TSTP Solution File: ITP015^5 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : ITP015^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n005.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 : Mon Jun 24 09:11:01 EDT 2024

% Result   : Theorem 44.59s 9.66s
% Output   : CNFRefutation 44.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   54 (  32 unt;   0 typ;   0 def)
%            Number of atoms       :   81 (  32 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  477 (  24   ~;  21   |;   1   &; 426   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    5 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  57   !;   0   ?;  57   :)

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

thf(decl_sort2,type,
    tp__ty_2Enum_2Enum: $tType ).

thf(decl_sort3,type,
    tp__ty_2Einteger_2Eint: $tType ).

thf(decl_22,type,
    bool: del ).

thf(decl_24,type,
    arr: del > del > del ).

thf(decl_25,type,
    mem: $i > del > $o ).

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

thf(decl_86,type,
    ty_2Enum_2Enum: del ).

thf(decl_87,type,
    inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).

thf(decl_90,type,
    fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).

thf(decl_845,type,
    ty_2Efcp_2Ecart: del > del > del ).

thf(decl_1313,type,
    ty_2Einteger_2Eint: del ).

thf(decl_1314,type,
    inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).

thf(decl_1315,type,
    surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).

thf(decl_1349,type,
    c_2Einteger_2Eint__neg: $i ).

thf(decl_1351,type,
    c_2Einteger_2Eint__of__num: $i ).

thf(decl_1409,type,
    c_2Ewords_2En2w: del > $i ).

thf(decl_2010,type,
    c_2Einteger__word_2Ei2w: del > $i ).

thf(decl_2019,type,
    c_2Einteger__word_2Ew2i: del > $i ).

thf(decl_2032,type,
    esk1_0: del ).

thf(ap_tp,axiom,
    ! [X3: del,X4: del,X5: $i] :
      ( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
     => ! [X6: $i] :
          ( ( mem @ X6 @ X3 )
         => ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',ap_tp) ).

thf(stp_iso_mem_ty_2Einteger_2Eint,axiom,
    ! [X17557: $i] :
      ( ( mem @ X17557 @ ty_2Einteger_2Eint )
     => ( X17557
        = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X17557 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',stp_iso_mem_ty_2Einteger_2Eint) ).

thf(mem_c_2Einteger_2Eint__neg,axiom,
    mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',mem_c_2Einteger_2Eint__neg) ).

thf(stp_inj_mem_ty_2Einteger_2Eint,axiom,
    ! [X17556: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X17556 ) @ ty_2Einteger_2Eint ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',stp_inj_mem_ty_2Einteger_2Eint) ).

thf(conj_thm_2Einteger_2EINT__NEG__SAME__EQ,axiom,
    ! [X18068: tp__ty_2Einteger_2Eint] :
      ( ( X18068
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X18068 ) ) ) )
    <=> ( X18068
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',conj_thm_2Einteger_2EINT__NEG__SAME__EQ) ).

thf(mem_c_2Einteger_2Eint__of__num,axiom,
    mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',mem_c_2Einteger_2Eint__of__num) ).

thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
    ! [X147: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X147 ) @ ty_2Enum_2Enum ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',stp_inj_mem_ty_2Enum_2Enum) ).

thf(mem_c_2Einteger__word_2Ew2i,axiom,
    ! [X13: del] : ( mem @ ( c_2Einteger__word_2Ew2i @ X13 ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ X13 ) @ ty_2Einteger_2Eint ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',mem_c_2Einteger__word_2Ew2i) ).

thf(conj_thm_2Einteger__word_2Eword__0__w2i,axiom,
    ! [X13: del] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ X13 ) @ ( ap @ ( c_2Ewords_2En2w @ X13 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',conj_thm_2Einteger__word_2Eword__0__w2i) ).

thf(conj_thm_2Einteger__word_2Ei2w__w2i,axiom,
    ! [X13: del,X14988: $i] :
      ( ( mem @ X14988 @ ( ty_2Efcp_2Ecart @ bool @ X13 ) )
     => ( ( ap @ ( c_2Einteger__word_2Ei2w @ X13 ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ X13 ) @ X14988 ) )
        = X14988 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',conj_thm_2Einteger__word_2Ei2w__w2i) ).

thf(mem_c_2Ewords_2En2w,axiom,
    ! [X13: del] : ( mem @ ( c_2Ewords_2En2w @ X13 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ X13 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',mem_c_2Ewords_2En2w) ).

thf(conj_thm_2Einteger__word_2Ei2w__0,conjecture,
    ! [X13: del] :
      ( ( ap @ ( c_2Einteger__word_2Ei2w @ X13 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      = ( ap @ ( c_2Ewords_2En2w @ X13 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p',conj_thm_2Einteger__word_2Ei2w__0) ).

thf(c_0_12,plain,
    ! [X23444: del,X23445: del,X23446: $i,X23447: $i] :
      ( ~ ( mem @ X23446 @ ( arr @ X23444 @ X23445 ) )
      | ~ ( mem @ X23447 @ X23444 )
      | ( mem @ ( ap @ X23446 @ X23447 ) @ X23445 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).

thf(c_0_13,plain,
    ! [X24370: $i] :
      ( ~ ( mem @ X24370 @ ty_2Einteger_2Eint )
      | ( X24370
        = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X24370 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_ty_2Einteger_2Eint])])]) ).

thf(c_0_14,plain,
    ! [X2: $i,X5: $i,X4: del,X3: del] :
      ( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
      | ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
      | ~ ( mem @ X5 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_15,plain,
    mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
    inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__neg]) ).

thf(c_0_16,plain,
    ! [X2: $i] :
      ( ( X2
        = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X2 ) ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_17,plain,
    ! [X2: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X2 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_18,plain,
    ! [X24369: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X24369 ) @ ty_2Einteger_2Eint ),
    inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Einteger_2Eint]) ).

thf(c_0_19,plain,
    ! [X25223: tp__ty_2Einteger_2Eint] :
      ( ( ( X25223
         != ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X25223 ) ) ) )
        | ( X25223
          = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
      & ( ( X25223
         != ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
        | ( X25223
          = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X25223 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger_2EINT__NEG__SAME__EQ])])]) ).

thf(c_0_20,plain,
    ! [X2: $i] :
      ( ( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ X2 ) ) )
        = ( ap @ c_2Einteger_2Eint__neg @ X2 ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_21,plain,
    ! [X17555: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X17555 ) @ ty_2Einteger_2Eint ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_22,plain,
    mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ),
    inference(split_conjunct,[status(thm)],[mem_c_2Einteger_2Eint__of__num]) ).

thf(c_0_23,plain,
    ! [X17555: tp__ty_2Einteger_2Eint] :
      ( ( X17555
        = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) )
      | ( X17555
       != ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_24,plain,
    ! [X17555: tp__ty_2Einteger_2Eint] :
      ( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ) )
      = ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_25,plain,
    ! [X2: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X2 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_22]) ).

thf(c_0_26,plain,
    ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
    = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
    inference(er,[status(thm)],[c_0_23]) ).

thf(c_0_27,plain,
    ! [X24111: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X24111 ) @ ty_2Enum_2Enum ),
    inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Enum_2Enum]) ).

thf(c_0_28,plain,
    ! [X24374: del] : ( mem @ ( c_2Einteger__word_2Ew2i @ X24374 ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ X24374 ) @ ty_2Einteger_2Eint ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Einteger__word_2Ew2i]) ).

thf(c_0_29,plain,
    ! [X17555: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X17555 ) ) @ ty_2Einteger_2Eint ),
    inference(spm,[status(thm)],[c_0_21,c_0_24]) ).

thf(c_0_30,plain,
    ! [X2: $i] :
      ( ( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ X2 ) ) )
        = ( ap @ c_2Einteger_2Eint__of__num @ X2 ) )
      | ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

thf(c_0_31,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
    = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_26]) ).

thf(c_0_32,plain,
    ! [X146: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X146 ) @ ty_2Enum_2Enum ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_33,plain,
    ! [X3: del] : ( mem @ ( c_2Einteger__word_2Ew2i @ X3 ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ X3 ) @ ty_2Einteger_2Eint ) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

thf(c_0_34,plain,
    ! [X2: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X2 ) ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

thf(c_0_35,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_32])]) ).

thf(c_0_36,plain,
    ! [X2: $i,X3: del] :
      ( ( mem @ ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ X2 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_33]) ).

thf(c_0_37,plain,
    ! [X24387: del] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ X24387 ) @ ( ap @ ( c_2Ewords_2En2w @ X24387 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
    inference(variable_rename,[status(thm)],[conj_thm_2Einteger__word_2Eword__0__w2i]) ).

thf(c_0_38,plain,
    mem @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ty_2Einteger_2Eint,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32])]) ).

thf(c_0_39,plain,
    ! [X23386: del,X23387: $i] :
      ( ~ ( mem @ X23387 @ ( ty_2Efcp_2Ecart @ bool @ X23386 ) )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X23386 ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ X23386 ) @ X23387 ) )
        = X23387 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Einteger__word_2Ei2w__w2i])])]) ).

thf(c_0_40,plain,
    ! [X2: $i,X3: del] :
      ( ( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ X2 ) ) )
        = ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ X2 ) )
      | ~ ( mem @ X2 @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_36]) ).

thf(c_0_41,plain,
    ! [X3: del] :
      ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
      = ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_42,plain,
    ( ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_38]) ).

thf(c_0_43,plain,
    ! [X23376: del] : ( mem @ ( c_2Ewords_2En2w @ X23376 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ X23376 ) ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Ewords_2En2w]) ).

thf(c_0_44,negated_conjecture,
    ~ ! [X13: del] :
        ( ( ap @ ( c_2Einteger__word_2Ei2w @ X13 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( ap @ ( c_2Ewords_2En2w @ X13 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(assume_negation,[status(cth)],[conj_thm_2Einteger__word_2Ei2w__0]) ).

thf(c_0_45,plain,
    ! [X2: $i,X3: del] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X3 ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ X2 ) )
        = X2 )
      | ~ ( mem @ X2 @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

thf(c_0_46,plain,
    ! [X3: del] :
      ( ( ( ap @ ( c_2Einteger__word_2Ew2i @ X3 ) @ ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

thf(c_0_47,plain,
    ! [X3: del] : ( mem @ ( c_2Ewords_2En2w @ X3 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

thf(c_0_48,negated_conjecture,
    ( ( ap @ ( c_2Einteger__word_2Ei2w @ esk1_0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
   != ( ap @ ( c_2Ewords_2En2w @ esk1_0 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).

thf(c_0_49,plain,
    ! [X3: del] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X3 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
        = ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ty_2Efcp_2Ecart @ bool @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

thf(c_0_50,plain,
    ! [X3: del,X2: $i] :
      ( ( mem @ ( ap @ ( c_2Ewords_2En2w @ X3 ) @ X2 ) @ ( ty_2Efcp_2Ecart @ bool @ X3 ) )
      | ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_47]) ).

thf(c_0_51,negated_conjecture,
    ( ( ap @ ( c_2Einteger__word_2Ei2w @ esk1_0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
   != ( ap @ ( c_2Ewords_2En2w @ esk1_0 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

thf(c_0_52,plain,
    ! [X3: del] :
      ( ( ap @ ( c_2Einteger__word_2Ei2w @ X3 ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
      = ( ap @ ( c_2Ewords_2En2w @ X3 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32])]) ).

thf(c_0_53,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ITP015^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n005.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   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Jun 18 22:48:10 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 2.74/2.90  Running higher-order theorem proving
% 2.74/2.90  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.RpI0ou2is6/E---3.1_10708.p
% 44.59/9.66  # Version: 3.2.0-ho
% 44.59/9.66  # Preprocessing class: HMLLSMLLSSLNSFA.
% 44.59/9.66  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 44.59/9.66  # Starting new_bool_8 with 1196s (4) cores
% 44.59/9.66  # Starting post_as_ho5 with 598s (2) cores
% 44.59/9.66  # Starting new_bool_9 with 299s (1) cores
% 44.59/9.66  # Starting new_bool_3 with 299s (1) cores
% 44.59/9.66  # new_bool_8 with pid 10786 completed with status 0
% 44.59/9.66  # Result found by new_bool_8
% 44.59/9.66  # Preprocessing class: HMLLSMLLSSLNSFA.
% 44.59/9.66  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 44.59/9.66  # Starting new_bool_8 with 1196s (4) cores
% 44.59/9.66  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 44.59/9.66  # Search class: HGHSM-SMLM32-DSFFFFNN
% 44.59/9.66  # partial match(1): HGHSM-SMLM32-DSFFFFBN
% 44.59/9.66  # Scheduled 6 strats onto 4 cores with 1196 seconds (1196 total)
% 44.59/9.66  # Starting post_as_ho7 with 646s (1) cores
% 44.59/9.66  # Starting new_bool_8 with 120s (1) cores
% 44.59/9.66  # Starting full_lambda_3 with 108s (1) cores
% 44.59/9.66  # Starting post_as_ho6 with 108s (1) cores
% 44.59/9.66  # new_bool_8 with pid 10792 completed with status 0
% 44.59/9.66  # Result found by new_bool_8
% 44.59/9.66  # Preprocessing class: HMLLSMLLSSLNSFA.
% 44.59/9.66  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 44.59/9.66  # Starting new_bool_8 with 1196s (4) cores
% 44.59/9.66  # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 44.59/9.66  # Search class: HGHSM-SMLM32-DSFFFFNN
% 44.59/9.66  # partial match(1): HGHSM-SMLM32-DSFFFFBN
% 44.59/9.66  # Scheduled 6 strats onto 4 cores with 1196 seconds (1196 total)
% 44.59/9.66  # Starting post_as_ho7 with 646s (1) cores
% 44.59/9.66  # Starting new_bool_8 with 120s (1) cores
% 44.59/9.66  # Preprocessing time       : 0.092 s
% 44.59/9.66  # Presaturation interreduction done
% 44.59/9.66  
% 44.59/9.66  # Proof found!
% 44.59/9.66  # SZS status Theorem
% 44.59/9.66  # SZS output start CNFRefutation
% See solution above
% 44.59/9.66  # Parsed axioms                        : 13423
% 44.59/9.66  # Removed by relevancy pruning/SinE    : 12713
% 44.59/9.66  # Initial clauses                      : 2451
% 44.59/9.66  # Removed in clause preprocessing      : 1054
% 44.59/9.66  # Initial clauses in saturation        : 1397
% 44.59/9.66  # Processed clauses                    : 4998
% 44.59/9.66  # ...of these trivial                  : 84
% 44.59/9.66  # ...subsumed                          : 1433
% 44.59/9.66  # ...remaining for further processing  : 3481
% 44.59/9.66  # Other redundant clauses eliminated   : 362
% 44.59/9.66  # Clauses deleted for lack of memory   : 0
% 44.59/9.66  # Backward-subsumed                    : 32
% 44.59/9.66  # Backward-rewritten                   : 36
% 44.59/9.66  # Generated clauses                    : 110491
% 44.59/9.66  # ...of the previous two non-redundant : 109180
% 44.59/9.66  # ...aggressively subsumed             : 0
% 44.59/9.66  # Contextual simplify-reflections      : 2
% 44.59/9.66  # Paramodulations                      : 110106
% 44.59/9.66  # Factorizations                       : 4
% 44.59/9.66  # NegExts                              : 0
% 44.59/9.66  # Equation resolutions                 : 388
% 44.59/9.66  # Disequality decompositions           : 0
% 44.59/9.66  # Total rewrite steps                  : 4799
% 44.59/9.66  # ...of those cached                   : 4464
% 44.59/9.66  # Propositional unsat checks           : 0
% 44.59/9.66  #    Propositional check models        : 0
% 44.59/9.66  #    Propositional check unsatisfiable : 0
% 44.59/9.66  #    Propositional clauses             : 0
% 44.59/9.66  #    Propositional clauses after purity: 0
% 44.59/9.66  #    Propositional unsat core size     : 0
% 44.59/9.66  #    Propositional preprocessing time  : 0.000
% 44.59/9.66  #    Propositional encoding time       : 0.000
% 44.59/9.66  #    Propositional solver time         : 0.000
% 44.59/9.66  #    Success case prop preproc time    : 0.000
% 44.59/9.66  #    Success case prop encoding time   : 0.000
% 44.59/9.66  #    Success case prop solver time     : 0.000
% 44.59/9.66  # Current number of processed clauses  : 2081
% 44.59/9.66  #    Positive orientable unit clauses  : 328
% 44.59/9.66  #    Positive unorientable unit clauses: 5
% 44.59/9.66  #    Negative unit clauses             : 197
% 44.59/9.66  #    Non-unit-clauses                  : 1551
% 44.59/9.66  # Current number of unprocessed clauses: 106809
% 44.59/9.66  # ...number of literals in the above   : 591841
% 44.59/9.66  # Current number of archived formulas  : 0
% 44.59/9.66  # Current number of archived clauses   : 1309
% 44.59/9.66  # Clause-clause subsumption calls (NU) : 327437
% 44.59/9.66  # Rec. Clause-clause subsumption calls : 54717
% 44.59/9.66  # Non-unit clause-clause subsumptions  : 607
% 44.59/9.66  # Unit Clause-clause subsumption calls : 3423
% 44.59/9.66  # Rewrite failures with RHS unbound    : 0
% 44.59/9.66  # BW rewrite match attempts            : 15495
% 44.59/9.66  # BW rewrite match successes           : 84
% 44.59/9.66  # Condensation attempts                : 0
% 44.59/9.66  # Condensation successes               : 0
% 44.59/9.66  # Termbank termtop insertions          : 4870036
% 44.59/9.66  # Search garbage collected termcells   : 338392
% 44.59/9.66  
% 44.59/9.66  # -------------------------------------------------
% 44.59/9.66  # User time                : 5.048 s
% 44.59/9.66  # System time              : 0.187 s
% 44.59/9.66  # Total time               : 5.235 s
% 44.59/9.66  # Maximum resident set size: 63616 pages
% 44.59/9.66  
% 44.59/9.66  # -------------------------------------------------
% 44.59/9.66  # User time                : 20.465 s
% 44.59/9.66  # System time              : 0.655 s
% 44.59/9.66  # Total time               : 21.120 s
% 44.59/9.66  # Maximum resident set size: 55956 pages
% 44.59/9.66  % E---3.1 exiting
% 44.59/9.67  % E exiting
%------------------------------------------------------------------------------