TSTP Solution File: ITP012^2 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 08:06:23 EDT 2024

% Result   : Theorem 0.37s 0.59s
% Output   : CNFRefutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   55 (  25 unt;  15 typ;   0 def)
%            Number of atoms       :   77 (  20 equ;   0 cnn)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  717 (  25   ~;  22   |;   7   &; 655   @)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   8 con; 0-2 aty)
%            Number of variables   :   64 (   0   ^  64   !;   0   ?;  64   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    tp__ty_2Einteger_2Eint: $tType ).

thf(decl_26,type,
    ap: $i > $i > $i ).

thf(decl_28,type,
    p: $i > $o ).

thf(decl_33,type,
    inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).

thf(decl_34,type,
    surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).

thf(decl_35,type,
    c_2Einteger_2Eint__sub: $i ).

thf(decl_36,type,
    fo__c_2Einteger_2Eint__sub: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).

thf(decl_37,type,
    c_2Einteger_2Eint__add: $i ).

thf(decl_38,type,
    fo__c_2Einteger_2Eint__add: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).

thf(decl_39,type,
    c_2Einteger_2Eint__neg: $i ).

thf(decl_40,type,
    fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).

thf(decl_41,type,
    c_2Einteger_2Eint__divides: $i ).

thf(decl_54,type,
    esk1_0: tp__ty_2Einteger_2Eint ).

thf(decl_55,type,
    esk2_0: tp__ty_2Einteger_2Eint ).

thf(decl_56,type,
    esk3_0: tp__ty_2Einteger_2Eint ).

thf(stp_inj_surj_ty_2Einteger_2Eint,axiom,
    ! [X16: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X16 ) )
      = X16 ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',stp_inj_surj_ty_2Einteger_2Eint) ).

thf(stp_eq_fo_c_2Einteger_2Eint__sub,axiom,
    ! [X19: tp__ty_2Einteger_2Eint,X20: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ X19 @ X20 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X19 ) ) @ ( inj__ty_2Einteger_2Eint @ X20 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',stp_eq_fo_c_2Einteger_2Eint__sub) ).

thf(stp_eq_fo_c_2Einteger_2Eint__add,axiom,
    ! [X19: tp__ty_2Einteger_2Eint,X20: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ X19 @ X20 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X19 ) ) @ ( inj__ty_2Einteger_2Eint @ X20 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',stp_eq_fo_c_2Einteger_2Eint__add) ).

thf(ax_thm_2Einteger_2Eint__sub,axiom,
    ! [X37: tp__ty_2Einteger_2Eint,X38: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X37 ) ) @ ( inj__ty_2Einteger_2Eint @ X38 ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X37 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X38 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',ax_thm_2Einteger_2Eint__sub) ).

thf(stp_eq_fo_c_2Einteger_2Eint__neg,axiom,
    ! [X19: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X19 ) )
      = ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).

thf(conj_thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
    ! [X39: tp__ty_2Einteger_2Eint,X40: tp__ty_2Einteger_2Eint,X41: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) )
     => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X41 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X41 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',conj_thm_2Einteger_2EINT__DIVIDES__RADD) ).

thf(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
    ! [X39: tp__ty_2Einteger_2Eint,X40: tp__ty_2Einteger_2Eint,X41: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) )
     => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X41 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X41 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',conj_thm_2Einteger_2EINT__DIVIDES__RSUB) ).

thf(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
    ! [X39: tp__ty_2Einteger_2Eint,X40: tp__ty_2Einteger_2Eint] :
      ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) )
      & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X39 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) )
      <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qvrcu5mbil/E---3.1_17643.p',conj_thm_2Einteger_2EINT__DIVIDES__NEG) ).

thf(c_0_8,plain,
    ! [X192: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X192 ) )
      = X192 ),
    inference(variable_rename,[status(thm)],[stp_inj_surj_ty_2Einteger_2Eint]) ).

thf(c_0_9,plain,
    ! [X195: tp__ty_2Einteger_2Eint,X196: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ X195 @ X196 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X195 ) ) @ ( inj__ty_2Einteger_2Eint @ X196 ) ) ),
    inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__sub]) ).

thf(c_0_10,plain,
    ! [X198: tp__ty_2Einteger_2Eint,X199: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ X198 @ X199 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X198 ) ) @ ( inj__ty_2Einteger_2Eint @ X199 ) ) ),
    inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__add]) ).

thf(c_0_11,plain,
    ! [X185: tp__ty_2Einteger_2Eint,X186: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X185 ) ) @ ( inj__ty_2Einteger_2Eint @ X186 ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X185 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X186 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[ax_thm_2Einteger_2Eint__sub]) ).

thf(c_0_12,plain,
    ! [X16: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X16 ) )
      = X16 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ X16 @ X17 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ X16 @ X17 ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ! [X197: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X197 ) )
      = ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X197 ) ) ),
    inference(variable_rename,[status(thm)],[stp_eq_fo_c_2Einteger_2Eint__neg]) ).

thf(c_0_16,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_17,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      = ( fo__c_2Einteger_2Eint__sub @ X16 @ X17 ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

thf(c_0_18,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      = ( fo__c_2Einteger_2Eint__add @ X16 @ X17 ) ),
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

thf(c_0_19,plain,
    ! [X16: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X16 ) )
      = ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X16 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_20,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ) )
      = ( fo__c_2Einteger_2Eint__sub @ X16 @ X17 ) ),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_21,plain,
    ! [X187: tp__ty_2Einteger_2Eint,X188: tp__ty_2Einteger_2Eint,X189: tp__ty_2Einteger_2Eint] :
      ( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X189 ) ) @ ( inj__ty_2Einteger_2Eint @ X188 ) ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( inj__ty_2Einteger_2Eint @ X189 ) ) )
        | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( inj__ty_2Einteger_2Eint @ X188 ) ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( inj__ty_2Einteger_2Eint @ X189 ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X189 ) ) @ ( inj__ty_2Einteger_2Eint @ X188 ) ) ) )
        | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X187 ) ) @ ( inj__ty_2Einteger_2Eint @ X188 ) ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__RADD])])])]) ).

thf(c_0_22,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( fo__c_2Einteger_2Eint__add @ X16 @ ( fo__c_2Einteger_2Eint__neg @ X17 ) )
      = ( fo__c_2Einteger_2Eint__sub @ X16 @ X17 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

thf(c_0_23,negated_conjecture,
    ~ ! [X39: tp__ty_2Einteger_2Eint,X40: tp__ty_2Einteger_2Eint,X41: tp__ty_2Einteger_2Eint] :
        ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) )
       => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X41 ) ) @ ( inj__ty_2Einteger_2Eint @ X40 ) ) ) )
        <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X39 ) ) @ ( inj__ty_2Einteger_2Eint @ X41 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj_thm_2Einteger_2EINT__DIVIDES__RSUB]) ).

thf(c_0_24,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint,X19: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X17 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_25,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      = ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_22]),c_0_13]),c_0_19]) ).

thf(c_0_26,negated_conjecture,
    ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) )
    & ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) )
    & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).

thf(c_0_27,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint,X19: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_25]) ).

thf(c_0_28,negated_conjecture,
    ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
    | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_29,plain,
    ! [X190: tp__ty_2Einteger_2Eint,X191: tp__ty_2Einteger_2Eint] :
      ( ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X191 ) ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X191 ) ) ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X190 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X190 ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) )
        | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X190 ) ) ) @ ( inj__ty_2Einteger_2Eint @ X191 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG])])]) ).

thf(c_0_30,negated_conjecture,
    ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_31,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_32,negated_conjecture,
    p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_33,negated_conjecture,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_34,negated_conjecture,
    p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

thf(c_0_35,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint,X19: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X17 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_36,negated_conjecture,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ esk3_0 ) ) @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).

thf(c_0_37,plain,
    ! [X16: tp__ty_2Einteger_2Eint,X19: tp__ty_2Einteger_2Eint,X17: tp__ty_2Einteger_2Eint] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X17 ) ) @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X19 ) ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ X16 ) ) @ ( inj__ty_2Einteger_2Eint @ X17 ) ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_19]),c_0_25]) ).

thf(c_0_38,negated_conjecture,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ esk1_0 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ esk2_0 ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34])]) ).

thf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : ITP012^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.03/0.15  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 12:59:24 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.23/0.51  Running higher-order theorem proving
% 0.23/0.51  Running: /export/starexec/sandbox/solver/bin/eprover-ho --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.qvrcu5mbil/E---3.1_17643.p
% 0.37/0.59  # Version: 3.1.0-ho
% 0.37/0.59  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.37/0.59  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.59  # Starting new_ho_10 with 900s (3) cores
% 0.37/0.59  # Starting sh2lt with 300s (1) cores
% 0.37/0.59  # Starting new_ho_5 with 300s (1) cores
% 0.37/0.59  # Starting full_lambda_5 with 300s (1) cores
% 0.37/0.59  # Starting sh9 with 300s (1) cores
% 0.37/0.59  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.37/0.59  # new_ho_5 with pid 17755 completed with status 0
% 0.37/0.59  # Result found by new_ho_5
% 0.37/0.59  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.37/0.59  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.59  # Starting new_ho_10 with 900s (3) cores
% 0.37/0.59  # Starting sh2lt with 300s (1) cores
% 0.37/0.59  # Starting new_ho_5 with 300s (1) cores
% 0.37/0.59  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.37/0.59  # Search class: HGHSM-FFMM32-MSFFFFNN
% 0.37/0.59  # partial match(1): HGHSM-FFMM32-MSFFFFBN
% 0.37/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.59  # Starting new_ho_10 with 135s (1) cores
% 0.37/0.59  # new_ho_10 with pid 17774 completed with status 0
% 0.37/0.59  # Result found by new_ho_10
% 0.37/0.59  # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.37/0.59  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.59  # Starting new_ho_10 with 900s (3) cores
% 0.37/0.59  # Starting sh2lt with 300s (1) cores
% 0.37/0.59  # Starting new_ho_5 with 300s (1) cores
% 0.37/0.59  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.37/0.59  # Search class: HGHSM-FFMM32-MSFFFFNN
% 0.37/0.59  # partial match(1): HGHSM-FFMM32-MSFFFFBN
% 0.37/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.59  # Starting new_ho_10 with 135s (1) cores
% 0.37/0.59  # Preprocessing time       : 0.003 s
% 0.37/0.59  # Presaturation interreduction done
% 0.37/0.59  
% 0.37/0.59  # Proof found!
% 0.37/0.59  # SZS status Theorem
% 0.37/0.59  # SZS output start CNFRefutation
% See solution above
% 0.37/0.60  # Parsed axioms                        : 90
% 0.37/0.60  # Removed by relevancy pruning/SinE    : 53
% 0.37/0.60  # Initial clauses                      : 316
% 0.37/0.60  # Removed in clause preprocessing      : 248
% 0.37/0.60  # Initial clauses in saturation        : 68
% 0.37/0.60  # Processed clauses                    : 227
% 0.37/0.60  # ...of these trivial                  : 3
% 0.37/0.60  # ...subsumed                          : 24
% 0.37/0.60  # ...remaining for further processing  : 200
% 0.37/0.60  # Other redundant clauses eliminated   : 0
% 0.37/0.60  # Clauses deleted for lack of memory   : 0
% 0.37/0.60  # Backward-subsumed                    : 0
% 0.37/0.60  # Backward-rewritten                   : 6
% 0.37/0.60  # Generated clauses                    : 1538
% 0.37/0.60  # ...of the previous two non-redundant : 1411
% 0.37/0.60  # ...aggressively subsumed             : 0
% 0.37/0.60  # Contextual simplify-reflections      : 0
% 0.37/0.60  # Paramodulations                      : 1537
% 0.37/0.60  # Factorizations                       : 0
% 0.37/0.60  # NegExts                              : 0
% 0.37/0.60  # Equation resolutions                 : 1
% 0.37/0.60  # Disequality decompositions           : 0
% 0.37/0.60  # Total rewrite steps                  : 269
% 0.37/0.60  # ...of those cached                   : 200
% 0.37/0.60  # Propositional unsat checks           : 0
% 0.37/0.60  #    Propositional check models        : 0
% 0.37/0.60  #    Propositional check unsatisfiable : 0
% 0.37/0.60  #    Propositional clauses             : 0
% 0.37/0.60  #    Propositional clauses after purity: 0
% 0.37/0.60  #    Propositional unsat core size     : 0
% 0.37/0.60  #    Propositional preprocessing time  : 0.000
% 0.37/0.60  #    Propositional encoding time       : 0.000
% 0.37/0.60  #    Propositional solver time         : 0.000
% 0.37/0.60  #    Success case prop preproc time    : 0.000
% 0.37/0.60  #    Success case prop encoding time   : 0.000
% 0.37/0.60  #    Success case prop solver time     : 0.000
% 0.37/0.60  # Current number of processed clauses  : 144
% 0.37/0.60  #    Positive orientable unit clauses  : 38
% 0.37/0.60  #    Positive unorientable unit clauses: 0
% 0.37/0.60  #    Negative unit clauses             : 2
% 0.37/0.60  #    Non-unit-clauses                  : 104
% 0.37/0.60  # Current number of unprocessed clauses: 1299
% 0.37/0.60  # ...number of literals in the above   : 3607
% 0.37/0.60  # Current number of archived formulas  : 0
% 0.37/0.60  # Current number of archived clauses   : 56
% 0.37/0.60  # Clause-clause subsumption calls (NU) : 1501
% 0.37/0.60  # Rec. Clause-clause subsumption calls : 730
% 0.37/0.60  # Non-unit clause-clause subsumptions  : 24
% 0.37/0.60  # Unit Clause-clause subsumption calls : 172
% 0.37/0.60  # Rewrite failures with RHS unbound    : 0
% 0.37/0.60  # BW rewrite match attempts            : 65
% 0.37/0.60  # BW rewrite match successes           : 3
% 0.37/0.60  # Condensation attempts                : 227
% 0.37/0.60  # Condensation successes               : 0
% 0.37/0.60  # Termbank termtop insertions          : 58769
% 0.37/0.60  # Search garbage collected termcells   : 4174
% 0.37/0.60  
% 0.37/0.60  # -------------------------------------------------
% 0.37/0.60  # User time                : 0.063 s
% 0.37/0.60  # System time              : 0.004 s
% 0.37/0.60  # Total time               : 0.067 s
% 0.37/0.60  # Maximum resident set size: 2576 pages
% 0.37/0.60  
% 0.37/0.60  # -------------------------------------------------
% 0.37/0.60  # User time                : 0.067 s
% 0.37/0.60  # System time              : 0.006 s
% 0.37/0.60  # Total time               : 0.073 s
% 0.37/0.60  # Maximum resident set size: 1852 pages
% 0.37/0.60  % E---3.1 exiting
% 0.37/0.60  % E exiting
%------------------------------------------------------------------------------