TSTP Solution File: ITP015+2 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Gpo0SdMHWD true
% Computer : n022.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 : Thu Aug 31 05:21:14 EDT 2023
% Result : Theorem 234.99s 34.24s
% Output : Refutation 234.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 58
% Syntax : Number of formulae : 257 ( 69 unt; 29 typ; 0 def)
% Number of atoms : 708 ( 166 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3175 ( 367 ~; 418 |; 8 &;2328 @)
% ( 8 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 14 con; 0-3 aty)
% Number of variables : 286 ( 0 ^; 286 !; 0 ?; 286 :)
% Comments :
%------------------------------------------------------------------------------
thf(zip_tseitin_3_type,type,
zip_tseitin_3: $i > $i > $i > $o ).
thf(bool_type,type,
bool: $i ).
thf(ty_2Einteger_2Eint_type,type,
ty_2Einteger_2Eint: $i ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(c_2Ewords_2Eword__2comp_type,type,
c_2Ewords_2Eword__2comp: $i > $i ).
thf(c_2Ewords_2En2w_type,type,
c_2Ewords_2En2w: $i > $i ).
thf(c_2Einteger__word_2Ei2w_type,type,
c_2Einteger__word_2Ei2w: $i > $i ).
thf(mem_type,type,
mem: $i > $i > $o ).
thf(c_2Ebool_2E_7E_type,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Einteger_2Eint__lt_type,type,
c_2Einteger_2Eint__lt: $i ).
thf(ne_type,type,
ne: $i > $o ).
thf(ty_2Efcp_2Ecart_type,type,
ty_2Efcp_2Ecart: $i > $i > $i ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND: $i > $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(c_2Einteger_2ENum_type,type,
c_2Einteger_2ENum: $i ).
thf(c_2Einteger_2Eint__of__num_type,type,
c_2Einteger_2Eint__of__num: $i ).
thf(zip_tseitin_5_type,type,
zip_tseitin_5: $i > $i > $o ).
thf(c_2Eprim__rec_2E_3C_type,type,
c_2Eprim__rec_2E_3C: $i ).
thf(c_2Einteger_2Eint__neg_type,type,
c_2Einteger_2Eint__neg: $i ).
thf(ty_2Enum_2Enum_type,type,
ty_2Enum_2Enum: $i ).
thf(p_type,type,
p: $i > $o ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: $i ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(arr_type,type,
arr: $i > $i > $i ).
thf(zip_tseitin_4_type,type,
zip_tseitin_4: $i > $i > $i > $o ).
thf(mem_c_2Einteger_2Eint__of__num,axiom,
mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ) ).
thf(zip_derived_cl30,plain,
mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ),
inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__of__num]) ).
thf(ap_tp,axiom,
! [A: $i,B: $i,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl696,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).
thf(mem_c_2Einteger_2Eint__lt,axiom,
mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).
thf(zip_derived_cl31,plain,
mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__lt]) ).
thf(zip_derived_cl3_001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl762,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ ( arr @ ty_2Einteger_2Eint @ bool ) )
| ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl3]) ).
thf(zip_derived_cl3_002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl1139,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
| ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ X1 ) @ bool )
| ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
inference('sup-',[status(thm)],[zip_derived_cl762,zip_derived_cl3]) ).
thf(ne_ty_2Efcp_2Ecart,axiom,
! [A0: $i] :
( ( ne @ A0 )
=> ! [A1: $i] :
( ( ne @ A1 )
=> ( ne @ ( ty_2Efcp_2Ecart @ A0 @ A1 ) ) ) ) ).
thf(zip_derived_cl33,plain,
! [X0: $i,X1: $i] :
( ~ ( ne @ X0 )
| ( ne @ ( ty_2Efcp_2Ecart @ X1 @ X0 ) )
| ~ ( ne @ X1 ) ),
inference(cnf,[status(esa)],[ne_ty_2Efcp_2Ecart]) ).
thf(mem_c_2Ewords_2En2w,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(zip_derived_cl48,plain,
! [X0: $i] :
( ( mem @ ( c_2Ewords_2En2w @ X0 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) )
| ~ ( ne @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Ewords_2En2w]) ).
thf(zip_derived_cl3_003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl896,plain,
! [X0: $i,X1: $i] :
( ~ ( ne @ X0 )
| ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ X1 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl3]) ).
thf(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ) ).
thf(zip_derived_cl94,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Ewords_2EWORD__NEG__0]) ).
thf(conj_thm_2Einteger_2EINT__NEG__0,axiom,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ).
thf(zip_derived_cl80,plain,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
thf(conj_thm_2Einteger_2ENUM__OF__INT,axiom,
! [V0n: $i] :
( ( mem @ V0n @ ty_2Enum_2Enum )
=> ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) )
= V0n ) ) ).
thf(zip_derived_cl89,plain,
! [X0: $i] :
( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
= X0 )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2ENUM__OF__INT]) ).
thf(ax_thm_2Einteger__word_2Ei2w__def,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [V0i: $i] :
( ( mem @ V0i @ ty_2Einteger_2Eint )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ V0i )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ V0i ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ V0i ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ V0i ) ) ) ) ) ) ).
thf(zip_derived_cl90,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ X0 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ X0 ) ) ) )
| ~ ( ne @ X1 ) ),
inference(cnf,[status(esa)],[ax_thm_2Einteger__word_2Ei2w__def]) ).
thf(zip_derived_cl1031,plain,
! [X0: $i,X1: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ X0 ) ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ~ ( ne @ X1 )
| ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint ) ),
inference('sup+',[status(thm)],[zip_derived_cl89,zip_derived_cl90]) ).
thf(zip_derived_cl696_004,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).
thf(zip_derived_cl6186,plain,
! [X0: $i,X1: $i] :
( ~ ( ne @ X1 )
| ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ X0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1031,zip_derived_cl696]) ).
thf(zip_derived_cl6187,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ~ ( ne @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl80,zip_derived_cl6186]) ).
thf(mem_c_2Enum_2E0,axiom,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ).
thf(zip_derived_cl47,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl6189,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
| ~ ( ne @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl6187,zip_derived_cl47]) ).
thf(zip_derived_cl89_005,plain,
! [X0: $i] :
( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
= X0 )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2ENUM__OF__INT]) ).
thf(mem_c_2Ebool_2EF,axiom,
mem @ c_2Ebool_2EF @ bool ).
thf(zip_derived_cl16,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl47_006,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl696_007,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).
thf(mem_c_2Einteger_2ENum,axiom,
mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ) ).
thf(zip_derived_cl29,plain,
mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ),
inference(cnf,[status(esa)],[mem_c_2Einteger_2ENum]) ).
thf(zip_derived_cl3_008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl697,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Einteger_2ENum @ X0 ) @ ty_2Enum_2Enum )
| ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl3]) ).
thf(mem_c_2Ebool_2E_7E,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
thf(zip_derived_cl36,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(cnf,[status(esa)],[mem_c_2Ebool_2E_7E]) ).
thf(zip_derived_cl3_009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl698,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(zip_derived_cl16_010,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(boolext,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( X1 = X0 )
| ( p @ X1 )
| ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[boolext]) ).
thf(zip_derived_cl703,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ c_2Ebool_2EF )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl5]) ).
thf(ax_false_p,axiom,
~ ( p @ c_2Ebool_2EF ) ).
thf(zip_derived_cl17,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl707,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl703,zip_derived_cl17]) ).
thf(zip_derived_cl722,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).
thf(zip_derived_cl698_011,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(conj_thm_2Einteger_2EINT__LT__CALCULATE,axiom,
! [V0n: $i] :
( ( mem @ V0n @ ty_2Enum_2Enum )
=> ! [V1m: $i] :
( ( mem @ V1m @ ty_2Enum_2Enum )
=> ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V0n ) @ V1m ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1m ) @ V0n ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) )
<=> ( ( V0n != c_2Enum_2E0 )
| ( V1m != c_2Enum_2E0 ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) ) )
<=> $false ) ) ) ) ).
thf(zip_derived_cl82,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( X1 = c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) )
| ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).
thf(zip_derived_cl80_012,plain,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
thf(zip_derived_cl86,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) )
| ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).
thf(zip_derived_cl971,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl86]) ).
thf(zip_derived_cl47_013,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl973,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl971,zip_derived_cl47]) ).
thf(zip_derived_cl1009,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( X0 = c_2Enum_2E0 )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl973]) ).
thf(zip_derived_cl47_014,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl1012,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( X0 = c_2Enum_2E0 )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(demod,[status(thm)],[zip_derived_cl1009,zip_derived_cl47]) ).
thf(zip_derived_cl1013,plain,
! [X0: $i] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ( X0 = c_2Enum_2E0 )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(simplify,[status(thm)],[zip_derived_cl1012]) ).
thf(mem_c_2Eprim__rec_2E_3C,axiom,
mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(zip_derived_cl35,plain,
mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ),
inference(cnf,[status(esa)],[mem_c_2Eprim__rec_2E_3C]) ).
thf(zip_derived_cl3_015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl768,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ ( arr @ ty_2Enum_2Enum @ bool ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).
thf(zip_derived_cl3_016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl1150,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( mem @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) @ bool )
| ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl768,zip_derived_cl3]) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( X1 = X0 )
| ~ ( p @ X1 )
| ~ ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[boolext]) ).
thf(zip_derived_cl1422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ~ ( mem @ X1 @ ty_2Enum_2Enum )
| ~ ( mem @ X2 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X1 ) @ X0 ) )
| ~ ( p @ X2 )
| ( X2
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1150,zip_derived_cl4]) ).
thf(zip_derived_cl5798,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( X0 = c_2Enum_2E0 )
| ( X1
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ~ ( p @ X1 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl1013,zip_derived_cl1422]) ).
thf(zip_derived_cl47_017,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl5802,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( X0 = c_2Enum_2E0 )
| ( X1
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ~ ( p @ X1 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(demod,[status(thm)],[zip_derived_cl5798,zip_derived_cl47]) ).
thf(zip_derived_cl5803,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X1 @ bool )
| ~ ( p @ X1 )
| ( X1
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
| ( X0 = c_2Enum_2E0 )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(simplify,[status(thm)],[zip_derived_cl5802]) ).
thf(zip_derived_cl5815,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X1 @ ty_2Enum_2Enum )
| ( X1 = c_2Enum_2E0 )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl5803]) ).
thf(zip_derived_cl5834,plain,
! [X0: $i,X1: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
| ( X1 = c_2Enum_2E0 )
| ~ ( mem @ X1 @ ty_2Enum_2Enum )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl722,zip_derived_cl5815]) ).
thf(zip_derived_cl5856,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X1 @ ty_2Enum_2Enum )
| ( X1 = c_2Enum_2E0 )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF ) ),
inference(simplify,[status(thm)],[zip_derived_cl5834]) ).
thf(zip_derived_cl5880,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
| ( ( ap @ c_2Ebool_2E_7E @ X1 )
= c_2Ebool_2EF )
| ~ ( mem @ X1 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X1 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ X0 ) ) )
| ( ( ap @ c_2Einteger_2ENum @ X0 )
= c_2Enum_2E0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl697,zip_derived_cl5856]) ).
thf(zip_derived_cl7340,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
= c_2Enum_2E0 )
| ( ( ap @ c_2Ebool_2E_7E @ X1 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
| ~ ( mem @ X1 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X1 )
= c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl696,zip_derived_cl5880]) ).
thf(zip_derived_cl8227,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
| ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl7340]) ).
thf(zip_derived_cl8249,plain,
( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl8227]) ).
thf(mem_c_2Ebool_2ET,axiom,
mem @ c_2Ebool_2ET @ bool ).
thf(zip_derived_cl14,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl698_018,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(zip_derived_cl14_019,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl4_020,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( X1 = X0 )
| ~ ( p @ X1 )
| ~ ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[boolext]) ).
thf(zip_derived_cl681,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ c_2Ebool_2ET )
| ~ ( p @ X0 )
| ( X0 = c_2Ebool_2ET ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl4]) ).
thf(ax_true_p,axiom,
p @ c_2Ebool_2ET ).
thf(zip_derived_cl15,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl685,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ X0 )
| ( X0 = c_2Ebool_2ET ) ),
inference(demod,[status(thm)],[zip_derived_cl681,zip_derived_cl15]) ).
thf(zip_derived_cl721,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl685]) ).
thf(zip_derived_cl722_021,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).
thf(zip_derived_cl776,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool ) ),
inference('sup+',[status(thm)],[zip_derived_cl721,zip_derived_cl722]) ).
thf(zip_derived_cl779,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2ET ) ),
inference(simplify,[status(thm)],[zip_derived_cl776]) ).
thf(zip_derived_cl698_022,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(zip_derived_cl16_023,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl722_024,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).
thf(zip_derived_cl698_025,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(ax_neg_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ) ).
thf(zip_derived_cl37,plain,
! [X0: $i] :
( ( p @ X0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( mem @ X0 @ bool ) ),
inference(cnf,[status(esa)],[ax_neg_p]) ).
thf(zip_derived_cl698_026,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(zip_derived_cl4_027,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( X1 = X0 )
| ~ ( p @ X1 )
| ~ ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[boolext]) ).
thf(zip_derived_cl719,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X1 @ bool )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( p @ X1 )
| ( X1
= ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl4]) ).
thf(zip_derived_cl1054,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X1
= ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( p @ X1 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl719]) ).
thf(zip_derived_cl1059,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X1 @ bool )
| ~ ( p @ X1 )
| ( X1
= ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ( p @ X0 )
| ~ ( mem @ X0 @ bool ) ),
inference(simplify,[status(thm)],[zip_derived_cl1054]) ).
thf(zip_derived_cl1087,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X1 @ bool )
| ( p @ X1 )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ X1 ) )
| ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl1059]) ).
thf(zip_derived_cl1474,plain,
! [X0: $i,X1: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ X1 ) )
| ( p @ X1 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl722,zip_derived_cl1087]) ).
thf(zip_derived_cl1479,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X1 @ bool )
| ( p @ X1 )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ X1 ) )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF ) ),
inference(simplify,[status(thm)],[zip_derived_cl1474]) ).
thf(zip_derived_cl1583,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
| ( p @ c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl1479]) ).
thf(zip_derived_cl17_028,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl1590,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1583,zip_derived_cl17]) ).
thf(zip_derived_cl1597,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
= ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
| ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
= c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl1590]) ).
thf(zip_derived_cl1764,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
!= c_2Ebool_2EF )
| ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl1597]) ).
thf(zip_derived_cl37_029,plain,
! [X0: $i] :
( ( p @ X0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( mem @ X0 @ bool ) ),
inference(cnf,[status(esa)],[ax_neg_p]) ).
thf(zip_derived_cl1771,plain,
! [X0: $i] :
( ( p @ c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
!= c_2Ebool_2EF )
| ~ ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1764,zip_derived_cl37]) ).
thf(zip_derived_cl17_030,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl1799,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
!= c_2Ebool_2EF )
| ~ ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1771,zip_derived_cl17]) ).
thf(zip_derived_cl698_031,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).
thf(zip_derived_cl1812,plain,
! [X0: $i] :
( ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
!= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool ) ),
inference(clc,[status(thm)],[zip_derived_cl1799,zip_derived_cl698]) ).
thf(zip_derived_cl1815,plain,
! [X0: $i] :
( ( c_2Ebool_2EF != c_2Ebool_2EF )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET )
| ~ ( mem @ c_2Ebool_2EF @ bool )
| ~ ( mem @ X0 @ bool )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl779,zip_derived_cl1812]) ).
thf(zip_derived_cl16_032,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl1819,plain,
! [X0: $i] :
( ( c_2Ebool_2EF != c_2Ebool_2EF )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1815,zip_derived_cl16]) ).
thf(zip_derived_cl1820,plain,
! [X0: $i] :
( ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET ) ),
inference(simplify,[status(thm)],[zip_derived_cl1819]) ).
thf(zip_derived_cl1830,plain,
( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET )
| ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1820]) ).
thf(zip_derived_cl38,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( p @ X0 )
| ~ ( mem @ X0 @ bool ) ),
inference(cnf,[status(esa)],[ax_neg_p]) ).
thf(zip_derived_cl14_033,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl1590_034,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1583,zip_derived_cl17]) ).
thf(zip_derived_cl1599,plain,
( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1590]) ).
thf(zip_derived_cl37_035,plain,
! [X0: $i] :
( ( p @ X0 )
| ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( mem @ X0 @ bool ) ),
inference(cnf,[status(esa)],[ax_neg_p]) ).
thf(zip_derived_cl1607,plain,
( ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= c_2Ebool_2EF )
| ~ ( mem @ c_2Ebool_2EF @ bool )
| ( p @ c_2Ebool_2EF ) ),
inference('sup+',[status(thm)],[zip_derived_cl1599,zip_derived_cl37]) ).
thf(zip_derived_cl16_036,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl17_037,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl1617,plain,
( ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl1607,zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl1675,plain,
( ~ ( mem @ c_2Ebool_2ET @ bool )
| ~ ( p @ c_2Ebool_2ET )
| ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= c_2Ebool_2EF ) ),
inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl1617]) ).
thf(zip_derived_cl14_038,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl15_039,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl1681,plain,
( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl1675,zip_derived_cl14,zip_derived_cl15]) ).
thf(zip_derived_cl17_040,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl1837,plain,
( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET ),
inference(demod,[status(thm)],[zip_derived_cl1830,zip_derived_cl1681,zip_derived_cl17]) ).
thf(zip_derived_cl1837_041,plain,
( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
= c_2Ebool_2ET ),
inference(demod,[status(thm)],[zip_derived_cl1830,zip_derived_cl1681,zip_derived_cl17]) ).
thf(zip_derived_cl8262,plain,
( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 )
| ( c_2Ebool_2ET
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
| ( c_2Ebool_2ET = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl8249,zip_derived_cl1837,zip_derived_cl1837]) ).
thf(zip_derived_cl14_042,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl779_043,plain,
! [X0: $i] :
( ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2EF )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2ET ) ),
inference(simplify,[status(thm)],[zip_derived_cl776]) ).
thf(zip_derived_cl836,plain,
! [X0: $i] :
( ( c_2Ebool_2EF != c_2Ebool_2ET )
| ( ( ap @ c_2Ebool_2E_7E @ X0 )
= c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl779]) ).
thf(zip_derived_cl38_044,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
| ~ ( p @ X0 )
| ~ ( mem @ X0 @ bool ) ),
inference(cnf,[status(esa)],[ax_neg_p]) ).
thf(zip_derived_cl852,plain,
! [X0: $i] :
( ~ ( p @ c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ~ ( p @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl836,zip_derived_cl38]) ).
thf(zip_derived_cl15_045,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl861,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ~ ( p @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl852,zip_derived_cl15]) ).
thf(zip_derived_cl862,plain,
! [X0: $i] :
( ~ ( p @ X0 )
| ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool ) ),
inference(simplify,[status(thm)],[zip_derived_cl861]) ).
thf(zip_derived_cl903,plain,
( ( c_2Ebool_2EF != c_2Ebool_2ET )
| ~ ( p @ c_2Ebool_2ET ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl862]) ).
thf(zip_derived_cl15_046,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl905,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(demod,[status(thm)],[zip_derived_cl903,zip_derived_cl15]) ).
thf(zip_derived_cl8263,plain,
( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 )
| ( c_2Ebool_2ET
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl8262,zip_derived_cl905]) ).
thf(zip_derived_cl8395,plain,
( ( c_2Ebool_2ET
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl89,zip_derived_cl8263]) ).
thf(zip_derived_cl47_047,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl8396,plain,
( ( c_2Ebool_2ET
= ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
| ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ) ),
inference(demod,[status(thm)],[zip_derived_cl8395,zip_derived_cl47]) ).
thf(zip_derived_cl85,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
| ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).
thf(zip_derived_cl8429,plain,
( ~ ( p @ c_2Ebool_2ET )
| ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl8396,zip_derived_cl85]) ).
thf(zip_derived_cl15_048,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl47_049,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl80_050,plain,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
thf(zip_derived_cl80_051,plain,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
thf(conj_thm_2Eprim__rec_2ENOT__LESS__0,axiom,
! [V0n: $i] :
( ( mem @ V0n @ ty_2Enum_2Enum )
=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V0n ) @ c_2Enum_2E0 ) ) ) ).
thf(zip_derived_cl91,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[conj_thm_2Eprim__rec_2ENOT__LESS__0]) ).
thf(zip_derived_cl80_052,plain,
( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).
thf(zip_derived_cl973_053,plain,
! [X0: $i] :
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( mem @ X0 @ ty_2Enum_2Enum )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl971,zip_derived_cl47]) ).
thf(zip_derived_cl1011,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
| ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl973]) ).
thf(zip_derived_cl47_054,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl1016,plain,
( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1011,zip_derived_cl47]) ).
thf(zip_derived_cl1021,plain,
( ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl91,zip_derived_cl1016]) ).
thf(zip_derived_cl47_055,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl1023,plain,
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1021,zip_derived_cl47]) ).
thf(zip_derived_cl47_056,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl8446,plain,
( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ),
inference(demod,[status(thm)],[zip_derived_cl8429,zip_derived_cl15,zip_derived_cl47,zip_derived_cl80,zip_derived_cl80,zip_derived_cl1023,zip_derived_cl47]) ).
thf(zip_derived_cl214762,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
| ~ ( ne @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl6189,zip_derived_cl8446]) ).
thf(zip_derived_cl214769,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
| ~ ( ne @ X0 )
| ~ ( ne @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl214762]) ).
thf(zip_derived_cl214776,plain,
! [X0: $i] :
( ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl214769]) ).
thf(conj_thm_2Ebool_2ECOND__CONG,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3x_27: $i] :
( ( mem @ V3x_27 @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ! [V5y_27: $i] :
( ( mem @ V5y_27 @ A_27a )
=> ( ( ( ~ ( p @ V1Q )
=> ( V4y = V5y_27 ) )
& ( ( p @ V1Q )
=> ( V2x = V3x_27 ) )
& ( ( p @ V0P )
<=> ( p @ V1Q ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [V1Q: $i,V0P: $i] :
( ( ( p @ V0P )
<=> ( p @ V1Q ) )
=> ( zip_tseitin_5 @ V1Q @ V0P ) ) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X1: $i] :
( ( zip_tseitin_5 @ X0 @ X1 )
| ( p @ X0 )
| ( p @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zf_stmt_1,axiom,
! [V3x_27: $i,V2x: $i,V1Q: $i] :
( ( ( p @ V1Q )
=> ( V2x = V3x_27 ) )
=> ( zip_tseitin_4 @ V3x_27 @ V2x @ V1Q ) ) ).
thf(zip_derived_cl74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zip_tseitin_4 @ X0 @ X1 @ X2 )
| ( p @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zf_stmt_2,axiom,
! [V5y_27: $i,V4y: $i,V1Q: $i] :
( ( ~ ( p @ V1Q )
=> ( V4y = V5y_27 ) )
=> ( zip_tseitin_3 @ V5y_27 @ V4y @ V1Q ) ) ).
thf(zip_derived_cl71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( zip_tseitin_3 @ X0 @ X1 @ X2 )
| ( X1 != X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zf_stmt_3,type,
zip_tseitin_5: $i > $i > $o ).
thf(zf_stmt_4,type,
zip_tseitin_4: $i > $i > $i > $o ).
thf(zf_stmt_5,type,
zip_tseitin_3: $i > $i > $i > $o ).
thf(zf_stmt_6,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ! [V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3x_27: $i] :
( ( mem @ V3x_27 @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ! [V5y_27: $i] :
( ( mem @ V5y_27 @ A_27a )
=> ( ( ( zip_tseitin_5 @ V1Q @ V0P )
& ( zip_tseitin_4 @ V3x_27 @ V2x @ V1Q )
& ( zip_tseitin_3 @ V5y_27 @ V4y @ V1Q ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X1 @ X2 )
| ~ ( mem @ X3 @ X2 )
| ~ ( zip_tseitin_5 @ X4 @ X0 )
| ~ ( zip_tseitin_4 @ X5 @ X1 @ X4 )
| ~ ( zip_tseitin_3 @ X6 @ X3 @ X4 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X1 ) @ X3 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X4 ) @ X5 ) @ X6 ) )
| ~ ( mem @ X6 @ X2 )
| ~ ( mem @ X5 @ X2 )
| ~ ( mem @ X4 @ bool )
| ~ ( ne @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X1 != X2 )
| ~ ( ne @ X4 )
| ~ ( mem @ X0 @ bool )
| ~ ( mem @ X6 @ X4 )
| ~ ( mem @ X2 @ X4 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X4 ) @ X3 ) @ X5 ) @ X1 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X4 ) @ X0 ) @ X6 ) @ X2 ) )
| ~ ( zip_tseitin_4 @ X6 @ X5 @ X0 )
| ~ ( zip_tseitin_5 @ X0 @ X3 )
| ~ ( mem @ X1 @ X4 )
| ~ ( mem @ X5 @ X4 )
| ~ ( mem @ X3 @ bool ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl71,zip_derived_cl77]) ).
thf(zip_derived_cl673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( p @ X0 )
| ~ ( mem @ X6 @ bool )
| ~ ( mem @ X1 @ X5 )
| ~ ( mem @ X3 @ X5 )
| ~ ( zip_tseitin_5 @ X0 @ X6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X5 ) @ X6 ) @ X1 ) @ X3 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X5 ) @ X0 ) @ X2 ) @ X4 ) )
| ~ ( mem @ X4 @ X5 )
| ~ ( mem @ X2 @ X5 )
| ~ ( mem @ X0 @ bool )
| ~ ( ne @ X5 )
| ( X3 != X4 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl74,zip_derived_cl661]) ).
thf(zip_derived_cl680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( p @ X0 )
| ( p @ X1 )
| ( X4 != X5 )
| ~ ( ne @ X2 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X6 @ X2 )
| ~ ( mem @ X5 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X3 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X6 ) @ X5 ) )
| ~ ( mem @ X4 @ X2 )
| ~ ( mem @ X3 @ X2 )
| ~ ( mem @ X0 @ bool )
| ( p @ X1 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl76,zip_derived_cl673]) ).
thf(zip_derived_cl1051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X3 @ X2 )
| ~ ( mem @ X4 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X3 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X6 ) @ X5 ) )
| ~ ( mem @ X5 @ X2 )
| ~ ( mem @ X6 @ X2 )
| ~ ( mem @ X1 @ bool )
| ~ ( ne @ X2 )
| ( X4 != X5 )
| ( p @ X1 )
| ( p @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl680]) ).
thf(zip_derived_cl1052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( p @ X0 )
| ( p @ X1 )
| ~ ( ne @ X2 )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X3 @ X2 )
| ~ ( mem @ X4 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X5 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X3 ) @ X4 ) )
| ~ ( mem @ X4 @ X2 )
| ~ ( mem @ X5 @ X2 )
| ~ ( mem @ X0 @ bool ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1051]) ).
thf(zip_derived_cl1053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X5 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X5 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X3 ) @ X4 ) )
| ~ ( mem @ X4 @ X2 )
| ~ ( mem @ X3 @ X2 )
| ~ ( mem @ X1 @ bool )
| ~ ( ne @ X2 )
| ( p @ X1 )
| ( p @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1052]) ).
thf(conj_thm_2Ebool_2Ebool__case__thm,axiom,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( ! [V0t1: $i] :
( ( mem @ V0t1 @ A_27a )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 ) ) )
& ! [V2t1: $i] :
( ( mem @ V2t1 @ A_27a )
=> ! [V3t2: $i] :
( ( mem @ V3t2 @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
= V3t2 ) ) ) ) ) ).
thf(zip_derived_cl79,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2EF ) @ X0 ) @ X2 )
= X2 )
| ~ ( mem @ X2 @ X1 )
| ~ ( ne @ X1 ) ),
inference(cnf,[status(esa)],[conj_thm_2Ebool_2Ebool__case__thm]) ).
thf(zip_derived_cl6742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
= X0 )
| ( p @ X2 )
| ( p @ c_2Ebool_2EF )
| ~ ( ne @ X3 )
| ~ ( mem @ c_2Ebool_2EF @ bool )
| ~ ( mem @ X4 @ X3 )
| ~ ( mem @ X0 @ X3 )
| ~ ( mem @ X1 @ X3 )
| ~ ( mem @ X2 @ bool )
| ~ ( ne @ X3 )
| ~ ( mem @ X0 @ X3 )
| ~ ( mem @ X4 @ X3 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1053,zip_derived_cl79]) ).
thf(zip_derived_cl17_057,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl16_058,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl6794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
= X0 )
| ( p @ X2 )
| ~ ( ne @ X3 )
| ~ ( mem @ X4 @ X3 )
| ~ ( mem @ X0 @ X3 )
| ~ ( mem @ X1 @ X3 )
| ~ ( mem @ X2 @ bool )
| ~ ( ne @ X3 )
| ~ ( mem @ X0 @ X3 )
| ~ ( mem @ X4 @ X3 ) ),
inference(demod,[status(thm)],[zip_derived_cl6742,zip_derived_cl17,zip_derived_cl16]) ).
thf(zip_derived_cl6795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( mem @ X2 @ bool )
| ~ ( mem @ X1 @ X3 )
| ~ ( mem @ X0 @ X3 )
| ~ ( mem @ X4 @ X3 )
| ~ ( ne @ X3 )
| ( p @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
= X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl6794]) ).
thf(zip_derived_cl16376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( mem @ X0 @ bool )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X0 ) @ X2 ) @ X1 )
= X1 )
| ~ ( mem @ X1 @ X3 )
| ~ ( mem @ X2 @ X3 )
| ~ ( ne @ X3 )
| ( p @ X0 ) ),
inference(condensation,[status(thm)],[zip_derived_cl6795]) ).
thf(zip_derived_cl222899,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 )
| ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference('sup+',[status(thm)],[zip_derived_cl214776,zip_derived_cl16376]) ).
thf(zip_derived_cl1023_059,plain,
~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1021,zip_derived_cl47]) ).
thf(zip_derived_cl222922,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference(demod,[status(thm)],[zip_derived_cl222899,zip_derived_cl1023]) ).
thf(zip_derived_cl222923,plain,
! [X0: $i] :
( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
| ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl222922]) ).
thf(zip_derived_cl222925,plain,
! [X0: $i] :
( ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
| ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl896,zip_derived_cl222923]) ).
thf(zip_derived_cl47_060,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl222926,plain,
! [X0: $i] :
( ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference(demod,[status(thm)],[zip_derived_cl222925,zip_derived_cl47]) ).
thf(zip_derived_cl222927,plain,
! [X0: $i] :
( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
| ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl222926]) ).
thf(zip_derived_cl223014,plain,
! [X0: $i] :
( ~ ( ne @ bool )
| ~ ( ne @ X0 )
| ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl33,zip_derived_cl222927]) ).
thf(bool_ne,axiom,
ne @ bool ).
thf(zip_derived_cl0,plain,
ne @ bool,
inference(cnf,[status(esa)],[bool_ne]) ).
thf(zip_derived_cl223015,plain,
! [X0: $i] :
( ~ ( ne @ X0 )
| ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
inference(demod,[status(thm)],[zip_derived_cl223014,zip_derived_cl0]) ).
thf(zip_derived_cl223016,plain,
! [X0: $i] :
( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl223015]) ).
thf(zip_derived_cl223031,plain,
! [X0: $i] :
( ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
| ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
| ~ ( ne @ X0 )
| ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1139,zip_derived_cl223016]) ).
thf(zip_derived_cl223038,plain,
! [X0: $i] :
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
| ~ ( ne @ X0 )
| ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ) ),
inference(simplify,[status(thm)],[zip_derived_cl223031]) ).
thf(conj_thm_2Einteger__word_2Ei2w__0,conjecture,
! [A_27a: $i] :
( ( ne @ A_27a )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ) ).
thf(zf_stmt_7,negated_conjecture,
~ ! [A_27a: $i] :
( ( ne @ A_27a )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ),
inference('cnf.neg',[status(esa)],[conj_thm_2Einteger__word_2Ei2w__0]) ).
thf(zip_derived_cl96,plain,
( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( ap @ ( c_2Ewords_2En2w @ sk__2 ) @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[zf_stmt_7]) ).
thf(zip_derived_cl223056,plain,
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
| ~ ( ne @ sk__2 ) ),
inference('sup-',[status(thm)],[zip_derived_cl223038,zip_derived_cl96]) ).
thf(zip_derived_cl95,plain,
ne @ sk__2,
inference(cnf,[status(esa)],[zf_stmt_7]) ).
thf(zip_derived_cl223070,plain,
( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ) ),
inference(demod,[status(thm)],[zip_derived_cl223056,zip_derived_cl95]) ).
thf(zip_derived_cl223071,plain,
~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ),
inference(simplify,[status(thm)],[zip_derived_cl223070]) ).
thf(zip_derived_cl223073,plain,
~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ),
inference('sup-',[status(thm)],[zip_derived_cl696,zip_derived_cl223071]) ).
thf(zip_derived_cl47_061,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).
thf(zip_derived_cl223074,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl223073,zip_derived_cl47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Gpo0SdMHWD true
% 0.14/0.34 % Computer : n022.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 14:50:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.39/0.82 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 234.99/34.24 % Solved by fo/fo3_bce.sh.
% 234.99/34.24 % BCE start: 97
% 234.99/34.24 % BCE eliminated: 3
% 234.99/34.24 % PE start: 94
% 234.99/34.24 logic: eq
% 234.99/34.24 % PE eliminated: 10
% 234.99/34.24 % done 13389 iterations in 33.449s
% 234.99/34.24 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 234.99/34.24 % SZS output start Refutation
% See solution above
% 234.99/34.24
% 234.99/34.24
% 234.99/34.24 % Terminating...
% 235.65/34.34 % Runner terminated.
% 235.69/34.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------