TSTP Solution File: ITP003_4 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : ITP003_4 : TPTP v8.1.2. 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 : Sat May 4 08:08:38 EDT 2024
% Result : Theorem 136.89s 18.26s
% Output : CNFRefutation 136.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 63
% Syntax : Number of formulae : 185 ( 89 unt; 27 typ; 0 def)
% Number of atoms : 341 ( 215 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 284 ( 101 ~; 99 |; 59 &)
% ( 19 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 32 ( 20 >; 12 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 5 con; 0-3 aty)
% Number of variables : 198 ( 0 sgn 195 !; 3 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(decl_sort2,type,
mono_2Etyop_2Enum_2Enum: $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_557,type,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_628,type,
mono_2Ec_2Earithmetic_2E_2A_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_630,type,
mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_634,type,
mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(decl_642,type,
mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_644,type,
mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_646,type,
mono_2Ec_2Earithmetic_2EDIV_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_650,type,
mono_2Ec_2Earithmetic_2EEVEN_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
tff(decl_652,type,
mono_2Ec_2Earithmetic_2EEXP_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_656,type,
mono_2Ec_2Earithmetic_2EMAX_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_658,type,
mono_2Ec_2Earithmetic_2EMIN_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_660,type,
mono_2Ec_2Earithmetic_2EMOD_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(decl_662,type,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_664,type,
mono_2Ec_2Earithmetic_2EODD_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
tff(decl_668,type,
mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).
tff(decl_677,type,
esk1_0: mono_2Etyop_2Enum_2Enum ).
tff(decl_685,type,
esk9_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_686,type,
esk10_1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
tff(decl_861,type,
esk185_2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(thm_2Earithmetic_2EMULT__CLAUSES,axiom,
! [X1498: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2E0_2E0,X1498) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X1498,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X1498) = X1498 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X1498,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = X1498 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(X1498),X616) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X1498,X616),X616) )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X1498,mono_2Ec_2Enum_2ESUC_2E1(X616)) = mono_2Ec_2Earithmetic_2E_2B_2E2(X1498,mono_2Ec_2Earithmetic_2E_2A_2E2(X1498,X616)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMULT__CLAUSES) ).
tff(thm_2Earithmetic_2EEXP,axiom,
( ! [X1432: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EEXP_2E2(X1432,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
& ! [X1433: mono_2Etyop_2Enum_2Enum,X1434: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EEXP_2E2(X1433,mono_2Ec_2Enum_2ESUC_2E1(X1434)) = mono_2Ec_2Earithmetic_2E_2A_2E2(X1433,mono_2Ec_2Earithmetic_2EEXP_2E2(X1433,X1434)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEXP) ).
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.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EBIT1) ).
tff(thm_2Earithmetic_2EADD__SUC,axiom,
! [X1448: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X1448,X616)) = mono_2Ec_2Earithmetic_2E_2B_2E2(X1448,mono_2Ec_2Enum_2ESUC_2E1(X616)) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EADD__SUC) ).
tff(thm_2Earithmetic_2EADD__0,axiom,
! [X1447: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X1447,mono_2Ec_2Enum_2E0_2E0) = X1447 ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EADD__0) ).
tff(thm_2Earithmetic_2EEVEN,axiom,
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ! [X614: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X614)))
<=> ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN) ).
tff(thm_2Earithmetic_2EODD__DOUBLE,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X614)))),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EODD__DOUBLE) ).
tff(thm_2Earithmetic_2ENUMERAL__DEF,axiom,
! [X1426: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1426) = X1426 ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ENUMERAL__DEF) ).
tff(thm_2Earithmetic_2EBIT2,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X614) = mono_2Ec_2Earithmetic_2E_2B_2E2(X614,mono_2Ec_2Earithmetic_2E_2B_2E2(X614,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)))) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EBIT2) ).
tff(thm_2Earithmetic_2ETIMES2,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X614) = mono_2Ec_2Earithmetic_2E_2B_2E2(X614,X614) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ETIMES2) ).
tff(thm_2Earithmetic_2EEVEN__ODD,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614))
<=> ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X614)) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN__ODD) ).
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.pqLWG2yIsE/E---3.1_7267.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(thm_2Earithmetic_2EEVEN__EXP__IFF,axiom,
! [X614: mono_2Etyop_2Enum_2Enum,X1648: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EEXP_2E2(X1648,X614)))
<=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X614))
& p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X1648)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN__EXP__IFF) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',reserved_2Eho_2Enotfalse) ).
tff(thm_2Earithmetic_2EMOD__2,conjecture,
! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMOD_2E2(X614,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMOD__2) ).
tff(thm_2Earithmetic_2EALT__ZERO,axiom,
mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EALT__ZERO) ).
tff(thm_2Earithmetic_2EADD__EQ__1,axiom,
! [X1510: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2B_2E2(X1510,X616) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
<=> ( ( ( X1510 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
& ( X616 = mono_2Ec_2Enum_2E0_2E0 ) )
| ( ( X1510 = mono_2Ec_2Enum_2E0_2E0 )
& ( X616 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EADD__EQ__1) ).
tff(thm_2Earithmetic_2EONE,axiom,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EONE) ).
tff(reserved_2Eho_2Etruth,axiom,
p(mono_2Ec_2Ebool_2ET_2E0),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',reserved_2Eho_2Etruth) ).
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.pqLWG2yIsE/E---3.1_7267.p',reserved_2Eho_2Ebool__cases__ax) ).
tff(thm_2Earithmetic_2EMIN__DEF,axiom,
! [X1442: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMIN_2E2(X1442,X616) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X1442,X616),X1442,X616) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMIN__DEF) ).
tff(thm_2Earithmetic_2EMIN__0,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN_2E2(X614,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2EMIN_2E2(mono_2Ec_2Enum_2E0_2E0,X614) = mono_2Ec_2Enum_2E0_2E0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMIN__0) ).
tff(thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV,axiom,
! [X1792: mono_2Etyop_2Enum_2Enum,X1793: mono_2Etyop_2Enum_2Enum,X1794: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X1794)),X1793) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792) )
<=> ( ( X1793 = mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X1794))) )
& ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X1794))) = mono_2Ec_2Enum_2E0_2E0 ) ) )
& ( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X1794)),X1793) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792) )
<=> ( ( X1793 = mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X1794))) )
& ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X1792),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X1794))) = mono_2Ec_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV) ).
tff(thm_2Earithmetic_2EEVEN__ODD__EXISTS,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614))
=> ? [X1644: mono_2Etyop_2Enum_2Enum] : ( X614 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X1644) ) )
& ( p(mono_2Ec_2Earithmetic_2EODD_2E1(X614))
=> ? [X1645: mono_2Etyop_2Enum_2Enum] : ( X614 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X1645)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN__ODD__EXISTS) ).
tff(thm_2Earithmetic_2EEVEN__DOUBLE,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X614))),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN__DOUBLE) ).
tff(thm_2Eprim__rec_2ENOT__LESS__0,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2E0_2E0)),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
tff(thm_2Earithmetic_2EEVEN__ADD,axiom,
! [X1640: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X1640,X616)))
<=> ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X1640) = mono_2Ec_2Earithmetic_2EEVEN_2E1(X616) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EEVEN__ADD) ).
tff(thm_2Earithmetic_2ELESS__EQUAL__ADD,axiom,
! [X1629: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X1629,X616))
=> ? [X1630: mono_2Etyop_2Enum_2Enum] : ( X616 = mono_2Ec_2Earithmetic_2E_2B_2E2(X1629,X1630) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ELESS__EQUAL__ADD) ).
tff(thm_2Earithmetic_2EMOD__LESS,axiom,
! [X1745: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X616))
=> p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2EMOD_2E2(X1745,X616),X616)) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMOD__LESS) ).
tff(thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC,axiom,
! [X614: mono_2Etyop_2Enum_2Enum,X1470: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X614,X1470) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2ESUC_2E1(X1470)) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) ).
tff(thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X614)),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EZERO__LESS__EQ) ).
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.pqLWG2yIsE/E---3.1_7267.p',reserved_2Eho_2Eboolext) ).
tff(thm_2Earithmetic_2EMULT__EQ__DIV,axiom,
! [X1789: mono_2Etyop_2Enum_2Enum,X1790: mono_2Etyop_2Enum_2Enum,X1791: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X1791))
=> ( ( mono_2Ec_2Earithmetic_2E_2A_2E2(X1791,X1790) = X1789 )
<=> ( ( X1790 = mono_2Ec_2Earithmetic_2EDIV_2E2(X1789,X1791) )
& ( mono_2Ec_2Earithmetic_2EMOD_2E2(X1789,X1791) = mono_2Ec_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMULT__EQ__DIV) ).
tff(thm_2Earithmetic_2ELESS__EQ__SUC__REFL,axiom,
! [X1483: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X1483,mono_2Ec_2Enum_2ESUC_2E1(X1483))),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2ELESS__EQ__SUC__REFL) ).
tff(thm_2Earithmetic_2EMAX__DEF,axiom,
! [X1441: mono_2Etyop_2Enum_2Enum,X616: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMAX_2E2(X1441,X616) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X1441,X616),X616,X1441) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMAX__DEF) ).
tff(thm_2Earithmetic_2EMAX__0,axiom,
! [X614: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX_2E2(X614,mono_2Ec_2Enum_2E0_2E0) = X614 )
& ( mono_2Ec_2Earithmetic_2EMAX_2E2(mono_2Ec_2Enum_2E0_2E0,X614) = X614 ) ),
file('/export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p',thm_2Earithmetic_2EMAX__0) ).
tff(c_0_36,plain,
! [X2009: mono_2Etyop_2Enum_2Enum,X2010: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2E0_2E0,X2009) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2009,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X2009) = X2009 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2009,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = X2009 )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(X2009),X2010) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(X2009,X2010),X2010) )
& ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2009,mono_2Ec_2Enum_2ESUC_2E1(X2010)) = mono_2Ec_2Earithmetic_2E_2B_2E2(X2009,mono_2Ec_2Earithmetic_2E_2A_2E2(X2009,X2010)) ) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMULT__CLAUSES]) ).
tff(c_0_37,plain,
! [X2001: mono_2Etyop_2Enum_2Enum,X2002: mono_2Etyop_2Enum_2Enum,X2003: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEXP_2E2(X2001,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
& ( mono_2Ec_2Earithmetic_2EEXP_2E2(X2002,mono_2Ec_2Enum_2ESUC_2E1(X2003)) = mono_2Ec_2Earithmetic_2E_2A_2E2(X2002,mono_2Ec_2Earithmetic_2EEXP_2E2(X2002,X2003)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EEXP])]) ).
tff(c_0_38,plain,
! [X2124: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X2124) = mono_2Ec_2Earithmetic_2E_2B_2E2(X2124,mono_2Ec_2Earithmetic_2E_2B_2E2(X2124,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EBIT1]) ).
tff(c_0_39,plain,
! [X3241: mono_2Etyop_2Enum_2Enum,X3242: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X3241,X3242)) = mono_2Ec_2Earithmetic_2E_2B_2E2(X3241,mono_2Ec_2Enum_2ESUC_2E1(X3242)) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD__SUC]) ).
tff(c_0_40,plain,
! [X2152: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2152,mono_2Ec_2Enum_2E0_2E0) = X2152 ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EADD__0]) ).
tcf(c_0_41,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2E0_2E0,X567) = mono_2Ec_2Enum_2E0_2E0,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tcf(c_0_42,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEXP_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X575)) = mono_2Ec_2Earithmetic_2E_2A_2E2(X567,mono_2Ec_2Earithmetic_2EEXP_2E2(X567,X575)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_43,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_38]) ).
tcf(c_0_44,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575)) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X575)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
tcf(c_0_45,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Enum_2E0_2E0) = X567,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
tff(c_0_46,plain,
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ! [X614: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X614)))
<=> ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614)) ) ),
inference(fof_simplification,[status(thm)],[thm_2Earithmetic_2EEVEN]) ).
tff(c_0_47,plain,
! [X2028: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X2028)))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EODD__DOUBLE]) ).
tff(c_0_48,plain,
! [X2000: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2000) = X2000 ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ENUMERAL__DEF]) ).
tff(c_0_49,plain,
! [X2357: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X2357) = mono_2Ec_2Earithmetic_2E_2B_2E2(X2357,mono_2Ec_2Earithmetic_2E_2B_2E2(X2357,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)))) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EBIT2]) ).
tff(c_0_50,plain,
! [X2019: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X2019) = mono_2Ec_2Earithmetic_2E_2B_2E2(X2019,X2019) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ETIMES2]) ).
tff(c_0_51,plain,
! [X614: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614))
<=> ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X614)) ),
inference(fof_simplification,[status(thm)],[thm_2Earithmetic_2EEVEN__ODD]) ).
tff(c_0_52,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_53,plain,
! [X2329: mono_2Etyop_2Enum_2Enum,X2330: mono_2Etyop_2Enum_2Enum] :
( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2329))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EEXP_2E2(X2330,X2329))) )
& ( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2330))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EEXP_2E2(X2330,X2329))) )
& ( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2329))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2330))
| p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EEXP_2E2(X2330,X2329))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EEVEN__EXP__IFF])])])]) ).
tcf(c_0_54,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEXP_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(X567)) = mono_2Ec_2Enum_2E0_2E0,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
tcf(c_0_55,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X567)) = mono_2Ec_2Earithmetic_2EBIT1_2E1(X567),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_44]) ).
tff(c_0_56,plain,
! [X2320: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X2320)))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2320)) )
& ( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2320))
| p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X2320))) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
tff(c_0_57,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_simplification,[status(thm)],[reserved_2Eho_2Enotfalse]) ).
tff(c_0_58,negated_conjecture,
~ ! [X614: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMOD_2E2(X614,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(X614),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ),
inference(assume_negation,[status(cth)],[thm_2Earithmetic_2EMOD__2]) ).
tcf(c_0_59,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X567)))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
tcf(c_0_60,plain,
mono_2Ec_2Earithmetic_2EZERO_2E0 = mono_2Ec_2Enum_2E0_2E0,
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EALT__ZERO]) ).
tcf(c_0_61,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X567) = X567,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
tcf(c_0_62,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EBIT2_2E1(X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Earithmetic_2E_2B_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)))),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
tcf(c_0_63,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X567),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
tff(c_0_64,plain,
! [X2321: mono_2Etyop_2Enum_2Enum] :
( ( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2321))
| ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X2321)) )
& ( p(mono_2Ec_2Earithmetic_2EODD_2E1(X2321))
| p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2321)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
tff(c_0_65,plain,
! [X3959: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 != X3959 )
| p(X3959) )
& ( ~ p(X3959)
| ( mono_2Ec_2Ebool_2ET_2E0 = X3959 ) )
& ( ( X3959 != mono_2Ec_2Ebool_2ET_2E0 )
| p(X3959) )
& ( ~ p(X3959)
| ( X3959 = mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 != X3959 )
| ~ p(X3959) )
& ( p(X3959)
| ( mono_2Ec_2Ebool_2EF_2E0 = X3959 ) )
& ( ( X3959 != mono_2Ec_2Ebool_2EF_2E0 )
| ~ p(X3959) )
& ( p(X3959)
| ( X3959 = mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
tff(c_0_66,plain,
! [X2011: mono_2Etyop_2Enum_2Enum,X2012: mono_2Etyop_2Enum_2Enum] :
( ( ( X2011 = mono_2Ec_2Enum_2E0_2E0 )
| ( X2011 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) )
& ( ( X2012 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( X2011 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) )
& ( ( X2011 = mono_2Ec_2Enum_2E0_2E0 )
| ( X2012 = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) )
& ( ( X2012 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( X2012 = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) )
& ( ( X2011 != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( X2012 != mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) )
& ( ( X2011 != mono_2Ec_2Enum_2E0_2E0 )
| ( X2012 != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X2011,X2012) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EADD__EQ__1])])])]) ).
tcf(c_0_67,plain,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(split_conjunct,[status(thm)],[thm_2Earithmetic_2EONE]) ).
tcf(c_0_68,plain,
! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X567))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EEXP_2E2(X575,X567))) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
tcf(c_0_69,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEXP_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)) = mono_2Ec_2Enum_2E0_2E0,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
tcf(c_0_70,plain,
mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2ET_2E0,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
tcf(c_0_71,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(split_conjunct,[status(thm)],[reserved_2Eho_2Etruth]) ).
tff(c_0_72,plain,
! [X3943: mono_2Etyop_2Emin_2Ebool] :
( ( X3943 = mono_2Ec_2Ebool_2ET_2E0 )
| ( X3943 = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(variable_rename,[status(thm)],[reserved_2Eho_2Ebool__cases__ax]) ).
tff(c_0_73,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(fof_nnf,[status(thm)],[c_0_57]) ).
tff(c_0_74,negated_conjecture,
mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
tcf(c_0_75,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Enum_2E0_2E0),X567)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
tcf(c_0_76,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X567))) = mono_2Ec_2Earithmetic_2EBIT2_2E1(X567),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_44]),c_0_44]),c_0_45]),c_0_44]),c_0_44]) ).
tcf(c_0_77,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Enum_2E0_2E0),X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X567),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_60]),c_0_61]) ).
tcf(c_0_78,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567))
| ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X567)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
tcf(c_0_79,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| ( X6 = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
tcf(c_0_80,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( ( X567 = mono_2Ec_2Enum_2E0_2E0 )
| ( X567 = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
tcf(c_0_81,plain,
mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(rw,[status(thm)],[c_0_67,c_0_60]) ).
tff(c_0_82,plain,
! [X1982: mono_2Etyop_2Enum_2Enum,X1983: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMIN_2E2(X1982,X1983) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X1982,X1983),X1982,X1983) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMIN__DEF]) ).
tcf(c_0_83,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71])]) ).
tcf(c_0_84,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_72]) ).
tcf(c_0_85,plain,
~ p(mono_2Ec_2Ebool_2EF_2E0),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
tff(c_0_86,plain,
! [X3675: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMIN_2E2(X3675,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Enum_2E0_2E0 )
& ( mono_2Ec_2Earithmetic_2EMIN_2E2(mono_2Ec_2Enum_2E0_2E0,X3675) = mono_2Ec_2Enum_2E0_2E0 ) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMIN__0]) ).
tff(c_0_87,plain,
! [X2059: mono_2Etyop_2Enum_2Enum,X2060: mono_2Etyop_2Enum_2Enum,X2061: mono_2Etyop_2Enum_2Enum] :
( ( ( X2060 = mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061))) )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061)),X2060) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061))) = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061)),X2060) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) )
& ( ( X2060 != mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061))) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061))) != mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X2061)),X2060) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) )
& ( ( X2060 = mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061))) )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061)),X2060) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) )
& ( ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061))) = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061)),X2060) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) )
& ( ( X2060 != mono_2Ec_2Earithmetic_2EDIV_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061))) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061))) != mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X2061)),X2060) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X2059) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV])])])]) ).
tff(c_0_88,plain,
! [X2029: mono_2Etyop_2Enum_2Enum,X2031: mono_2Etyop_2Enum_2Enum] :
( ( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X2029))
| ( X2029 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk9_1(X2029)) ) )
& ( ~ p(mono_2Ec_2Earithmetic_2EODD_2E1(X2031))
| ( X2031 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk10_1(X2031))) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EEVEN__ODD__EXISTS])])])])])]) ).
tff(c_0_89,plain,
! [X2027: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X2027))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EEVEN__DOUBLE]) ).
tcf(c_0_90,negated_conjecture,
mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) != mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
tff(c_0_91,plain,
! [X614: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X614,mono_2Ec_2Enum_2E0_2E0)),
inference(fof_simplification,[status(thm)],[thm_2Eprim__rec_2ENOT__LESS__0]) ).
tff(c_0_92,plain,
! [X2325: mono_2Etyop_2Enum_2Enum,X2326: mono_2Etyop_2Enum_2Enum] :
( ( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X2325,X2326)))
| ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X2325) = mono_2Ec_2Earithmetic_2EEVEN_2E1(X2326) ) )
& ( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X2325) != mono_2Ec_2Earithmetic_2EEVEN_2E1(X2326) )
| p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X2325,X2326))) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EEVEN__ADD])])]) ).
tcf(c_0_93,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),X567)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_45]) ).
tcf(c_0_94,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),X567) = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X567),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_76]),c_0_45]) ).
tcf(c_0_95,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EODD_2E1(X567) = mono_2Ec_2Ebool_2EF_2E0 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
tcf(c_0_96,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( ( X567 = mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( X567 = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575) != mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_60]),c_0_61]),c_0_60]),c_0_61]) ).
tcf(c_0_97,plain,
mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0),
inference(rw,[status(thm)],[c_0_81,c_0_61]) ).
tff(c_0_98,plain,
! [X3745: mono_2Etyop_2Enum_2Enum,X3746: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X3745,X3746))
| ( X3746 = mono_2Ec_2Earithmetic_2E_2B_2E2(X3745,esk185_2(X3745,X3746)) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2ELESS__EQUAL__ADD])])])]) ).
tff(c_0_99,plain,
! [X2253: mono_2Etyop_2Enum_2Enum,X2254: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2254))
| p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2EMOD_2E2(X2253,X2254),X2254)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EMOD__LESS])])]) ).
tff(c_0_100,plain,
! [X3257: mono_2Etyop_2Enum_2Enum,X3258: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X3257,X3258) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X3257,mono_2Ec_2Enum_2ESUC_2E1(X3258)) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC]) ).
tff(c_0_101,plain,
! [X2159: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X2159)),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EZERO__LESS__EQ]) ).
tff(c_0_102,plain,
! [X3320: mono_2Etyop_2Emin_2Ebool,X3321: mono_2Etyop_2Emin_2Ebool] :
( ( ~ p(X3320)
| ~ p(X3321)
| ( X3320 = X3321 ) )
& ( p(X3320)
| p(X3321)
| ( X3320 = X3321 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reserved_2Eho_2Eboolext])])])]) ).
tcf(c_0_103,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMIN_2E2(X567,X575) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,X575),X567,X575),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
tcf(c_0_104,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)) = mono_2Ec_2Ebool_2ET_2E0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
tcf(c_0_105,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMIN_2E2(mono_2Ec_2Enum_2E0_2E0,X567) = mono_2Ec_2Enum_2E0_2E0,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
tcf(c_0_106,plain,
! [X576: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X567),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X575))) = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(X575)),X576) != mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X567) ) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
tcf(c_0_107,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EBIT2_2E1(X567) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)),
inference(rw,[status(thm)],[c_0_76,c_0_55]) ).
tcf(c_0_108,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( X567 = mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),esk9_1(X567)) )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
tcf(c_0_109,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),X567))),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
tff(c_0_110,plain,
! [X2350: mono_2Etyop_2Enum_2Enum,X2351: mono_2Etyop_2Enum_2Enum,X2352: mono_2Etyop_2Enum_2Enum] :
( ( ( X2351 = mono_2Ec_2Earithmetic_2EDIV_2E2(X2350,X2352) )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2352,X2351) != X2350 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2352)) )
& ( ( mono_2Ec_2Earithmetic_2EMOD_2E2(X2350,X2352) = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2352,X2351) != X2350 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2352)) )
& ( ( X2351 != mono_2Ec_2Earithmetic_2EDIV_2E2(X2350,X2352) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X2350,X2352) != mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2A_2E2(X2352,X2351) = X2350 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X2352)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Earithmetic_2EMULT__EQ__DIV])])])]) ).
tcf(c_0_111,negated_conjecture,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Enum_2E0_2E0))) != mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Enum_2E0_2E0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_60]),c_0_60]) ).
tff(c_0_112,plain,
! [X2129: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X2129,mono_2Ec_2Enum_2E0_2E0)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_91])]) ).
tcf(c_0_113,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575)))
| ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X567) != mono_2Ec_2Earithmetic_2EEVEN_2E1(X575) ) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
tcf(c_0_114,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EODD_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X567))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_55]) ).
tcf(c_0_115,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X567) = mono_2Ec_2Ebool_2EF_2E0 )
| ( mono_2Ec_2Earithmetic_2EODD_2E1(X567) = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_79]) ).
tcf(c_0_116,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( ( X567 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( X567 = mono_2Ec_2Enum_2E0_2E0 )
| ( mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575) != mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_97]) ).
tcf(c_0_117,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( ( X575 = mono_2Ec_2Earithmetic_2E_2B_2E2(X567,esk185_2(X567,X575)) )
| ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,X575)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
tcf(c_0_118,plain,
! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2EMOD_2E2(X575,X567),X567))
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X567)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
tcf(c_0_119,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_100]) ).
tcf(c_0_120,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Enum_2E0_2E0,X567)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
tcf(c_0_121,plain,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ( X6 = mono_2Ec_2Ebool_2ET_2E0 )
| ~ p(X6) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
tcf(c_0_122,plain,
! [X6: mono_2Etyop_2Emin_2Ebool,X7: mono_2Etyop_2Emin_2Ebool] :
( p(X6)
| p(X7)
| ( X6 = X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
tcf(c_0_123,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)) = mono_2Ec_2Enum_2E0_2E0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]) ).
tcf(c_0_124,plain,
! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)),X575),mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X567))) = mono_2Ec_2Enum_2E0_2E0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_61]),c_0_61]),c_0_61]),c_0_61])]),c_0_107]),c_0_107]) ).
tcf(c_0_125,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Enum_2E0_2E0),esk9_1(X567)) = X567 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_60]),c_0_61]) ).
tcf(c_0_126,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Enum_2E0_2E0),X567))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_60]),c_0_61]) ).
tcf(c_0_127,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum,X576: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(X576,X567) = X575 )
| ( X567 != mono_2Ec_2Earithmetic_2EDIV_2E2(X575,X576) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X575,X576) != mono_2Ec_2Enum_2E0_2E0 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X576)) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
tff(c_0_128,plain,
! [X3268: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X3268,mono_2Ec_2Enum_2ESUC_2E1(X3268))),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2ELESS__EQ__SUC__REFL]) ).
tcf(c_0_129,negated_conjecture,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) != mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_81]),c_0_61]),c_0_76]),c_0_45]) ).
tff(c_0_130,plain,
! [X1980: mono_2Etyop_2Enum_2Enum,X1981: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMAX_2E2(X1980,X1981) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X1980,X1981),X1981,X1980) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMAX__DEF]) ).
tcf(c_0_131,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Enum_2E0_2E0)),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
tff(c_0_132,plain,
! [X3660: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMAX_2E2(X3660,mono_2Ec_2Enum_2E0_2E0) = X3660 )
& ( mono_2Ec_2Earithmetic_2EMAX_2E2(mono_2Ec_2Enum_2E0_2E0,X3660) = X3660 ) ),
inference(variable_rename,[status(thm)],[thm_2Earithmetic_2EMAX__0]) ).
tcf(c_0_133,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Earithmetic_2E_2B_2E2(X567,X575))))
| ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X567) != mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X575)) ) ),
inference(spm,[status(thm)],[c_0_113,c_0_44]) ).
tcf(c_0_134,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(X567)) = mono_2Ec_2Ebool_2EF_2E0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_85]) ).
tcf(c_0_135,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X567)))
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
tcf(c_0_136,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( X567 = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( X567 = mono_2Ec_2Enum_2E0_2E0 )
| ~ p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117])]) ).
tcf(c_0_137,plain,
! [X567: mono_2Etyop_2Enum_2Enum,X575: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2EMOD_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X575)),X575)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_119]),c_0_120])]) ).
tcf(c_0_138,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_121,c_0_122]) ).
tcf(c_0_139,plain,
mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Enum_2E0_2E0,
inference(spm,[status(thm)],[c_0_123,c_0_97]) ).
tcf(c_0_140,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMOD_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),X567),mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) = mono_2Ec_2Enum_2E0_2E0,
inference(spm,[status(thm)],[c_0_124,c_0_97]) ).
tcf(c_0_141,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),esk9_1(X567)) = X567 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_76]),c_0_45]) ).
tcf(c_0_142,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)),X567))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_76]),c_0_45]) ).
tcf(c_0_143,plain,
! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_2A_2E2(X567,mono_2Ec_2Earithmetic_2EDIV_2E2(X575,X567)) = X575 )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X575,X567) != mono_2Ec_2Enum_2E0_2E0 )
| ~ p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,X567)) ),
inference(er,[status(thm)],[c_0_127]) ).
tcf(c_0_144,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(X567))),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
tcf(c_0_145,negated_conjecture,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0))
| p(X6)
| ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X6,mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)) != mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) ) ),
inference(spm,[status(thm)],[c_0_129,c_0_122]) ).
tcf(c_0_146,plain,
! [X575: mono_2Etyop_2Enum_2Enum,X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMAX_2E2(X567,X575) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,X575),X575,X567),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
tcf(c_0_147,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eprim__rec_2E_3C_2E2(X567,mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2EF_2E0,
inference(spm,[status(thm)],[c_0_131,c_0_79]) ).
tcf(c_0_148,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EMAX_2E2(X567,mono_2Ec_2Enum_2E0_2E0) = X567,
inference(split_conjunct,[status(thm)],[c_0_132]) ).
tcf(c_0_149,plain,
! [X567: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X567)) != mono_2Ec_2Earithmetic_2EEVEN_2E1(X567),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_55]),c_0_134]),c_0_85]) ).
tcf(c_0_150,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(mono_2Ec_2Enum_2ESUC_2E1(X567)) = mono_2Ec_2Ebool_2EF_2E0 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(spm,[status(thm)],[c_0_135,c_0_79]) ).
tcf(c_0_151,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) = mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) )
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) = mono_2Ec_2Enum_2E0_2E0 ) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
tcf(c_0_152,negated_conjecture,
! [X6: mono_2Etyop_2Emin_2Ebool] :
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0) = X6 )
| p(X6)
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) != mono_2Ec_2Enum_2E0_2E0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_138]),c_0_139]) ).
tcf(c_0_153,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EMOD_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) = mono_2Ec_2Enum_2E0_2E0 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
tcf(c_0_154,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(X567,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) != mono_2Ec_2Enum_2E0_2E0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_119]),c_0_144])]) ).
tcf(c_0_155,negated_conjecture,
( p(mono_2Ec_2Earithmetic_2EEVEN_2E1(esk1_0))
| ( mono_2Ec_2Earithmetic_2EMOD_2E2(esk1_0,mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))) != mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0) ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_148]),c_0_85]) ).
tcf(c_0_156,plain,
! [X567: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2EEVEN_2E1(X567) != mono_2Ec_2Ebool_2EF_2E0 )
| ~ p(mono_2Ec_2Earithmetic_2EEVEN_2E1(X567)) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_157,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_151,c_0_152,c_0_153,c_0_154,c_0_155,c_0_156,c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP003_4 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 12:46:41 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.69/0.86 Running first-order model finding
% 0.69/0.86 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.pqLWG2yIsE/E---3.1_7267.p
% 136.89/18.26 # Version: 3.1.0
% 136.89/18.26 # Preprocessing class: FMLMSMMLSSSNFFN.
% 136.89/18.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.89/18.26 # Starting new_bool_3 with 900s (3) cores
% 136.89/18.26 # Starting new_bool_1 with 900s (3) cores
% 136.89/18.26 # Starting sh5l with 300s (1) cores
% 136.89/18.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S032N with 300s (1) cores
% 136.89/18.26 # sh5l with pid 7556 completed with status 0
% 136.89/18.26 # Result found by sh5l
% 136.89/18.26 # Preprocessing class: FMLMSMMLSSSNFFN.
% 136.89/18.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.89/18.26 # Starting new_bool_3 with 900s (3) cores
% 136.89/18.26 # Starting new_bool_1 with 900s (3) cores
% 136.89/18.26 # Starting sh5l with 300s (1) cores
% 136.89/18.26 # SinE strategy is gf500_gu_R04_F100_L20000
% 136.89/18.26 # Search class: FGHSM-SMLM32-DFFFFFNN
% 136.89/18.26 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 136.89/18.26 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 23s (1) cores
% 136.89/18.26 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 7608 completed with status 0
% 136.89/18.26 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 136.89/18.26 # Preprocessing class: FMLMSMMLSSSNFFN.
% 136.89/18.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.89/18.26 # Starting new_bool_3 with 900s (3) cores
% 136.89/18.26 # Starting new_bool_1 with 900s (3) cores
% 136.89/18.26 # Starting sh5l with 300s (1) cores
% 136.89/18.26 # SinE strategy is gf500_gu_R04_F100_L20000
% 136.89/18.26 # Search class: FGHSM-SMLM32-DFFFFFNN
% 136.89/18.26 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 136.89/18.26 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 23s (1) cores
% 136.89/18.26 # Preprocessing time : 0.036 s
% 136.89/18.26 # Presaturation interreduction done
% 136.89/18.26 # SatCheck found unsatisfiable ground set
% 136.89/18.26
% 136.89/18.26 # Proof found!
% 136.89/18.26 # SZS status Theorem
% 136.89/18.26 # SZS output start CNFRefutation
% See solution above
% 136.89/18.26 # Parsed axioms : 3867
% 136.89/18.26 # Removed by relevancy pruning/SinE : 2348
% 136.89/18.26 # Initial clauses : 3188
% 136.89/18.26 # Removed in clause preprocessing : 741
% 136.89/18.26 # Initial clauses in saturation : 2447
% 136.89/18.26 # Processed clauses : 16868
% 136.89/18.26 # ...of these trivial : 469
% 136.89/18.26 # ...subsumed : 11399
% 136.89/18.26 # ...remaining for further processing : 5000
% 136.89/18.26 # Other redundant clauses eliminated : 2994
% 136.89/18.26 # Clauses deleted for lack of memory : 0
% 136.89/18.26 # Backward-subsumed : 154
% 136.89/18.26 # Backward-rewritten : 220
% 136.89/18.26 # Generated clauses : 524873
% 136.89/18.26 # ...of the previous two non-redundant : 474719
% 136.89/18.26 # ...aggressively subsumed : 0
% 136.89/18.26 # Contextual simplify-reflections : 13
% 136.89/18.26 # Paramodulations : 521755
% 136.89/18.26 # Factorizations : 48
% 136.89/18.26 # NegExts : 0
% 136.89/18.26 # Equation resolutions : 3073
% 136.89/18.26 # Disequality decompositions : 0
% 136.89/18.26 # Total rewrite steps : 98626
% 136.89/18.26 # ...of those cached : 73581
% 136.89/18.26 # Propositional unsat checks : 1
% 136.89/18.26 # Propositional check models : 0
% 136.89/18.26 # Propositional check unsatisfiable : 1
% 136.89/18.26 # Propositional clauses : 463700
% 136.89/18.26 # Propositional clauses after purity: 118010
% 136.89/18.26 # Propositional unsat core size : 7
% 136.89/18.26 # Propositional preprocessing time : 0.000
% 136.89/18.26 # Propositional encoding time : 2.906
% 136.89/18.26 # Propositional solver time : 0.446
% 136.89/18.26 # Success case prop preproc time : 0.000
% 136.89/18.26 # Success case prop encoding time : 2.906
% 136.89/18.26 # Success case prop solver time : 0.446
% 136.89/18.26 # Current number of processed clauses : 3038
% 136.89/18.26 # Positive orientable unit clauses : 477
% 136.89/18.26 # Positive unorientable unit clauses: 77
% 136.89/18.26 # Negative unit clauses : 371
% 136.89/18.26 # Non-unit-clauses : 2113
% 136.89/18.26 # Current number of unprocessed clauses: 460662
% 136.89/18.26 # ...number of literals in the above : 1605810
% 136.89/18.26 # Current number of archived formulas : 0
% 136.89/18.26 # Current number of archived clauses : 1855
% 136.89/18.26 # Clause-clause subsumption calls (NU) : 2550669
% 136.89/18.26 # Rec. Clause-clause subsumption calls : 944094
% 136.89/18.26 # Non-unit clause-clause subsumptions : 3723
% 136.89/18.26 # Unit Clause-clause subsumption calls : 213774
% 136.89/18.26 # Rewrite failures with RHS unbound : 0
% 136.89/18.26 # BW rewrite match attempts : 24380
% 136.89/18.26 # BW rewrite match successes : 781
% 136.89/18.26 # Condensation attempts : 0
% 136.89/18.26 # Condensation successes : 0
% 136.89/18.26 # Termbank termtop insertions : 48598010
% 136.89/18.26 # Search garbage collected termcells : 46449
% 136.89/18.26
% 136.89/18.26 # -------------------------------------------------
% 136.89/18.26 # User time : 16.453 s
% 136.89/18.26 # System time : 0.548 s
% 136.89/18.26 # Total time : 17.001 s
% 136.89/18.26 # Maximum resident set size: 16540 pages
% 136.89/18.26
% 136.89/18.26 # -------------------------------------------------
% 136.89/18.26 # User time : 16.595 s
% 136.89/18.26 # System time : 0.557 s
% 136.89/18.26 # Total time : 17.151 s
% 136.89/18.26 # Maximum resident set size: 6884 pages
% 136.89/18.26 % E---3.1 exiting
%------------------------------------------------------------------------------