceeded, terminating
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47  eprover: No such file or directory
% 0.27/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48  eprover: No such file or directory
% 0.27/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------