TSTP Solution File: ITP012_4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP012_4 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 08:06:24 EDT 2024

% Result   : Theorem 156.04s 42.92s
% Output   : CNFRefutation 156.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   41
% Syntax   : Number of formulae    :  107 (  46 unt;  21 typ;   0 def)
%            Number of atoms       :  214 (  95 equ)
%            Maximal formula atoms :   29 (   2 avg)
%            Number of connectives :  186 (  58   ~;  50   |;  45   &)
%                                         (  18 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   16 (  11   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :   99 (   0 sgn  99   !;   0   ?;  99   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(decl_sort2,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

tff(decl_sort3,type,
    mono_2Etyop_2Einteger_2Eint: $tType ).

tff(decl_26,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(decl_52,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(decl_53,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(decl_228,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(decl_236,type,
    mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(decl_553,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(decl_677,type,
    mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(decl_685,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(decl_693,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(decl_695,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(decl_725,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(decl_746,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(decl_5298,type,
    mono_2Ec_2Einteger_2Eint__divides_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Ebool ).

tff(decl_5312,type,
    mono_2Ec_2Einteger_2Eint__neg_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

tff(decl_5320,type,
    mono_2Ec_2Einteger_2Eint__sub_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint ).

tff(decl_5374,type,
    esk1_0: mono_2Etyop_2Einteger_2Eint ).

tff(decl_5375,type,
    esk2_0: mono_2Etyop_2Einteger_2Eint ).

tff(decl_5376,type,
    esk3_0: mono_2Etyop_2Einteger_2Eint ).

tff(thm_2Enumeral_2Enumeral__suc,axiom,
    ( ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) )
    & ! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X614)) = mono_2Ec_2Earithmetic_2EBIT2_2E1(X614) )
    & ! [X616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X616)) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2ESUC_2E1(X616)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Enumeral_2Enumeral__suc) ).

tff(thm_2Earithmetic_2EADD1,axiom,
    ! [X1750: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X1750) = mono_2Ec_2Earithmetic_2E_2B_2E2(X1750,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2EADD1) ).

tff(thm_2Earithmetic_2ENUMERAL__DEF,axiom,
    ! [X1647: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1647) = X1647 ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2ENUMERAL__DEF) ).

tff(thm_2Earithmetic_2EBIT1,axiom,
    ! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X614) = mono_2Ec_2Earithmetic_2E_2B_2E2(X614,mono_2Ec_2Earithmetic_2E_2B_2E2(X614,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2EBIT1) ).

tff(thm_2Earithmetic_2EALT__ZERO,axiom,
    mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2EALT__ZERO) ).

tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
      <=> p(X8) )
      & ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
      <=> p(X8) )
      & ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
      <=> ~ p(X8) )
      & ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
      <=> ~ p(X8) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Ebool_2EEQ__CLAUSES) ).

tff(thm_2Earithmetic_2ELESS__EQ__ADD,axiom,
    ! [X1737: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X1737,mono_2Ec_2Earithmetic_2E_2B_2E2(X1737,X616))),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2ELESS__EQ__ADD) ).

tff(thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
    ! [X34494: mono_2Etyop_2Einteger_2Eint,X34495: mono_2Etyop_2Einteger_2Eint,X34496: mono_2Etyop_2Einteger_2Eint] :
      ( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,X34495))
     => ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,mono_2Ec_2Einteger_2Eint__sub_2E2(X34496,X34495)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,X34496) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X6)
      <=> p(X7) )
     => ( X6 = X7 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',reserved_2Eho_2Eboolext) ).

tff(thm_2Earithmetic_2ELESS__ANTISYM,axiom,
    ! [X1721: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
      ~ ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X1721,X616))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X616,X1721)) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2ELESS__ANTISYM) ).

tff(thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC,axiom,
    ! [X614: mono_2Etyop_2Enum_2Enum,X1729: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X1729) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2ESUC_2E1(X1729)) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) ).

tff(thm_2Earithmetic_2ELESS__EQ,axiom,
    ! [X1726: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X1726,X616) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2ESUC_2E1(X1726),X616) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Earithmetic_2ELESS__EQ) ).

tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(mono_2Ec_2Ebool_2ET_2E0)
         => p(X8) )
      <=> p(X8) )
      & ( ( p(X8)
         => p(mono_2Ec_2Ebool_2ET_2E0) )
      <=> p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ( p(mono_2Ec_2Ebool_2EF_2E0)
         => p(X8) )
      <=> p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ( p(X8)
         => p(X8) )
      <=> p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ( p(X8)
         => p(mono_2Ec_2Ebool_2EF_2E0) )
      <=> ~ p(X8) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Ebool_2EIMP__CLAUSES) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( X8 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',reserved_2Eho_2Ebool__cases__ax) ).

tff(thm_2Ebool_2ENOT__F,axiom,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X8)
     => ( X8 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Ebool_2ENOT__F) ).

tff(thm_2Einteger_2EINT__DIVIDES__LSUB,axiom,
    ! [X34491: mono_2Etyop_2Einteger_2Eint,X34492: mono_2Etyop_2Einteger_2Eint,X34493: mono_2Etyop_2Einteger_2Eint] :
      ( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X34491,X34492))
     => ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34491,mono_2Ec_2Einteger_2Eint__sub_2E2(X34492,X34493)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34491,X34493) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',reserved_2Eho_2Enotfalse) ).

tff(thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
    ! [X34489: mono_2Etyop_2Einteger_2Eint,X34490: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34489,mono_2Ec_2Einteger_2Eint__neg_2E1(X34490)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34489,X34490) )
      & ( mono_2Ec_2Einteger_2Eint__divides_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(X34489),X34490) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34489,X34490) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).

tff(thm_2Einteger_2EINT__NEG__SUB,axiom,
    ! [X33966: mono_2Etyop_2Einteger_2Eint,X33967: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__sub_2E2(X33966,X33967)) = mono_2Ec_2Einteger_2Eint__sub_2E2(X33967,X33966) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Einteger_2EINT__NEG__SUB) ).

tff(thm_2Ebool_2EBOOL__EQ__DISTINCT,axiom,
    ( ( mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0 )
    & ( mono_2Ec_2Ebool_2EF_2E0 != mono_2Ec_2Ebool_2ET_2E0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p',thm_2Ebool_2EBOOL__EQ__DISTINCT) ).

tff(c_0_20,plain,
    ! [X36996: mono_2Etyop_2Enum_2Enum,X36997: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) )
      & ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X36996)) = mono_2Ec_2Earithmetic_2EBIT2_2E1(X36996) )
      & ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X36997)) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2ESUC_2E1(X36997)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Enumeral_2Enumeral__suc])]) ).

tff(c_0_21,plain,
    ! [X35919: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X35919) = mono_2Ec_2Earithmetic_2E_2B_2E2(X35919,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD1]) ).

tff(c_0_22,plain,
    ! [X35616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X35616) = X35616 ),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ENUMERAL__DEF]) ).

tff(c_0_23,plain,
    ! [X35918: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X35918) = mono_2Ec_2Earithmetic_2E_2B_2E2(X35918,mono_2Ec_2Earithmetic_2E_2B_2E2(X35918,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) ),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EBIT1]) ).

tcf(c_0_24,plain,
    mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

tcf(c_0_25,plain,
    mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
    inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EALT__ZERO]) ).

tcf(c_0_26,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Enum_2ESUC_2E1(X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

tcf(c_0_27,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X567) = X567,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

tff(c_0_28,plain,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Ebool_2ET_2E0 = X8 )
      <=> p(X8) )
      & ( ( X8 = mono_2Ec_2Ebool_2ET_2E0 )
      <=> p(X8) )
      & ( ( mono_2Ec_2Ebool_2EF_2E0 = X8 )
      <=> ~ p(X8) )
      & ( ( X8 = mono_2Ec_2Ebool_2EF_2E0 )
      <=> ~ p(X8) ) ),
    inference(fof_simplification,[status(thm)],[thm_2Ebool_2EEQ__CLAUSES]) ).

tff(c_0_29,plain,
    ! [X36256: mono_2Etyop_2Enum_2Enum,X36257: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X36256,mono_2Ec_2Earithmetic_2E_2B_2E2(X36256,X36257))),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__EQ__ADD]) ).

tcf(c_0_30,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EBIT1_2E1(X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

tcf(c_0_31,plain,
    mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).

tcf(c_0_32,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(X567),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_25]),c_0_27]) ).

tff(c_0_33,plain,
    ! [X37364: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Ebool_2ET_2E0 != X37364 )
        | p(X37364) )
      & ( ~ p(X37364)
        | ( mono_2Ec_2Ebool_2ET_2E0 = X37364 ) )
      & ( ( X37364 != mono_2Ec_2Ebool_2ET_2E0 )
        | p(X37364) )
      & ( ~ p(X37364)
        | ( X37364 = mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( mono_2Ec_2Ebool_2EF_2E0 != X37364 )
        | ~ p(X37364) )
      & ( p(X37364)
        | ( mono_2Ec_2Ebool_2EF_2E0 = X37364 ) )
      & ( ( X37364 != mono_2Ec_2Ebool_2EF_2E0 )
        | ~ p(X37364) )
      & ( p(X37364)
        | ( X37364 = mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).

tcf(c_0_34,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575))),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

tcf(c_0_35,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X567)) = mono_2Ec_2Earithmetic_2EBIT1_2E1(X567),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

tff(c_0_36,negated_conjecture,
    ~ ! [X34494: mono_2Etyop_2Einteger_2Eint,X34495: mono_2Etyop_2Einteger_2Eint,X34496: mono_2Etyop_2Einteger_2Eint] :
        ( p(mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,X34495))
       => ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,mono_2Ec_2Einteger_2Eint__sub_2E2(X34496,X34495)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34494,X34496) ) ),
    inference(assume_negation,[status(cth)],[thm_2Einteger_2EINT__DIVIDES__RSUB]) ).

tff(c_0_37,plain,
    ! [X34612: mono_2Etyop_2Emin_2Ebool,X34613: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ p(X34612)
        | ~ p(X34613)
        | ( X34612 = X34613 ) )
      & ( p(X34612)
        | p(X34613)
        | ( X34612 = X34613 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).

tff(c_0_38,plain,
    ! [X37027: mono_2Etyop_2Enum_2Enum,X37028: mono_2Etyop_2Enum_2Enum] :
      ( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X37027,X37028))
      | ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X37028,X37027)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2ELESS__ANTISYM])])]) ).

tff(c_0_39,plain,
    ! [X36249: mono_2Etyop_2Enum_2Enum,X36250: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X36249,X36250) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X36249,mono_2Ec_2Enum_2ESUC_2E1(X36250)) ),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC]) ).

tff(c_0_40,plain,
    ! [X36243: mono_2Etyop_2Enum_2Enum,X36244: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X36243,X36244) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2ESUC_2E1(X36243),X36244) ),
    inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__EQ]) ).

tcf(c_0_41,plain,
    ! [X6: mono_2Etyop_2Emin_2Ebool] :
      ( ( X6 = mono_2Ec_2Ebool_2ET_2E0 )
      | ~ p(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

tcf(c_0_42,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567))),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

tff(c_0_43,plain,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(mono_2Ec_2Ebool_2ET_2E0)
         => p(X8) )
      <=> p(X8) )
      & ( ( p(X8)
         => p(mono_2Ec_2Ebool_2ET_2E0) )
      <=> p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ( p(mono_2Ec_2Ebool_2EF_2E0)
         => p(X8) )
      <=> p(mono_2Ec_2Ebool_2ET_2E0) )
      & p(mono_2Ec_2Ebool_2ET_2E0)
      & ( ( p(X8)
         => p(mono_2Ec_2Ebool_2EF_2E0) )
      <=> ~ p(X8) ) ),
    inference(fof_simplification,[status(thm)],[thm_2Ebool_2EIMP__CLAUSES]) ).

tff(c_0_44,negated_conjecture,
    ( p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk2_0))
    & ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) != mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).

tcf(c_0_45,plain,
    ! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
      ( p(X6)
      | p(X7)
      | ( X6 = X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

tcf(c_0_46,plain,
    ! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
      ( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,X575))
      | ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X575,X567)) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

tcf(c_0_47,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,X575) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X575)),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

tcf(c_0_48,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,X575) = mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2ESUC_2E1(X567),X575),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

tcf(c_0_49,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)) = mono_2Ec_2Ebool_2ET_2E0,
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

tff(c_0_50,plain,
    ! [X37363: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(mono_2Ec_2Ebool_2ET_2E0)
        | p(X37363) )
      & ( ~ p(X37363)
        | p(X37363) )
      & ( ~ p(X37363)
        | ~ p(mono_2Ec_2Ebool_2ET_2E0)
        | p(X37363) )
      & ( p(X37363)
        | p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ~ p(mono_2Ec_2Ebool_2ET_2E0)
        | p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ~ p(mono_2Ec_2Ebool_2ET_2E0)
        | ~ p(X37363)
        | p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( p(mono_2Ec_2Ebool_2EF_2E0)
        | p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ~ p(X37363)
        | p(mono_2Ec_2Ebool_2ET_2E0) )
      & ( ~ p(mono_2Ec_2Ebool_2ET_2E0)
        | ~ p(mono_2Ec_2Ebool_2EF_2E0)
        | p(X37363) )
      & p(mono_2Ec_2Ebool_2ET_2E0)
      & ( p(X37363)
        | ~ p(X37363) )
      & ( ~ p(mono_2Ec_2Ebool_2EF_2E0)
        | ~ p(X37363) )
      & ( p(X37363)
        | ~ p(X37363)
        | p(mono_2Ec_2Ebool_2EF_2E0) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).

tcf(c_0_51,negated_conjecture,
    mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) != mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

tcf(c_0_52,plain,
    ! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
      ( ( X6 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( X6 = X7 )
      | p(X7) ),
    inference(spm,[status(thm)],[c_0_41,c_0_45]) ).

tff(c_0_53,plain,
    ! [X37351: mono_2Etyop_2Emin_2Ebool] :
      ( ( X37351 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( X37351 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).

tcf(c_0_54,plain,
    ! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
      ( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2ESUC_2E1(X567),X575))
      | ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X575,X567)) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

tcf(c_0_55,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2ESUC_2E1(X567))) = mono_2Ec_2Ebool_2ET_2E0,
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

tcf(c_0_56,plain,
    p(mono_2Ec_2Ebool_2ET_2E0),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

tcf(c_0_57,negated_conjecture,
    ! [X6: mono_2Etyop_2Emin_2Ebool] :
      ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) = X6 )
      | p(X6)
      | ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0) != mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

tcf(c_0_58,plain,
    ! [X6: mono_2Etyop_2Emin_2Ebool] :
      ( ( X6 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( X6 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

tff(c_0_59,plain,
    ! [X8: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X8)
     => ( X8 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(fof_simplification,[status(thm)],[thm_2Ebool_2ENOT__F]) ).

tcf(c_0_60,plain,
    ! [X567: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(X567))),X567)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).

tcf(c_0_61,negated_conjecture,
    ! [X6: mono_2Etyop_2Emin_2Ebool] :
      ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) = X6 )
      | ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0) = mono_2Ec_2Ebool_2EF_2E0 )
      | p(X6) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

tff(c_0_62,plain,
    ! [X34534: mono_2Etyop_2Einteger_2Eint,X34535: mono_2Etyop_2Einteger_2Eint,X34536: mono_2Etyop_2Einteger_2Eint] :
      ( ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(X34534,X34535))
      | ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34534,mono_2Ec_2Einteger_2Eint__sub_2E2(X34535,X34536)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34534,X34536) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Einteger_2EINT__DIVIDES__LSUB])])]) ).

tcf(c_0_63,negated_conjecture,
    p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

tff(c_0_64,plain,
    ! [X37360: mono_2Etyop_2Emin_2Ebool] :
      ( p(X37360)
      | ( X37360 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).

tff(c_0_65,plain,
    ~ p(mono_2Ec_2Ebool_2EF_2E0),
    inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).

tcf(c_0_66,negated_conjecture,
    ( p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)))
    | p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0)) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45])]) ).

tcf(c_0_67,negated_conjecture,
    ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0) = mono_2Ec_2Ebool_2EF_2E0 )
    | ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_60]) ).

tcf(c_0_68,plain,
    ! [X33706: mono_2Etyop_2Einteger_2Eint,X33733: mono_2Etyop_2Einteger_2Eint,X33727: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,mono_2Ec_2Einteger_2Eint__sub_2E2(X33727,X33733)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,X33733) )
      | ~ p(mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,X33727)) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

tcf(c_0_69,negated_conjecture,
    mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk2_0) = mono_2Ec_2Ebool_2ET_2E0,
    inference(spm,[status(thm)],[c_0_41,c_0_63]) ).

tcf(c_0_70,plain,
    ! [X6: mono_2Etyop_2Emin_2Ebool] :
      ( p(X6)
      | ( X6 = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

tff(c_0_71,plain,
    ~ p(mono_2Ec_2Ebool_2EF_2E0),
    inference(fof_nnf,[status(thm)],[c_0_65]) ).

tff(c_0_72,plain,
    ! [X34532: mono_2Etyop_2Einteger_2Eint,X34533: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(X34532,mono_2Ec_2Einteger_2Eint__neg_2E1(X34533)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34532,X34533) )
      & ( mono_2Ec_2Einteger_2Eint__divides_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(X34532),X34533) = mono_2Ec_2Einteger_2Eint__divides_2E2(X34532,X34533) ) ),
    inference(variable_rename,[status(thm)],[thm_2Einteger_2EINT__DIVIDES__NEG]) ).

tff(c_0_73,plain,
    ! [X34551: mono_2Etyop_2Einteger_2Eint,X34552: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__sub_2E2(X34551,X34552)) = mono_2Ec_2Einteger_2Eint__sub_2E2(X34552,X34551) ),
    inference(variable_rename,[status(thm)],[thm_2Einteger_2EINT__NEG__SUB]) ).

tcf(c_0_74,negated_conjecture,
    ( ( mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) = mono_2Ec_2Ebool_2ET_2E0 )
    | p(mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_66]) ).

tcf(c_0_75,negated_conjecture,
    mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,esk3_0) = mono_2Ec_2Ebool_2EF_2E0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_56])]),c_0_70]) ).

tcf(c_0_76,plain,
    ~ p(mono_2Ec_2Ebool_2EF_2E0),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

tcf(c_0_77,plain,
    ! [X33706: mono_2Etyop_2Einteger_2Eint,X33727: mono_2Etyop_2Einteger_2Eint] : mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,mono_2Ec_2Einteger_2Eint__neg_2E1(X33727)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,X33727),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

tcf(c_0_78,plain,
    ! [X33727: mono_2Etyop_2Einteger_2Eint,X33706: mono_2Etyop_2Einteger_2Eint] : mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__sub_2E2(X33706,X33727)) = mono_2Ec_2Einteger_2Eint__sub_2E2(X33727,X33706),
    inference(split_conjunct,[status(thm)],[c_0_73]) ).

tff(c_0_79,plain,
    ( ( mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0 )
    & ( mono_2Ec_2Ebool_2EF_2E0 != mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(fof_simplification,[status(thm)],[thm_2Ebool_2EBOOL__EQ__DISTINCT]) ).

tcf(c_0_80,negated_conjecture,
    mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk3_0,esk2_0)) = mono_2Ec_2Ebool_2ET_2E0,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).

tcf(c_0_81,plain,
    ! [X33706: mono_2Etyop_2Einteger_2Eint,X33733: mono_2Etyop_2Einteger_2Eint,X33727: mono_2Etyop_2Einteger_2Eint] : mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,mono_2Ec_2Einteger_2Eint__sub_2E2(X33727,X33733)) = mono_2Ec_2Einteger_2Eint__divides_2E2(X33706,mono_2Ec_2Einteger_2Eint__sub_2E2(X33733,X33727)),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

tff(c_0_82,plain,
    ( ( mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0 )
    & ( mono_2Ec_2Ebool_2EF_2E0 != mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(fof_nnf,[status(thm)],[c_0_79]) ).

tcf(c_0_83,negated_conjecture,
    mono_2Ec_2Einteger_2Eint__divides_2E2(esk1_0,mono_2Ec_2Einteger_2Eint__sub_2E2(esk2_0,esk3_0)) = mono_2Ec_2Ebool_2ET_2E0,
    inference(rw,[status(thm)],[c_0_80,c_0_81]) ).

tcf(c_0_84,plain,
    mono_2Ec_2Ebool_2EF_2E0 != mono_2Ec_2Ebool_2ET_2E0,
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_85,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_83]),c_0_75]),c_0_69]),c_0_56])]),c_0_84]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 4.09/4.12  % Problem    : ITP012_4 : TPTP v8.1.2. Bugfixed v7.5.0.
% 4.13/4.14  % Command    : run_E %s %d THM
% 4.14/4.33  % Computer : n020.cluster.edu
% 4.14/4.33  % Model    : x86_64 x86_64
% 4.14/4.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 4.14/4.33  % Memory   : 8042.1875MB
% 4.14/4.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 4.14/4.33  % CPULimit   : 300
% 4.14/4.33  % WCLimit    : 300
% 4.14/4.33  % DateTime   : Fri May  3 12:35:21 EDT 2024
% 4.14/4.33  % CPUTime    : 
% 22.93/23.16  Running first-order theorem proving
% 22.93/23.16  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.93sqZKqm82/E---3.1_10940.p
% 156.04/42.92  # Version: 3.1.0
% 156.04/42.92  # Preprocessing class: FMLLSMLLSSSNFFN.
% 156.04/42.92  # Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 156.04/42.92  # Starting new_bool_3 with 894s (3) cores
% 156.04/42.92  # Starting new_bool_1 with 894s (3) cores
% 156.04/42.92  # Starting sh5l with 298s (1) cores
% 156.04/42.92  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 298s (1) cores
% 156.04/42.92  # new_bool_3 with pid 11598 completed with status 0
% 156.04/42.92  # Result found by new_bool_3
% 156.04/42.92  # Preprocessing class: FMLLSMLLSSSNFFN.
% 156.04/42.92  # Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 156.04/42.92  # Starting new_bool_3 with 894s (3) cores
% 156.04/42.92  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 156.04/42.92  # Search class: FGHSM-SMLM33-DFFFFFNN
% 156.04/42.92  # Scheduled 6 strats onto 3 cores with 894 seconds (894 total)
% 156.04/42.92  # Starting SAT001_MinMin_p005000_rr with 483s (1) cores
% 156.04/42.92  # Starting new_bool_3 with 90s (1) cores
% 156.04/42.92  # Starting SAT001_CA_MinMin_p005000_rr with 81s (1) cores
% 156.04/42.92  # SAT001_MinMin_p005000_rr with pid 11602 completed with status 0
% 156.04/42.92  # Result found by SAT001_MinMin_p005000_rr
% 156.04/42.92  # Preprocessing class: FMLLSMLLSSSNFFN.
% 156.04/42.92  # Scheduled 4 strats onto 8 cores with 298 seconds (2384 total)
% 156.04/42.92  # Starting new_bool_3 with 894s (3) cores
% 156.04/42.92  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 156.04/42.92  # Search class: FGHSM-SMLM33-DFFFFFNN
% 156.04/42.92  # Scheduled 6 strats onto 3 cores with 894 seconds (894 total)
% 156.04/42.92  # Starting SAT001_MinMin_p005000_rr with 483s (1) cores
% 156.04/42.92  # Preprocessing time       : 0.136 s
% 156.04/42.92  # Presaturation interreduction done
% 156.04/42.92  
% 156.04/42.92  # Proof found!
% 156.04/42.92  # SZS status Theorem
% 156.04/42.92  # SZS output start CNFRefutation
% See solution above
% 156.04/42.92  # Parsed axioms                        : 36789
% 156.04/42.92  # Removed by relevancy pruning/SinE    : 35375
% 156.04/42.92  # Initial clauses                      : 3312
% 156.04/42.92  # Removed in clause preprocessing      : 880
% 156.04/42.92  # Initial clauses in saturation        : 2432
% 156.04/42.92  # Processed clauses                    : 17112
% 156.04/42.92  # ...of these trivial                  : 464
% 156.04/42.92  # ...subsumed                          : 12262
% 156.04/42.92  # ...remaining for further processing  : 4386
% 156.04/42.92  # Other redundant clauses eliminated   : 2289
% 156.04/42.92  # Clauses deleted for lack of memory   : 0
% 156.04/42.92  # Backward-subsumed                    : 92
% 156.04/42.92  # Backward-rewritten                   : 219
% 156.04/42.92  # Generated clauses                    : 161026
% 156.04/42.92  # ...of the previous two non-redundant : 146137
% 156.04/42.92  # ...aggressively subsumed             : 0
% 156.04/42.92  # Contextual simplify-reflections      : 46
% 156.04/42.92  # Paramodulations                      : 158474
% 156.04/42.92  # Factorizations                       : 123
% 156.04/42.92  # NegExts                              : 0
% 156.04/42.92  # Equation resolutions                 : 2443
% 156.04/42.92  # Disequality decompositions           : 0
% 156.04/42.92  # Total rewrite steps                  : 49899
% 156.04/42.92  # ...of those cached                   : 44567
% 156.04/42.92  # Propositional unsat checks           : 0
% 156.04/42.92  #    Propositional check models        : 0
% 156.04/42.92  #    Propositional check unsatisfiable : 0
% 156.04/42.92  #    Propositional clauses             : 0
% 156.04/42.92  #    Propositional clauses after purity: 0
% 156.04/42.92  #    Propositional unsat core size     : 0
% 156.04/42.92  #    Propositional preprocessing time  : 0.000
% 156.04/42.92  #    Propositional encoding time       : 0.000
% 156.04/42.92  #    Propositional solver time         : 0.000
% 156.04/42.92  #    Success case prop preproc time    : 0.000
% 156.04/42.92  #    Success case prop encoding time   : 0.000
% 156.04/42.92  #    Success case prop solver time     : 0.000
% 156.04/42.92  # Current number of processed clauses  : 2546
% 156.04/42.92  #    Positive orientable unit clauses  : 278
% 156.04/42.92  #    Positive unorientable unit clauses: 12
% 156.04/42.92  #    Negative unit clauses             : 592
% 156.04/42.92  #    Non-unit-clauses                  : 1664
% 156.04/42.92  # Current number of unprocessed clauses: 132153
% 156.04/42.92  # ...number of literals in the above   : 635954
% 156.04/42.92  # Current number of archived formulas  : 0
% 156.04/42.92  # Current number of archived clauses   : 1717
% 156.04/42.92  # Clause-clause subsumption calls (NU) : 4067158
% 156.04/42.92  # Rec. Clause-clause subsumption calls : 418447
% 156.04/42.92  # Non-unit clause-clause subsumptions  : 5183
% 156.04/42.92  # Unit Clause-clause subsumption calls : 40319
% 156.04/42.92  # Rewrite failures with RHS unbound    : 0
% 156.04/42.92  # BW rewrite match attempts            : 1840
% 156.04/42.92  # BW rewrite match successes           : 295
% 156.04/42.92  # Condensation attempts                : 0
% 156.04/42.92  # Condensation successes               : 0
% 156.04/42.92  # Termbank termtop insertions          : 13300373
% 156.04/42.92  # Search garbage collected termcells   : 349473
% 156.04/42.92  
% 156.04/42.92  # -------------------------------------------------
% 156.04/42.92  # User time                : 16.341 s
% 156.04/42.92  # System time              : 0.310 s
% 156.04/42.92  # Total time               : 16.651 s
% 156.04/42.92  # Maximum resident set size: 79152 pages
% 156.04/42.92  
% 156.04/42.92  # -------------------------------------------------
% 156.04/42.92  # User time                : 50.655 s
% 156.04/42.92  # System time              : 0.683 s
% 156.04/42.92  # Total time               : 51.338 s
% 156.04/42.92  # Maximum resident set size: 68308 pages
% 156.04/42.92  % E---3.1 exiting
% 156.04/42.93  % E exiting
%------------------------------------------------------------------------------