TSTP Solution File: SEU078+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.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 19:24:42 EDT 2023

% Result   : Theorem 0.17s 0.51s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  104 (  28 unt;   0 def)
%            Number of atoms       :  347 (  78 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  409 ( 166   ~; 179   |;  39   &)
%                                         (  12 <=>;  13  =>;   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   :  183 (  14 sgn;  91   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(rc1_subset_1,axiom,
    ! [X1] :
      ( ~ empty(X1)
     => ? [X2] :
          ( element(X2,powerset(X1))
          & ~ empty(X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',rc1_subset_1) ).

fof(t3_subset,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t3_subset) ).

fof(fc2_subset_1,axiom,
    ! [X1] : ~ empty(singleton(X1)),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',fc2_subset_1) ).

fof(t56_zfmisc_1,axiom,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t56_zfmisc_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t6_boole) ).

fof(rc2_subset_1,axiom,
    ! [X1] :
    ? [X2] :
      ( element(X2,powerset(X1))
      & empty(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',rc2_subset_1) ).

fof(t39_zfmisc_1,axiom,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t39_zfmisc_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/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t159_funct_1) ).

fof(symmetry_r1_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',symmetry_r1_xboole_0) ).

fof(t173_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X2)
     => ( relation_inverse_image(X2,X1) = empty_set
      <=> disjoint(relation_rng(X2),X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t173_relat_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/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t144_funct_1) ).

fof(t5_subset,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t5_subset) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',reflexivity_r1_tarski) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',d1_tarski) ).

fof(fc12_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set)
    & relation_empty_yielding(empty_set) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',fc12_relat_1) ).

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/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',d13_funct_1) ).

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/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',d5_funct_1) ).

fof(t2_xboole_1,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t2_xboole_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',t2_subset) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p',existence_m1_subset_1) ).

fof(c_0_20,plain,
    ! [X1] :
      ( ~ empty(X1)
     => ? [X2] :
          ( element(X2,powerset(X1))
          & ~ empty(X2) ) ),
    inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).

fof(c_0_21,plain,
    ! [X77,X78] :
      ( ( ~ element(X77,powerset(X78))
        | subset(X77,X78) )
      & ( ~ subset(X77,X78)
        | element(X77,powerset(X78)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).

fof(c_0_22,plain,
    ! [X45] :
      ( ( element(esk9_1(X45),powerset(X45))
        | empty(X45) )
      & ( ~ empty(esk9_1(X45))
        | empty(X45) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).

fof(c_0_23,plain,
    ! [X1] : ~ empty(singleton(X1)),
    inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).

fof(c_0_24,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[t56_zfmisc_1]) ).

fof(c_0_25,plain,
    ! [X87] :
      ( ~ empty(X87)
      | X87 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_26,plain,
    ! [X50] :
      ( element(esk13_1(X50),powerset(X50))
      & empty(esk13_1(X50)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).

fof(c_0_27,plain,
    ! [X75,X76] :
      ( ( ~ subset(X75,singleton(X76))
        | X75 = empty_set
        | X75 = singleton(X76) )
      & ( X75 != empty_set
        | subset(X75,singleton(X76)) )
      & ( X75 != singleton(X76)
        | subset(X75,singleton(X76)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).

cnf(c_0_28,plain,
    ( subset(X1,X2)
    | ~ element(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    ( element(esk9_1(X1),powerset(X1))
    | empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_30,plain,
    ! [X38] : ~ empty(singleton(X38)),
    inference(variable_rename,[status(thm)],[c_0_23]) ).

fof(c_0_31,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]) ).

fof(c_0_32,plain,
    ! [X56,X57] :
      ( ~ disjoint(X56,X57)
      | disjoint(X57,X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).

fof(c_0_33,plain,
    ! [X82,X83] :
      ( in(X82,X83)
      | disjoint(singleton(X82),X83) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).

cnf(c_0_34,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_35,plain,
    empty(esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    ( subset(esk9_1(X1),X1)
    | empty(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_38,plain,
    ~ empty(singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_39,negated_conjecture,
    ! [X65,X66] :
      ( relation(esk19_0)
      & function(esk19_0)
      & ( ~ one_to_one(esk19_0)
        | ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X65)) )
      & ( one_to_one(esk19_0)
        | subset(relation_inverse_image(esk19_0,singleton(X66)),singleton(esk21_1(X66))) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).

fof(c_0_40,plain,
    ! [X68,X69] :
      ( ( relation_inverse_image(X69,X68) != empty_set
        | disjoint(relation_rng(X69),X68)
        | ~ relation(X69) )
      & ( ~ disjoint(relation_rng(X69),X68)
        | relation_inverse_image(X69,X68) = empty_set
        | ~ relation(X69) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])]) ).

cnf(c_0_41,plain,
    ( disjoint(X2,X1)
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_42,plain,
    ( in(X1,X2)
    | disjoint(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_43,plain,
    ! [X58,X60,X61] :
      ( ( in(esk17_1(X58),relation_rng(X58))
        | one_to_one(X58)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( relation_inverse_image(X58,singleton(esk17_1(X58))) != singleton(X60)
        | one_to_one(X58)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( ~ one_to_one(X58)
        | ~ in(X61,relation_rng(X58))
        | relation_inverse_image(X58,singleton(X61)) = singleton(esk18_2(X58,X61))
        | ~ relation(X58)
        | ~ function(X58) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_funct_1])])])])]) ).

fof(c_0_44,plain,
    ! [X84,X85,X86] :
      ( ~ in(X84,X85)
      | ~ element(X85,powerset(X86))
      | ~ empty(X86) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).

cnf(c_0_45,plain,
    element(esk13_1(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_46,plain,
    esk13_1(X1) = empty_set,
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_47,plain,
    ( esk9_1(singleton(X1)) = singleton(X1)
    | esk9_1(singleton(X1)) = empty_set ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_48,negated_conjecture,
    ( one_to_one(esk19_0)
    | subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_49,plain,
    ( relation_inverse_image(X1,X2) = empty_set
    | ~ disjoint(relation_rng(X1),X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_50,plain,
    ( disjoint(X1,singleton(X2))
    | in(X2,X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_51,negated_conjecture,
    ( ~ one_to_one(esk19_0)
    | ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,plain,
    ( relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2))
    | ~ one_to_one(X1)
    | ~ in(X2,relation_rng(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_53,plain,
    ! [X55] : subset(X55,X55),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

cnf(c_0_54,plain,
    ( ~ in(X1,X2)
    | ~ element(X2,powerset(X3))
    | ~ empty(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_55,plain,
    element(empty_set,powerset(X1)),
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_56,plain,
    ! [X18,X19,X20,X21,X22,X23] :
      ( ( ~ in(X20,X19)
        | X20 = X18
        | X19 != singleton(X18) )
      & ( X21 != X18
        | in(X21,X19)
        | X19 != singleton(X18) )
      & ( ~ in(esk2_2(X22,X23),X23)
        | esk2_2(X22,X23) != X22
        | X23 = singleton(X22) )
      & ( in(esk2_2(X22,X23),X23)
        | esk2_2(X22,X23) = X22
        | X23 = singleton(X22) ) ),
    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)],[d1_tarski])])])])])]) ).

cnf(c_0_57,plain,
    ( empty(X1)
    | ~ empty(esk9_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_58,plain,
    ( esk9_1(singleton(X1)) = empty_set
    | singleton(X1) != empty_set ),
    inference(ef,[status(thm)],[c_0_47]) ).

cnf(c_0_59,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).

fof(c_0_60,plain,
    ! [X10,X11,X12,X13,X14,X15,X16] :
      ( ( in(X13,relation_dom(X10))
        | ~ in(X13,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(apply(X10,X13),X11)
        | ~ in(X13,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(X14,relation_dom(X10))
        | ~ in(apply(X10,X14),X11)
        | in(X14,X12)
        | X12 != relation_inverse_image(X10,X11)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(esk1_3(X10,X15,X16),X16)
        | ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
        | ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
        | X16 = relation_inverse_image(X10,X15)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(esk1_3(X10,X15,X16),relation_dom(X10))
        | in(esk1_3(X10,X15,X16),X16)
        | X16 = relation_inverse_image(X10,X15)
        | ~ relation(X10)
        | ~ function(X10) )
      & ( in(apply(X10,esk1_3(X10,X15,X16)),X15)
        | in(esk1_3(X10,X15,X16),X16)
        | X16 = relation_inverse_image(X10,X15)
        | ~ relation(X10)
        | ~ function(X10) ) ),
    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)],[d13_funct_1])])])])])]) ).

fof(c_0_61,plain,
    ! [X25,X26,X27,X29,X30,X31,X33] :
      ( ( in(esk3_3(X25,X26,X27),relation_dom(X25))
        | ~ in(X27,X26)
        | X26 != relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( X27 = apply(X25,esk3_3(X25,X26,X27))
        | ~ in(X27,X26)
        | X26 != relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( ~ in(X30,relation_dom(X25))
        | X29 != apply(X25,X30)
        | in(X29,X26)
        | X26 != relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( ~ in(esk4_2(X25,X31),X31)
        | ~ in(X33,relation_dom(X25))
        | esk4_2(X25,X31) != apply(X25,X33)
        | X31 = relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( in(esk5_2(X25,X31),relation_dom(X25))
        | in(esk4_2(X25,X31),X31)
        | X31 = relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( esk4_2(X25,X31) = apply(X25,esk5_2(X25,X31))
        | in(esk4_2(X25,X31),X31)
        | X31 = relation_rng(X25)
        | ~ relation(X25)
        | ~ function(X25) ) ),
    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)],[d5_funct_1])])])])])]) ).

cnf(c_0_62,plain,
    ( one_to_one(X1)
    | relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_63,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_36,c_0_48]) ).

cnf(c_0_64,plain,
    ( relation_inverse_image(X1,singleton(X2)) = empty_set
    | in(X2,relation_rng(X1))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_65,negated_conjecture,
    relation(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

fof(c_0_66,plain,
    ! [X74] : subset(empty_set,X74),
    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_51,c_0_52]) ).

cnf(c_0_68,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_69,negated_conjecture,
    function(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_70,plain,
    ( ~ empty(X1)
    | ~ in(X2,empty_set) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_71,plain,
    ( in(esk2_2(X1,X2),X2)
    | esk2_2(X1,X2) = X1
    | X2 = singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_72,plain,
    singleton(X1) != empty_set,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]),c_0_38]) ).

cnf(c_0_73,plain,
    ( in(X1,X4)
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),X3)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_74,plain,
    ( X1 = apply(X2,esk3_3(X2,X3,X1))
    | ~ in(X1,X3)
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_75,plain,
    ( in(esk3_3(X1,X2,X3),relation_dom(X1))
    | ~ in(X3,X2)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_76,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
    | one_to_one(esk19_0)
    | 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_62,c_0_63]) ).

cnf(c_0_77,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
    | in(X1,relation_rng(esk19_0)) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_78,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_79,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_65]),c_0_69])]) ).

cnf(c_0_80,plain,
    ( esk2_2(X1,empty_set) = X1
    | ~ empty(X2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).

fof(c_0_81,plain,
    ! [X72,X73] :
      ( ~ element(X72,X73)
      | empty(X73)
      | in(X72,X73) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_82,plain,
    ! [X35] : element(esk6_1(X35),X35),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

cnf(c_0_83,plain,
    ( in(X1,relation_inverse_image(X2,X3))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(apply(X2,X1),X3)
    | ~ in(X1,relation_dom(X2)) ),
    inference(er,[status(thm)],[c_0_73]) ).

cnf(c_0_84,plain,
    ( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_74]) ).

cnf(c_0_85,plain,
    ( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1)) ),
    inference(er,[status(thm)],[c_0_75]) ).

cnf(c_0_86,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set
    | one_to_one(esk19_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_76]),c_0_65]),c_0_69])]) ).

cnf(c_0_87,negated_conjecture,
    ~ one_to_one(esk19_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_77]),c_0_78])]),c_0_79]) ).

cnf(c_0_88,plain,
    ( X2 = singleton(X1)
    | ~ in(esk2_2(X1,X2),X2)
    | esk2_2(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_89,plain,
    esk2_2(X1,empty_set) = X1,
    inference(spm,[status(thm)],[c_0_80,c_0_59]) ).

cnf(c_0_90,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_91,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_92,plain,
    element(esk6_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_93,plain,
    ( in(esk17_1(X1),relation_rng(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_94,plain,
    ( in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_rng(X1))
    | ~ in(X2,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).

cnf(c_0_95,negated_conjecture,
    relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
    inference(sr,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_96,plain,
    ~ in(X1,empty_set),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_72]) ).

cnf(c_0_97,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_90]) ).

cnf(c_0_98,plain,
    ( empty(X1)
    | in(esk6_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_99,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk17_1(esk19_0),relation_rng(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_65]),c_0_69])]) ).

cnf(c_0_100,negated_conjecture,
    ( ~ in(X1,singleton(esk17_1(esk19_0)))
    | ~ in(X1,relation_rng(esk19_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_65]),c_0_69])]),c_0_96]) ).

cnf(c_0_101,plain,
    esk6_1(singleton(X1)) = X1,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_38]) ).

cnf(c_0_102,negated_conjecture,
    in(esk17_1(esk19_0),relation_rng(esk19_0)),
    inference(sr,[status(thm)],[c_0_99,c_0_87]) ).

cnf(c_0_103,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_100,c_0_98]),c_0_101]),c_0_102])]),c_0_38]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 2400
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Oct  2 08:48:08 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.JF9QgJ5ocG/E---3.1_32716.p
% 0.17/0.51  # Version: 3.1pre001
% 0.17/0.51  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.51  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.51  # Starting sh5l with 300s (1) cores
% 0.17/0.51  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 326 completed with status 0
% 0.17/0.51  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.51  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.51  # No SInE strategy applied
% 0.17/0.51  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.17/0.51  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.51  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 113s (1) cores
% 0.17/0.51  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.51  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.17/0.51  # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.17/0.51  # Starting U----_206c_02_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.17/0.51  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 334 completed with status 0
% 0.17/0.51  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.51  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.51  # No SInE strategy applied
% 0.17/0.51  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.17/0.51  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.51  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 113s (1) cores
% 0.17/0.51  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.51  # Preprocessing time       : 0.002 s
% 0.17/0.51  # Presaturation interreduction done
% 0.17/0.51  
% 0.17/0.51  # Proof found!
% 0.17/0.51  # SZS status Theorem
% 0.17/0.51  # SZS output start CNFRefutation
% See solution above
% 0.17/0.51  # Parsed axioms                        : 43
% 0.17/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.51  # Initial clauses                      : 82
% 0.17/0.51  # Removed in clause preprocessing      : 2
% 0.17/0.51  # Initial clauses in saturation        : 80
% 0.17/0.51  # Processed clauses                    : 717
% 0.17/0.51  # ...of these trivial                  : 9
% 0.17/0.51  # ...subsumed                          : 336
% 0.17/0.51  # ...remaining for further processing  : 372
% 0.17/0.51  # Other redundant clauses eliminated   : 15
% 0.17/0.51  # Clauses deleted for lack of memory   : 0
% 0.17/0.51  # Backward-subsumed                    : 23
% 0.17/0.51  # Backward-rewritten                   : 14
% 0.17/0.51  # Generated clauses                    : 1674
% 0.17/0.51  # ...of the previous two non-redundant : 1408
% 0.17/0.51  # ...aggressively subsumed             : 0
% 0.17/0.51  # Contextual simplify-reflections      : 17
% 0.17/0.51  # Paramodulations                      : 1644
% 0.17/0.51  # Factorizations                       : 4
% 0.17/0.51  # NegExts                              : 0
% 0.17/0.51  # Equation resolutions                 : 17
% 0.17/0.51  # Total rewrite steps                  : 774
% 0.17/0.51  # Propositional unsat checks           : 0
% 0.17/0.51  #    Propositional check models        : 0
% 0.17/0.51  #    Propositional check unsatisfiable : 0
% 0.17/0.51  #    Propositional clauses             : 0
% 0.17/0.51  #    Propositional clauses after purity: 0
% 0.17/0.51  #    Propositional unsat core size     : 0
% 0.17/0.51  #    Propositional preprocessing time  : 0.000
% 0.17/0.51  #    Propositional encoding time       : 0.000
% 0.17/0.51  #    Propositional solver time         : 0.000
% 0.17/0.51  #    Success case prop preproc time    : 0.000
% 0.17/0.51  #    Success case prop encoding time   : 0.000
% 0.17/0.51  #    Success case prop solver time     : 0.000
% 0.17/0.51  # Current number of processed clauses  : 239
% 0.17/0.51  #    Positive orientable unit clauses  : 39
% 0.17/0.51  #    Positive unorientable unit clauses: 0
% 0.17/0.51  #    Negative unit clauses             : 16
% 0.17/0.51  #    Non-unit-clauses                  : 184
% 0.17/0.51  # Current number of unprocessed clauses: 805
% 0.17/0.51  # ...number of literals in the above   : 3861
% 0.17/0.51  # Current number of archived formulas  : 0
% 0.17/0.51  # Current number of archived clauses   : 123
% 0.17/0.51  # Clause-clause subsumption calls (NU) : 7609
% 0.17/0.51  # Rec. Clause-clause subsumption calls : 3337
% 0.17/0.51  # Non-unit clause-clause subsumptions  : 183
% 0.17/0.51  # Unit Clause-clause subsumption calls : 297
% 0.17/0.51  # Rewrite failures with RHS unbound    : 0
% 0.17/0.51  # BW rewrite match attempts            : 17
% 0.17/0.51  # BW rewrite match successes           : 11
% 0.17/0.51  # Condensation attempts                : 0
% 0.17/0.51  # Condensation successes               : 0
% 0.17/0.51  # Termbank termtop insertions          : 30786
% 0.17/0.51  
% 0.17/0.51  # -------------------------------------------------
% 0.17/0.51  # User time                : 0.046 s
% 0.17/0.51  # System time              : 0.004 s
% 0.17/0.51  # Total time               : 0.050 s
% 0.17/0.51  # Maximum resident set size: 1888 pages
% 0.17/0.51  
% 0.17/0.51  # -------------------------------------------------
% 0.17/0.51  # User time                : 0.215 s
% 0.17/0.51  # System time              : 0.022 s
% 0.17/0.51  # Total time               : 0.236 s
% 0.17/0.51  # Maximum resident set size: 1732 pages
% 0.17/0.51  % E---3.1 exiting
% 0.17/0.51  % E---3.1 exiting
%------------------------------------------------------------------------------