TSTP Solution File: SEU213+2 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SEU213+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 19:30:55 EDT 2023

% Result   : Theorem 1154.92s 145.65s
% Output   : CNFRefutation 1154.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   55 (  13 unt;   0 def)
%            Number of atoms       :  260 (  28 equ)
%            Maximal formula atoms :   38 (   4 avg)
%            Number of connectives :  336 ( 131   ~; 141   |;  37   &)
%                                         (   9 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-5 aty)
%            Number of variables   :   96 (   1 sgn;  49   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',d4_funct_1) ).

fof(t21_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(relation_composition(X3,X2)))
          <=> ( in(X1,relation_dom(X3))
              & in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',t21_funct_1) ).

fof(fc1_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & relation(X2)
        & function(X2) )
     => ( relation(relation_composition(X1,X2))
        & function(relation_composition(X1,X2)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',fc1_funct_1) ).

fof(d8_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ! [X3] :
              ( relation(X3)
             => ( X3 = relation_composition(X1,X2)
              <=> ! [X4,X5] :
                    ( in(ordered_pair(X4,X5),X3)
                  <=> ? [X6] :
                        ( in(ordered_pair(X4,X6),X1)
                        & in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',d8_relat_1) ).

fof(dt_k5_relat_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & relation(X2) )
     => relation(relation_composition(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',dt_k5_relat_1) ).

fof(t20_relat_1,lemma,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',t20_relat_1) ).

fof(t8_funct_1,lemma,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(ordered_pair(X1,X2),X3)
      <=> ( in(X1,relation_dom(X3))
          & X2 = apply(X3,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Yc7l2AEVmR/E---3.1_9827.p',t8_funct_1) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_funct_1]) ).

fof(c_0_8,plain,
    ! [X40,X41,X42] :
      ( ( X42 != apply(X40,X41)
        | in(ordered_pair(X41,X42),X40)
        | ~ in(X41,relation_dom(X40))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( ~ in(ordered_pair(X41,X42),X40)
        | X42 = apply(X40,X41)
        | ~ in(X41,relation_dom(X40))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( X42 != apply(X40,X41)
        | X42 = empty_set
        | in(X41,relation_dom(X40))
        | ~ relation(X40)
        | ~ function(X40) )
      & ( X42 != empty_set
        | X42 = apply(X40,X41)
        | in(X41,relation_dom(X40))
        | ~ relation(X40)
        | ~ function(X40) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ! [X3] :
            ( ( relation(X3)
              & function(X3) )
           => ( in(X1,relation_dom(relation_composition(X3,X2)))
            <=> ( in(X1,relation_dom(X3))
                & in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
    inference(assume_negation,[status(cth)],[t21_funct_1]) ).

cnf(c_0_10,plain,
    ( in(ordered_pair(X3,X1),X2)
    | X1 != apply(X2,X3)
    | ~ in(X3,relation_dom(X2))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,negated_conjecture,
    ( relation(esk2_0)
    & function(esk2_0)
    & relation(esk3_0)
    & function(esk3_0)
    & ( ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
      | ~ in(esk1_0,relation_dom(esk3_0))
      | ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0)) )
    & ( in(esk1_0,relation_dom(esk3_0))
      | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) )
    & ( in(apply(esk3_0,esk1_0),relation_dom(esk2_0))
      | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

cnf(c_0_12,plain,
    ( in(ordered_pair(X1,apply(X2,X1)),X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,relation_dom(X2)) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ( in(esk1_0,relation_dom(esk3_0))
    | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X74,X75] :
      ( ( relation(relation_composition(X74,X75))
        | ~ relation(X74)
        | ~ function(X74)
        | ~ relation(X75)
        | ~ function(X75) )
      & ( function(relation_composition(X74,X75))
        | ~ relation(X74)
        | ~ function(X74)
        | ~ relation(X75)
        | ~ function(X75) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).

fof(c_0_15,plain,
    ! [X46,X47,X48,X49,X50,X52,X53,X54,X57] :
      ( ( in(ordered_pair(X49,esk9_5(X46,X47,X48,X49,X50)),X46)
        | ~ in(ordered_pair(X49,X50),X48)
        | X48 != relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) )
      & ( in(ordered_pair(esk9_5(X46,X47,X48,X49,X50),X50),X47)
        | ~ in(ordered_pair(X49,X50),X48)
        | X48 != relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) )
      & ( ~ in(ordered_pair(X52,X54),X46)
        | ~ in(ordered_pair(X54,X53),X47)
        | in(ordered_pair(X52,X53),X48)
        | X48 != relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) )
      & ( ~ in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48)
        | ~ in(ordered_pair(esk10_3(X46,X47,X48),X57),X46)
        | ~ in(ordered_pair(X57,esk11_3(X46,X47,X48)),X47)
        | X48 = relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) )
      & ( in(ordered_pair(esk10_3(X46,X47,X48),esk12_3(X46,X47,X48)),X46)
        | in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48)
        | X48 = relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) )
      & ( in(ordered_pair(esk12_3(X46,X47,X48),esk11_3(X46,X47,X48)),X47)
        | in(ordered_pair(esk10_3(X46,X47,X48),esk11_3(X46,X47,X48)),X48)
        | X48 = relation_composition(X46,X47)
        | ~ relation(X48)
        | ~ relation(X47)
        | ~ relation(X46) ) ),
    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)],[d8_relat_1])])])])])]) ).

fof(c_0_16,plain,
    ! [X59,X60] :
      ( ~ relation(X59)
      | ~ relation(X60)
      | relation(relation_composition(X59,X60)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).

cnf(c_0_17,negated_conjecture,
    ( in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0))
    | in(esk1_0,relation_dom(esk3_0))
    | ~ relation(relation_composition(esk3_0,esk2_0))
    | ~ function(relation_composition(esk3_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    ( function(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    relation(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,negated_conjecture,
    function(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,negated_conjecture,
    function(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_23,plain,
    ( in(ordered_pair(X1,esk9_5(X2,X3,X4,X1,X5)),X2)
    | ~ in(ordered_pair(X1,X5),X4)
    | X4 != relation_composition(X2,X3)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( relation(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    ( in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0))
    | in(esk1_0,relation_dom(esk3_0))
    | ~ relation(relation_composition(esk3_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).

fof(c_0_26,lemma,
    ! [X33,X34,X35] :
      ( ( in(X33,relation_dom(X35))
        | ~ in(ordered_pair(X33,X34),X35)
        | ~ relation(X35) )
      & ( in(X34,relation_rng(X35))
        | ~ in(ordered_pair(X33,X34),X35)
        | ~ relation(X35) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).

cnf(c_0_27,plain,
    ( in(ordered_pair(X1,esk9_5(X2,X3,relation_composition(X2,X3),X1,X4)),X2)
    | ~ relation(X3)
    | ~ relation(X2)
    | ~ in(ordered_pair(X1,X4),relation_composition(X2,X3)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    ( in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0))
    | in(esk1_0,relation_dom(esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_19]),c_0_20])]) ).

cnf(c_0_29,plain,
    ( in(ordered_pair(X1,X4),X6)
    | ~ in(ordered_pair(X1,X2),X3)
    | ~ in(ordered_pair(X2,X4),X5)
    | X6 != relation_composition(X3,X5)
    | ~ relation(X6)
    | ~ relation(X5)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_30,negated_conjecture,
    ( in(apply(esk3_0,esk1_0),relation_dom(esk2_0))
    | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_31,lemma,
    ( in(X1,relation_dom(X2))
    | ~ in(ordered_pair(X1,X3),X2)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    ( in(ordered_pair(esk1_0,esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0))),esk3_0)
    | in(esk1_0,relation_dom(esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_20])]) ).

cnf(c_0_33,plain,
    ( in(ordered_pair(X1,X2),relation_composition(X3,X4))
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ in(ordered_pair(X5,X2),X4)
    | ~ in(ordered_pair(X1,X5),X3) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_29]),c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    ( in(ordered_pair(apply(esk3_0,esk1_0),apply(esk2_0,apply(esk3_0,esk1_0))),esk2_0)
    | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_30]),c_0_19]),c_0_21])]) ).

cnf(c_0_35,lemma,
    in(esk1_0,relation_dom(esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]) ).

cnf(c_0_36,negated_conjecture,
    ( in(ordered_pair(X1,apply(esk2_0,apply(esk3_0,esk1_0))),relation_composition(X2,esk2_0))
    | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
    | ~ relation(X2)
    | ~ in(ordered_pair(X1,apply(esk3_0,esk1_0)),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]) ).

cnf(c_0_37,lemma,
    in(ordered_pair(esk1_0,apply(esk3_0,esk1_0)),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_35]),c_0_20]),c_0_22])]) ).

cnf(c_0_38,lemma,
    ( in(ordered_pair(esk1_0,apply(esk2_0,apply(esk3_0,esk1_0))),relation_composition(esk3_0,esk2_0))
    | in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20])]) ).

cnf(c_0_39,lemma,
    ( in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
    | ~ relation(relation_composition(esk3_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_38]) ).

cnf(c_0_40,lemma,
    in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_19]),c_0_20])]) ).

cnf(c_0_41,lemma,
    ( in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0))
    | ~ relation(relation_composition(esk3_0,esk2_0))
    | ~ function(relation_composition(esk3_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_40]) ).

cnf(c_0_42,lemma,
    ( in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0))
    | ~ relation(relation_composition(esk3_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).

fof(c_0_43,lemma,
    ! [X43,X44,X45] :
      ( ( in(X43,relation_dom(X45))
        | ~ in(ordered_pair(X43,X44),X45)
        | ~ relation(X45)
        | ~ function(X45) )
      & ( X44 = apply(X45,X43)
        | ~ in(ordered_pair(X43,X44),X45)
        | ~ relation(X45)
        | ~ function(X45) )
      & ( ~ in(X43,relation_dom(X45))
        | X44 != apply(X45,X43)
        | in(ordered_pair(X43,X44),X45)
        | ~ relation(X45)
        | ~ function(X45) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_1])])]) ).

cnf(c_0_44,lemma,
    in(ordered_pair(esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)),relation_composition(esk3_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_19]),c_0_20])]) ).

cnf(c_0_45,plain,
    ( in(ordered_pair(esk9_5(X1,X2,X3,X4,X5),X5),X2)
    | ~ in(ordered_pair(X4,X5),X3)
    | X3 != relation_composition(X1,X2)
    | ~ relation(X3)
    | ~ relation(X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_46,lemma,
    ( X1 = apply(X2,X3)
    | ~ in(ordered_pair(X3,X1),X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_47,lemma,
    in(ordered_pair(esk1_0,esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0))),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_19]),c_0_20])]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
    | ~ in(esk1_0,relation_dom(esk3_0))
    | ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_49,plain,
    ( in(ordered_pair(esk9_5(X1,X2,relation_composition(X1,X2),X3,X4),X4),X2)
    | ~ relation(X2)
    | ~ relation(X1)
    | ~ in(ordered_pair(X3,X4),relation_composition(X1,X2)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_24]) ).

cnf(c_0_50,lemma,
    esk9_5(esk3_0,esk2_0,relation_composition(esk3_0,esk2_0),esk1_0,apply(relation_composition(esk3_0,esk2_0),esk1_0)) = apply(esk3_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]),c_0_22])]) ).

cnf(c_0_51,negated_conjecture,
    ( ~ in(esk1_0,relation_dom(relation_composition(esk3_0,esk2_0)))
    | ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_35])]) ).

cnf(c_0_52,lemma,
    in(ordered_pair(apply(esk3_0,esk1_0),apply(relation_composition(esk3_0,esk2_0),esk1_0)),esk2_0),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_19]),c_0_20])]),c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    ~ in(apply(esk3_0,esk1_0),relation_dom(esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_40])]) ).

cnf(c_0_54,lemma,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_19])]),c_0_53]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU213+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 2400
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Oct  2 09:53:51 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running first-order model finding
% 0.21/0.49  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.Yc7l2AEVmR/E---3.1_9827.p
% 1154.92/145.65  # Version: 3.1pre001
% 1154.92/145.65  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1154.92/145.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1154.92/145.65  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1154.92/145.65  # Starting new_bool_3 with 300s (1) cores
% 1154.92/145.65  # Starting new_bool_1 with 300s (1) cores
% 1154.92/145.65  # Starting sh5l with 300s (1) cores
% 1154.92/145.65  # new_bool_3 with pid 9945 completed with status 0
% 1154.92/145.65  # Result found by new_bool_3
% 1154.92/145.65  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1154.92/145.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1154.92/145.65  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1154.92/145.65  # Starting new_bool_3 with 300s (1) cores
% 1154.92/145.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1154.92/145.65  # Search class: FGHSM-FFMM31-SFFFFFNN
% 1154.92/145.65  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1154.92/145.65  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 9954 completed with status 7
% 1154.92/145.65  # Starting new_bool_3 with 31s (1) cores
% 1154.92/145.65  # new_bool_3 with pid 10890 completed with status 7
% 1154.92/145.65  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 28s (1) cores
% 1154.92/145.65  # G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 12407 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 13150 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 14491 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 28s (1) cores
% 1154.92/145.65  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 15887 completed with status 0
% 1154.92/145.65  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 1154.92/145.65  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1154.92/145.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1154.92/145.65  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1154.92/145.65  # Starting new_bool_3 with 300s (1) cores
% 1154.92/145.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1154.92/145.65  # Search class: FGHSM-FFMM31-SFFFFFNN
% 1154.92/145.65  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1154.92/145.65  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 9954 completed with status 7
% 1154.92/145.65  # Starting new_bool_3 with 31s (1) cores
% 1154.92/145.65  # new_bool_3 with pid 10890 completed with status 7
% 1154.92/145.65  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 28s (1) cores
% 1154.92/145.65  # G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 12407 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 13150 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 28s (1) cores
% 1154.92/145.65  # G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 14491 completed with status 7
% 1154.92/145.65  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 28s (1) cores
% 1154.92/145.65  # Preprocessing time       : 0.003 s
% 1154.92/145.65  # Presaturation interreduction done
% 1154.92/145.65  
% 1154.92/145.65  # Proof found!
% 1154.92/145.65  # SZS status Theorem
% 1154.92/145.65  # SZS output start CNFRefutation
% See solution above
% 1154.92/145.65  # Parsed axioms                        : 217
% 1154.92/145.65  # Removed by relevancy pruning/SinE    : 154
% 1154.92/145.65  # Initial clauses                      : 123
% 1154.92/145.65  # Removed in clause preprocessing      : 2
% 1154.92/145.65  # Initial clauses in saturation        : 121
% 1154.92/145.65  # Processed clauses                    : 7636
% 1154.92/145.65  # ...of these trivial                  : 21
% 1154.92/145.65  # ...subsumed                          : 6349
% 1154.92/145.65  # ...remaining for further processing  : 1266
% 1154.92/145.65  # Other redundant clauses eliminated   : 141
% 1154.92/145.65  # Clauses deleted for lack of memory   : 0
% 1154.92/145.65  # Backward-subsumed                    : 108
% 1154.92/145.65  # Backward-rewritten                   : 147
% 1154.92/145.65  # Generated clauses                    : 60201
% 1154.92/145.65  # ...of the previous two non-redundant : 55399
% 1154.92/145.65  # ...aggressively subsumed             : 0
% 1154.92/145.65  # Contextual simplify-reflections      : 82
% 1154.92/145.65  # Paramodulations                      : 60039
% 1154.92/145.65  # Factorizations                       : 16
% 1154.92/145.65  # NegExts                              : 0
% 1154.92/145.65  # Equation resolutions                 : 143
% 1154.92/145.65  # Total rewrite steps                  : 14484
% 1154.92/145.65  # Propositional unsat checks           : 0
% 1154.92/145.65  #    Propositional check models        : 0
% 1154.92/145.65  #    Propositional check unsatisfiable : 0
% 1154.92/145.65  #    Propositional clauses             : 0
% 1154.92/145.65  #    Propositional clauses after purity: 0
% 1154.92/145.65  #    Propositional unsat core size     : 0
% 1154.92/145.65  #    Propositional preprocessing time  : 0.000
% 1154.92/145.65  #    Propositional encoding time       : 0.000
% 1154.92/145.65  #    Propositional solver time         : 0.000
% 1154.92/145.65  #    Success case prop preproc time    : 0.000
% 1154.92/145.65  #    Success case prop encoding time   : 0.000
% 1154.92/145.65  #    Success case prop solver time     : 0.000
% 1154.92/145.65  # Current number of processed clauses  : 884
% 1154.92/145.65  #    Positive orientable unit clauses  : 59
% 1154.92/145.65  #    Positive unorientable unit clauses: 0
% 1154.92/145.65  #    Negative unit clauses             : 29
% 1154.92/145.65  #    Non-unit-clauses                  : 796
% 1154.92/145.65  # Current number of unprocessed clauses: 47400
% 1154.92/145.65  # ...number of literals in the above   : 234388
% 1154.92/145.65  # Current number of archived formulas  : 0
% 1154.92/145.65  # Current number of archived clauses   : 366
% 1154.92/145.65  # Clause-clause subsumption calls (NU) : 169840
% 1154.92/145.65  # Rec. Clause-clause subsumption calls : 85463
% 1154.92/145.65  # Non-unit clause-clause subsumptions  : 4161
% 1154.92/145.65  # Unit Clause-clause subsumption calls : 1625
% 1154.92/145.65  # Rewrite failures with RHS unbound    : 0
% 1154.92/145.65  # BW rewrite match attempts            : 19
% 1154.92/145.65  # BW rewrite match successes           : 10
% 1154.92/145.65  # Condensation attempts                : 0
% 1154.92/145.65  # Condensation successes               : 0
% 1154.92/145.65  # Termbank termtop insertions          : 875989
% 1154.92/145.65  
% 1154.92/145.65  # -------------------------------------------------
% 1154.92/145.65  # User time                : 140.266 s
% 1154.92/145.65  # System time              : 3.829 s
% 1154.92/145.65  # Total time               : 144.095 s
% 1154.92/145.65  # Maximum resident set size: 2272 pages
% 1154.92/145.65  
% 1154.92/145.65  # -------------------------------------------------
% 1154.92/145.65  # User time                : 140.275 s
% 1154.92/145.65  # System time              : 3.832 s
% 1154.92/145.65  # Total time               : 144.107 s
% 1154.92/145.65  # Maximum resident set size: 1892 pages
% 1154.92/145.65  % E---3.1 exiting
%------------------------------------------------------------------------------