TSTP Solution File: SEU063+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SEU063+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 19:30:18 EDT 2023

% Result   : Theorem 1141.02s 143.88s
% Output   : CNFRefutation 1141.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   80 (  11 unt;   0 def)
%            Number of atoms       :  340 (  87 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  427 ( 167   ~; 213   |;  32   &)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   2 con; 0-3 aty)
%            Number of variables   :  126 (   4 sgn;  44   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
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.iM2TLUf0bR/E---3.1_7993.p',d5_funct_1) ).

fof(t144_funct_1,conjecture,
    ! [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.iM2TLUf0bR/E---3.1_7993.p',t144_funct_1) ).

fof(d8_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
      <=> ! [X2,X3] :
            ( ( in(X2,relation_dom(X1))
              & in(X3,relation_dom(X1))
              & apply(X1,X2) = apply(X1,X3) )
           => X2 = X3 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.iM2TLUf0bR/E---3.1_7993.p',d8_funct_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.iM2TLUf0bR/E---3.1_7993.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/sandbox/tmp/tmp.iM2TLUf0bR/E---3.1_7993.p',d13_funct_1) ).

fof(c_0_5,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])])])])])]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ( ! [X2] :
              ~ ( in(X2,relation_rng(X1))
                & ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
        <=> one_to_one(X1) ) ),
    inference(assume_negation,[status(cth)],[t144_funct_1]) ).

cnf(c_0_7,plain,
    ( in(X3,X4)
    | ~ in(X1,relation_dom(X2))
    | X3 != apply(X2,X1)
    | X4 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X35,X36,X37] :
      ( ( ~ one_to_one(X35)
        | ~ in(X36,relation_dom(X35))
        | ~ in(X37,relation_dom(X35))
        | apply(X35,X36) != apply(X35,X37)
        | X36 = X37
        | ~ relation(X35)
        | ~ function(X35) )
      & ( in(esk6_1(X35),relation_dom(X35))
        | one_to_one(X35)
        | ~ relation(X35)
        | ~ function(X35) )
      & ( in(esk7_1(X35),relation_dom(X35))
        | one_to_one(X35)
        | ~ relation(X35)
        | ~ function(X35) )
      & ( apply(X35,esk6_1(X35)) = apply(X35,esk7_1(X35))
        | one_to_one(X35)
        | ~ relation(X35)
        | ~ function(X35) )
      & ( esk6_1(X35) != esk7_1(X35)
        | one_to_one(X35)
        | ~ relation(X35)
        | ~ function(X35) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).

fof(c_0_9,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])])])])])]) ).

fof(c_0_10,negated_conjecture,
    ! [X63,X64] :
      ( relation(esk19_0)
      & function(esk19_0)
      & ( in(esk20_0,relation_rng(esk19_0))
        | ~ one_to_one(esk19_0) )
      & ( relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X63)
        | ~ one_to_one(esk19_0) )
      & ( ~ in(X64,relation_rng(esk19_0))
        | relation_inverse_image(esk19_0,singleton(X64)) = singleton(esk21_1(X64))
        | one_to_one(esk19_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

cnf(c_0_11,plain,
    ( in(apply(X1,X2),relation_rng(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(X1)) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).

cnf(c_0_12,plain,
    ( in(esk7_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,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])])])])])]) ).

cnf(c_0_14,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(X1)) = singleton(esk21_1(X1))
    | one_to_one(esk19_0)
    | ~ in(X1,relation_rng(esk19_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( one_to_one(X1)
    | in(apply(X1,esk7_1(X1)),relation_rng(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    relation(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,negated_conjecture,
    function(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,X3)
    | X3 != relation_inverse_image(X2,X4)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).

cnf(c_0_21,negated_conjecture,
    ( singleton(esk21_1(apply(esk19_0,esk7_1(esk19_0)))) = relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))
    | one_to_one(esk19_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).

cnf(c_0_22,plain,
    ( in(apply(X1,X2),X3)
    | ~ in(X2,X4)
    | X4 != relation_inverse_image(X1,X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    ( in(X1,relation_dom(X2))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,relation_inverse_image(X2,X3)) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk21_1(apply(esk19_0,esk7_1(esk19_0))),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,plain,
    ( in(apply(X1,X2),X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_inverse_image(X1,X3)) ),
    inference(er,[status(thm)],[c_0_22]) ).

cnf(c_0_27,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_13]) ).

cnf(c_0_28,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk21_1(apply(esk19_0,esk7_1(esk19_0))),relation_dom(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_18])]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))),singleton(apply(esk19_0,esk7_1(esk19_0)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_17]),c_0_18])]) ).

cnf(c_0_31,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_27]) ).

cnf(c_0_32,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))),relation_rng(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_28]),c_0_17]),c_0_18])]) ).

cnf(c_0_33,negated_conjecture,
    ( apply(esk19_0,esk21_1(apply(esk19_0,esk7_1(esk19_0)))) = apply(esk19_0,esk7_1(esk19_0))
    | one_to_one(esk19_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,plain,
    ( one_to_one(X1)
    | in(esk7_1(X1),relation_inverse_image(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(apply(X1,esk7_1(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_12]) ).

cnf(c_0_35,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(apply(esk19_0,esk7_1(esk19_0)),relation_rng(esk19_0)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk7_1(esk19_0),relation_inverse_image(esk19_0,relation_rng(esk19_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_17]),c_0_18])]) ).

cnf(c_0_37,plain,
    ( in(esk6_1(X1),relation_dom(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_38,plain,
    ( apply(X1,esk6_1(X1)) = apply(X1,esk7_1(X1))
    | one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_39,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk7_1(esk19_0),relation_dom(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_17]),c_0_18])]) ).

cnf(c_0_40,plain,
    ( one_to_one(X1)
    | in(esk6_1(X1),relation_inverse_image(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(apply(X1,esk6_1(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(apply(esk19_0,esk6_1(esk19_0)),relation_rng(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_17]),c_0_18])]) ).

cnf(c_0_42,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk7_1(esk19_0),relation_inverse_image(esk19_0,X1))
    | ~ in(apply(esk19_0,esk7_1(esk19_0)),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_17]),c_0_18])]) ).

cnf(c_0_43,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk6_1(esk19_0),relation_inverse_image(esk19_0,relation_rng(esk19_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_17]),c_0_18])]) ).

cnf(c_0_44,negated_conjecture,
    ( X1 = esk21_1(apply(esk19_0,esk7_1(esk19_0)))
    | one_to_one(esk19_0)
    | ~ in(X1,relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
    inference(spm,[status(thm)],[c_0_29,c_0_21]) ).

cnf(c_0_45,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk7_1(esk19_0),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk7_1(esk19_0))))) ),
    inference(spm,[status(thm)],[c_0_42,c_0_20]) ).

cnf(c_0_46,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk6_1(esk19_0),relation_dom(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_17]),c_0_18])]) ).

cnf(c_0_47,negated_conjecture,
    ( esk21_1(apply(esk19_0,esk7_1(esk19_0))) = esk7_1(esk19_0)
    | one_to_one(esk19_0) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk6_1(esk19_0),relation_inverse_image(esk19_0,X1))
    | ~ in(apply(esk19_0,esk6_1(esk19_0)),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_17]),c_0_18])]) ).

cnf(c_0_49,negated_conjecture,
    ( singleton(esk21_1(apply(esk19_0,esk6_1(esk19_0)))) = relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0))))
    | one_to_one(esk19_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_38]),c_0_17]),c_0_18])]) ).

cnf(c_0_50,negated_conjecture,
    ( esk21_1(apply(esk19_0,esk6_1(esk19_0))) = esk7_1(esk19_0)
    | one_to_one(esk19_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_17]),c_0_18])]) ).

cnf(c_0_51,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk6_1(esk19_0),relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0))))) ),
    inference(spm,[status(thm)],[c_0_48,c_0_20]) ).

cnf(c_0_52,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(apply(esk19_0,esk6_1(esk19_0)))) = singleton(esk7_1(esk19_0))
    | one_to_one(esk19_0) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    ( one_to_one(esk19_0)
    | in(esk6_1(esk19_0),singleton(esk7_1(esk19_0))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_54,plain,
    ( one_to_one(X1)
    | esk6_1(X1) != esk7_1(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_55,negated_conjecture,
    ( esk7_1(esk19_0) = esk6_1(esk19_0)
    | one_to_one(esk19_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_53]) ).

cnf(c_0_56,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_5]) ).

cnf(c_0_57,negated_conjecture,
    ( in(esk20_0,relation_rng(esk19_0))
    | ~ one_to_one(esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_58,negated_conjecture,
    one_to_one(esk19_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_17]),c_0_18])]) ).

cnf(c_0_59,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_5]) ).

cnf(c_0_60,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_56]) ).

cnf(c_0_61,negated_conjecture,
    in(esk20_0,relation_rng(esk19_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

cnf(c_0_62,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_59]) ).

cnf(c_0_63,plain,
    ( in(esk2_2(X1,X2),X2)
    | esk2_2(X1,X2) = X1
    | X2 = singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_64,plain,
    ( X2 = X3
    | ~ one_to_one(X1)
    | ~ in(X2,relation_dom(X1))
    | ~ in(X3,relation_dom(X1))
    | apply(X1,X2) != apply(X1,X3)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_65,negated_conjecture,
    apply(esk19_0,esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)) = esk20_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_17]),c_0_18])]) ).

cnf(c_0_66,negated_conjecture,
    in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_dom(esk19_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_17]),c_0_18])]) ).

cnf(c_0_67,plain,
    ( esk2_2(X1,relation_inverse_image(X2,X3)) = X1
    | relation_inverse_image(X2,X3) = singleton(X1)
    | in(apply(X2,esk2_2(X1,relation_inverse_image(X2,X3))),X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_63]) ).

cnf(c_0_68,negated_conjecture,
    ( relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X1)
    | ~ one_to_one(esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_69,negated_conjecture,
    ( esk3_3(esk19_0,relation_rng(esk19_0),esk20_0) = X1
    | apply(esk19_0,X1) != esk20_0
    | ~ in(X1,relation_dom(esk19_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_58]),c_0_17]),c_0_18])]),c_0_66])]) ).

cnf(c_0_70,plain,
    ( apply(X1,esk2_2(X2,relation_inverse_image(X1,singleton(X3)))) = X3
    | esk2_2(X2,relation_inverse_image(X1,singleton(X3))) = X2
    | relation_inverse_image(X1,singleton(X3)) = singleton(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_67]) ).

cnf(c_0_71,negated_conjecture,
    relation_inverse_image(esk19_0,singleton(esk20_0)) != singleton(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_58])]) ).

cnf(c_0_72,negated_conjecture,
    ( esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)
    | esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = X1
    | ~ in(esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))),relation_dom(esk19_0)) ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_17]),c_0_18])])]),c_0_71]) ).

cnf(c_0_73,plain,
    ( esk2_2(X1,relation_inverse_image(X2,X3)) = X1
    | relation_inverse_image(X2,X3) = singleton(X1)
    | in(esk2_2(X1,relation_inverse_image(X2,X3)),relation_dom(X2))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_63]) ).

cnf(c_0_74,negated_conjecture,
    ( esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0)
    | esk2_2(X1,relation_inverse_image(esk19_0,singleton(esk20_0))) = X1 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_17]),c_0_18])]),c_0_71]) ).

cnf(c_0_75,negated_conjecture,
    ( in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,X1))
    | ~ in(esk20_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_66]),c_0_17]),c_0_18]),c_0_65])]) ).

cnf(c_0_76,plain,
    ( X2 = singleton(X1)
    | ~ in(esk2_2(X1,X2),X2)
    | esk2_2(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_77,negated_conjecture,
    esk2_2(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,singleton(esk20_0))) = esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_74])]) ).

cnf(c_0_78,negated_conjecture,
    in(esk3_3(esk19_0,relation_rng(esk19_0),esk20_0),relation_inverse_image(esk19_0,singleton(esk20_0))),
    inference(spm,[status(thm)],[c_0_75,c_0_20]) ).

cnf(c_0_79,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]),c_0_71]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU063+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 2400
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Oct  2 08:45:44 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.20/0.47  Running first-order model finding
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.iM2TLUf0bR/E---3.1_7993.p
% 1141.02/143.88  # Version: 3.1pre001
% 1141.02/143.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1141.02/143.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1141.02/143.88  # Starting new_bool_3 with 300s (1) cores
% 1141.02/143.88  # Starting new_bool_1 with 300s (1) cores
% 1141.02/143.88  # Starting sh5l with 300s (1) cores
% 1141.02/143.88  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8072 completed with status 0
% 1141.02/143.88  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1141.02/143.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1141.02/143.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1141.02/143.88  # No SInE strategy applied
% 1141.02/143.88  # Search class: FGHSM-FFMM31-SFFFFFNN
% 1141.02/143.88  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1141.02/143.88  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1141.02/143.88  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 136s (1) cores
% 1141.02/143.88  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 8080 completed with status 7
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1141.02/143.88  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 8079 completed with status 7
% 1141.02/143.88  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 8076 completed with status 7
% 1141.02/143.88  # Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 8078 completed with status 7
% 1141.02/143.88  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S3S with 136s (1) cores
% 1141.02/143.88  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 8149 completed with status 0
% 1141.02/143.88  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 1141.02/143.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1141.02/143.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1141.02/143.88  # No SInE strategy applied
% 1141.02/143.88  # Search class: FGHSM-FFMM31-SFFFFFNN
% 1141.02/143.88  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1141.02/143.88  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1141.02/143.88  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1141.02/143.88  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 136s (1) cores
% 1141.02/143.88  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 8080 completed with status 7
% 1141.02/143.88  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1141.02/143.88  # Preprocessing time       : 0.001 s
% 1141.02/143.88  # Presaturation interreduction done
% 1141.02/143.88  
% 1141.02/143.88  # Proof found!
% 1141.02/143.88  # SZS status Theorem
% 1141.02/143.88  # SZS output start CNFRefutation
% See solution above
% 1141.02/143.88  # Parsed axioms                        : 39
% 1141.02/143.88  # Removed by relevancy pruning/SinE    : 0
% 1141.02/143.88  # Initial clauses                      : 78
% 1141.02/143.88  # Removed in clause preprocessing      : 2
% 1141.02/143.88  # Initial clauses in saturation        : 76
% 1141.02/143.88  # Processed clauses                    : 37820
% 1141.02/143.88  # ...of these trivial                  : 12
% 1141.02/143.88  # ...subsumed                          : 33444
% 1141.02/143.88  # ...remaining for further processing  : 4364
% 1141.02/143.88  # Other redundant clauses eliminated   : 1340
% 1141.02/143.88  # Clauses deleted for lack of memory   : 0
% 1141.02/143.88  # Backward-subsumed                    : 452
% 1141.02/143.88  # Backward-rewritten                   : 1296
% 1141.02/143.88  # Generated clauses                    : 356752
% 1141.02/143.88  # ...of the previous two non-redundant : 350189
% 1141.02/143.88  # ...aggressively subsumed             : 0
% 1141.02/143.88  # Contextual simplify-reflections      : 171
% 1141.02/143.88  # Paramodulations                      : 355386
% 1141.02/143.88  # Factorizations                       : 25
% 1141.02/143.88  # NegExts                              : 0
% 1141.02/143.88  # Equation resolutions                 : 1343
% 1141.02/143.88  # Total rewrite steps                  : 16013
% 1141.02/143.88  # Propositional unsat checks           : 0
% 1141.02/143.88  #    Propositional check models        : 0
% 1141.02/143.88  #    Propositional check unsatisfiable : 0
% 1141.02/143.88  #    Propositional clauses             : 0
% 1141.02/143.88  #    Propositional clauses after purity: 0
% 1141.02/143.88  #    Propositional unsat core size     : 0
% 1141.02/143.88  #    Propositional preprocessing time  : 0.000
% 1141.02/143.88  #    Propositional encoding time       : 0.000
% 1141.02/143.88  #    Propositional solver time         : 0.000
% 1141.02/143.88  #    Success case prop preproc time    : 0.000
% 1141.02/143.88  #    Success case prop encoding time   : 0.000
% 1141.02/143.88  #    Success case prop solver time     : 0.000
% 1141.02/143.88  # Current number of processed clauses  : 2535
% 1141.02/143.88  #    Positive orientable unit clauses  : 60
% 1141.02/143.88  #    Positive unorientable unit clauses: 0
% 1141.02/143.88  #    Negative unit clauses             : 29
% 1141.02/143.88  #    Non-unit-clauses                  : 2446
% 1141.02/143.88  # Current number of unprocessed clauses: 295680
% 1141.02/143.88  # ...number of literals in the above   : 2389849
% 1141.02/143.88  # Current number of archived formulas  : 0
% 1141.02/143.88  # Current number of archived clauses   : 1821
% 1141.02/143.88  # Clause-clause subsumption calls (NU) : 4650799
% 1141.02/143.88  # Rec. Clause-clause subsumption calls : 1066571
% 1141.02/143.88  # Non-unit clause-clause subsumptions  : 24927
% 1141.02/143.88  # Unit Clause-clause subsumption calls : 6539
% 1141.02/143.88  # Rewrite failures with RHS unbound    : 0
% 1141.02/143.88  # BW rewrite match attempts            : 27
% 1141.02/143.88  # BW rewrite match successes           : 11
% 1141.02/143.88  # Condensation attempts                : 0
% 1141.02/143.88  # Condensation successes               : 0
% 1141.02/143.88  # Termbank termtop insertions          : 7070282
% 1141.02/143.88  
% 1141.02/143.88  # -------------------------------------------------
% 1141.02/143.88  # User time                : 545.645 s
% 1141.02/143.88  # System time              : 5.687 s
% 1141.02/143.88  # Total time               : 551.332 s
% 1141.02/143.88  # Maximum resident set size: 1892 pages
% 1141.02/143.88  
% 1141.02/143.88  # -------------------------------------------------
% 1141.02/143.88  # User time                : 704.002 s
% 1141.02/143.88  # System time              : 8.118 s
% 1141.02/143.88  # Total time               : 712.119 s
% 1141.02/143.88  # Maximum resident set size: 1728 pages
% 1141.02/143.88  % E---3.1 exiting
%------------------------------------------------------------------------------