%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP002_2 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2zgIVI2q8E 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 Oct 2 04:38:07 PM UTC 2025
% Result : Theorem 114.08s 16.88s
% Output : Refutation 114.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 22
% Syntax : Number of formulae : 232 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 653 ( 202 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 6900 ( 434 ~; 388 |; 9 &;6045 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 14 con; 0-3 aty)
% Number of variables : 256 ( 0 ^; 256 !; 0 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(tp__o_type,type,
tp__o: $tType ).
thf(mem_type,type,
mem: $i > del > $o ).
thf(sk__6_type,type,
sk__6: $i ).
thf(fo__c_2Ebool_2EF_type,type,
fo__c_2Ebool_2EF: tp__o ).
thf(sk__7_type,type,
sk__7: $i ).
thf(p_type,type,
p: $i > $o ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(sk__4_type,type,
sk__4: del ).
thf(c_2Eoption_2ENONE_type,type,
c_2Eoption_2ENONE: del > $i ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND: del > $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(fo__c_2Ebool_2E_2F_5C_type,type,
fo__c_2Ebool_2E_2F_5C: tp__o > tp__o > tp__o ).
thf(arr_type,type,
arr: del > del > del ).
thf(c_2Eoption_2ESOME_type,type,
c_2Eoption_2ESOME: del > $i ).
thf(inj__o_type,type,
inj__o: tp__o > $i ).
thf(sk__2_type,type,
sk__2: del ).
thf(bool_type,type,
bool: del ).
thf(c_2Eoption_2ETHE_type,type,
c_2Eoption_2ETHE: del > $i ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $i ).
thf(fo__c_2Ebool_2ET_type,type,
fo__c_2Ebool_2ET: tp__o ).
thf(sk__3_type,type,
sk__3: del ).
thf(surj__o_type,type,
surj__o: $i > tp__o ).
thf(sk__5_type,type,
sk__5: $i ).
thf(c_2Eoption_2EOPTION__MAP2_type,type,
c_2Eoption_2EOPTION__MAP2: del > del > del > $i ).
thf(c_2Eoption_2EIS__SOME_type,type,
c_2Eoption_2EIS__SOME: del > $i ).
thf(ty_2Eoption_2Eoption_type,type,
ty_2Eoption_2Eoption: del > del ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(mem_c_2Eoption_2ETHE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ETHE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ) ).
thf(zip_derived_cl17,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ETHE @ X0 ) @ ( arr @ ( ty_2Eoption_2Eoption @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ETHE]) ).
thf(ap_tp,axiom,
! [A: del,B: del,F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [X: $i] :
( ( mem @ X @ A )
=> ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl322,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ETHE @ X0 ) @ X1 ) @ X0 )
| ~ ( mem @ X1 @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl0]) ).
thf(zip_derived_cl322_001,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ETHE @ X0 ) @ X1 ) @ X0 )
| ~ ( mem @ X1 @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl0]) ).
thf(mem_c_2Eoption_2ESOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ESOME @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(zip_derived_cl18,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ESOME @ X0 ) @ ( arr @ X0 @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ESOME]) ).
thf(zip_derived_cl0_002,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl300,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(conj_thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_thm_2Eoption_2EOPTION__MAP2__THM]) ).
thf(zip_derived_cl45,plain,
mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_003,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl345,plain,
! [X0: $i] :
( ( mem @ ( ap @ sk__5 @ X0 ) @ ( arr @ sk__4 @ sk__2 ) )
| ~ ( mem @ X0 @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl0]) ).
thf(zip_derived_cl0_004,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl405,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ sk__3 )
| ( mem @ ( ap @ ( ap @ sk__5 @ X0 ) @ X1 ) @ sk__2 )
| ~ ( mem @ X1 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl345,zip_derived_cl0]) ).
thf(zip_derived_cl405_005,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ sk__3 )
| ( mem @ ( ap @ ( ap @ sk__5 @ X0 ) @ X1 ) @ sk__2 )
| ~ ( mem @ X1 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl345,zip_derived_cl0]) ).
thf(zip_derived_cl405_006,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ sk__3 )
| ( mem @ ( ap @ ( ap @ sk__5 @ X0 ) @ X1 ) @ sk__2 )
| ~ ( mem @ X1 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl345,zip_derived_cl0]) ).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [A_27a: del,V0t1: $i] :
( ( mem @ V0t1 @ A_27a )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( inj__o @ fo__c_2Ebool_2ET ) ) @ V0t1 ) @ V1t2 )
= V0t1 )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( inj__o @ fo__c_2Ebool_2EF ) ) @ V0t1 ) @ V1t2 )
= V1t2 ) ) ) ) ).
thf(zip_derived_cl37,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ ( inj__o @ fo__c_2Ebool_2EF ) ) @ X2 ) @ X0 )
= X0 )
| ~ ( mem @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[conj_thm_2Ebool_2ECOND__CLAUSES]) ).
thf(stp_eq_fo_c_2Ebool_2EF,axiom,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ) ).
thf(zip_derived_cl11,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2EF]) ).
thf(zip_derived_cl484,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2EF ) @ X2 ) @ X0 )
= X0 )
| ~ ( mem @ X2 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl484_007,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2EF ) @ X2 ) @ X0 )
= X0 )
| ~ ( mem @ X2 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl484_008,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2EF ) @ X2 ) @ X0 )
= X0 )
| ~ ( mem @ X2 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl38,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ ( inj__o @ fo__c_2Ebool_2ET ) ) @ X2 ) @ X0 )
= X2 )
| ~ ( mem @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[conj_thm_2Ebool_2ECOND__CLAUSES]) ).
thf(stp_eq_fo_c_2Ebool_2ET,axiom,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ) ).
thf(zip_derived_cl14,plain,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2ET]) ).
thf(zip_derived_cl487,plain,
! [X0: $i,X1: del,X2: $i] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2ET ) @ X2 ) @ X0 )
= X2 )
| ~ ( mem @ X2 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl38,zip_derived_cl14]) ).
thf(mem_c_2Eoption_2EIS__SOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
thf(zip_derived_cl19,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( arr @ ( ty_2Eoption_2Eoption @ X0 ) @ bool ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2EIS__SOME]) ).
thf(zip_derived_cl0_009,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl339,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ X1 ) @ bool )
| ~ ( mem @ X1 @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl0]) ).
thf(mem_c_2Ebool_2ET,axiom,
mem @ c_2Ebool_2ET @ bool ).
thf(zip_derived_cl13,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(boolext,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( ( p @ Q )
<=> ( p @ R ) )
=> ( Q = R ) ) ) ) ).
thf(zip_derived_cl1,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_cl283,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ c_2Ebool_2ET )
| ~ ( p @ X0 )
| ( X0 = c_2Ebool_2ET ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl1]) ).
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_cl287,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ X0 )
| ( X0 = c_2Ebool_2ET ) ),
inference(demod,[status(thm)],[zip_derived_cl283,zip_derived_cl15]) ).
thf(zip_derived_cl1415,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ ( ty_2Eoption_2Eoption @ X1 ) )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl339,zip_derived_cl287]) ).
thf(ax_thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a: del] :
( ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $false )
& ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
<=> $true ) ) ) ).
thf(zip_derived_cl41,plain,
! [X0: del,X1: $i] :
( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) ) )
| ~ ( mem @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2EIS__SOME__DEF]) ).
thf(zip_derived_cl1453,plain,
! [X0: $i,X1: del] :
( ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= c_2Ebool_2ET )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) @ ( ty_2Eoption_2Eoption @ X1 ) )
| ~ ( mem @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1415,zip_derived_cl41]) ).
thf(zip_derived_cl300_010,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl27090,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= c_2Ebool_2ET ) ),
inference(clc,[status(thm)],[zip_derived_cl1453,zip_derived_cl300]) ).
thf(ax_and_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
<=> ( ( p @ Q )
& ( p @ R ) ) ) ) ) ).
thf(zip_derived_cl24,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ X1 )
| ~ ( p @ X0 )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 ) )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[ax_and_p]) ).
thf(mem_c_2Ebool_2E_2F_5C,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
thf(zip_derived_cl20,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(cnf,[status(esa)],[mem_c_2Ebool_2E_2F_5C]) ).
thf(zip_derived_cl0_011,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl323,plain,
! [X0: $i] :
( ( mem @ ( ap @ c_2Ebool_2E_2F_5C @ X0 ) @ ( arr @ bool @ bool ) )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl0]) ).
thf(zip_derived_cl0_012,plain,
! [X0: $i,X1: del,X2: $i,X3: del] :
( ~ ( mem @ X0 @ X1 )
| ( mem @ ( ap @ X2 @ X0 ) @ X3 )
| ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl972,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X0 ) @ X1 ) @ bool )
| ~ ( mem @ X1 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl323,zip_derived_cl0]) ).
thf(zip_derived_cl287_013,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ X0 )
| ( X0 = c_2Ebool_2ET ) ),
inference(demod,[status(thm)],[zip_derived_cl283,zip_derived_cl15]) ).
thf(zip_derived_cl14434,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( mem @ X1 @ bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 )
= c_2Ebool_2ET )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl972,zip_derived_cl287]) ).
thf(zip_derived_cl20193,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X1 @ bool )
| ~ ( p @ X0 )
| ~ ( p @ X1 )
| ~ ( mem @ X0 @ bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 )
= c_2Ebool_2ET )
| ~ ( mem @ X1 @ bool )
| ~ ( mem @ X0 @ bool ) ),
inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl14434]) ).
thf(zip_derived_cl20194,plain,
! [X0: $i,X1: $i] :
( ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 )
= c_2Ebool_2ET )
| ~ ( mem @ X0 @ bool )
| ~ ( p @ X1 )
| ~ ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(simplify,[status(thm)],[zip_derived_cl20193]) ).
thf(zip_derived_cl27090_014,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= c_2Ebool_2ET ) ),
inference(clc,[status(thm)],[zip_derived_cl1453,zip_derived_cl300]) ).
thf(zip_derived_cl27090_015,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= c_2Ebool_2ET ) ),
inference(clc,[status(thm)],[zip_derived_cl1453,zip_derived_cl300]) ).
thf(zip_derived_cl27090_016,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ X1 )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= c_2Ebool_2ET ) ),
inference(clc,[status(thm)],[zip_derived_cl1453,zip_derived_cl300]) ).
thf(ax_thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) )
= V0x ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= X0 )
| ~ ( mem @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2ETHE__DEF]) ).
thf(ax_thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27b ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27c ) @ V2y ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Eoption_2ETHE @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27c ) @ V2y ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: del,X2: del,X3: del,X4: $i,X5: $i] :
( ~ ( mem @ X0 @ ( ty_2Eoption_2Eoption @ X1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X2 @ X1 @ X3 ) @ X5 ) @ X0 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X3 ) @ X4 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2ETHE @ X3 ) @ X4 ) ) ) ) @ ( c_2Eoption_2ENONE @ X2 ) ) )
| ~ ( mem @ X4 @ ( ty_2Eoption_2Eoption @ X3 ) )
| ~ ( mem @ X5 @ ( arr @ X1 @ ( arr @ X3 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2EOPTION__MAP2__DEF]) ).
thf(zip_derived_cl43_017,plain,
! [X0: $i,X1: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= X0 )
| ~ ( mem @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2ETHE__DEF]) ).
thf(zip_derived_cl44_018,plain,
! [X0: $i,X1: del,X2: del,X3: del,X4: $i,X5: $i] :
( ~ ( mem @ X0 @ ( ty_2Eoption_2Eoption @ X1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X2 @ X1 @ X3 ) @ X5 ) @ X0 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X3 ) @ X4 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2ETHE @ X3 ) @ X4 ) ) ) ) @ ( c_2Eoption_2ENONE @ X2 ) ) )
| ~ ( mem @ X4 @ ( ty_2Eoption_2Eoption @ X3 ) )
| ~ ( mem @ X5 @ ( arr @ X1 @ ( arr @ X3 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2EOPTION__MAP2__DEF]) ).
thf(zip_derived_cl519,plain,
! [X0: $i,X1: del,X2: del,X3: $i,X4: del,X5: $i] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X1 @ X4 @ X2 ) @ X5 ) @ X3 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X1 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X4 ) @ X3 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X2 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X4 ) @ X3 ) ) @ X0 ) ) ) @ ( c_2Eoption_2ENONE @ X1 ) ) )
| ~ ( mem @ X0 @ X2 )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X2 @ X1 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) @ ( ty_2Eoption_2Eoption @ X2 ) )
| ~ ( mem @ X3 @ ( ty_2Eoption_2Eoption @ X4 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl43,zip_derived_cl44]) ).
thf(zip_derived_cl300_019,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl7016,plain,
! [X0: $i,X1: del,X2: del,X3: $i,X4: del,X5: $i] :
( ~ ( mem @ X3 @ ( ty_2Eoption_2Eoption @ X4 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X2 @ X1 ) ) )
| ~ ( mem @ X0 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X1 @ X4 @ X2 ) @ X5 ) @ X3 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X1 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X4 ) @ X3 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X2 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X4 ) @ X3 ) ) @ X0 ) ) ) @ ( c_2Eoption_2ENONE @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl519,zip_derived_cl300]) ).
thf(zip_derived_cl43_020,plain,
! [X0: $i,X1: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ X0 ) )
= X0 )
| ~ ( mem @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2ETHE__DEF]) ).
thf(zip_derived_cl44_021,plain,
! [X0: $i,X1: del,X2: del,X3: del,X4: $i,X5: $i] :
( ~ ( mem @ X0 @ ( ty_2Eoption_2Eoption @ X1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X2 @ X1 @ X3 ) @ X5 ) @ X0 ) @ X4 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X3 ) @ X4 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X1 ) @ X0 ) ) @ ( ap @ ( c_2Eoption_2ETHE @ X3 ) @ X4 ) ) ) ) @ ( c_2Eoption_2ENONE @ X2 ) ) )
| ~ ( mem @ X4 @ ( ty_2Eoption_2Eoption @ X3 ) )
| ~ ( mem @ X5 @ ( arr @ X1 @ ( arr @ X3 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2EOPTION__MAP2__DEF]) ).
thf(zip_derived_cl525,plain,
! [X0: $i,X1: del,X2: $i,X3: del,X4: del,X5: $i] :
( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X1 @ X4 @ X3 ) @ X5 ) @ ( ap @ ( c_2Eoption_2ESOME @ X4 ) @ X0 ) ) @ X2 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X1 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X4 ) @ ( ap @ ( c_2Eoption_2ESOME @ X4 ) @ X0 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X3 ) @ X2 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ ( ap @ ( ap @ X5 @ X0 ) @ ( ap @ ( c_2Eoption_2ETHE @ X3 ) @ X2 ) ) ) ) @ ( c_2Eoption_2ENONE @ X1 ) ) )
| ~ ( mem @ X0 @ X4 )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X3 @ X1 ) ) )
| ~ ( mem @ X2 @ ( ty_2Eoption_2Eoption @ X3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X4 ) @ X0 ) @ ( ty_2Eoption_2Eoption @ X4 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl43,zip_derived_cl44]) ).
thf(zip_derived_cl300_022,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl9381,plain,
! [X0: $i,X1: del,X2: $i,X3: del,X4: del,X5: $i] :
( ~ ( mem @ X2 @ ( ty_2Eoption_2Eoption @ X3 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X3 @ X1 ) ) )
| ~ ( mem @ X0 @ X4 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X1 @ X4 @ X3 ) @ X5 ) @ ( ap @ ( c_2Eoption_2ESOME @ X4 ) @ X0 ) ) @ X2 )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X1 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X4 ) @ ( ap @ ( c_2Eoption_2ESOME @ X4 ) @ X0 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X3 ) @ X2 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ ( ap @ ( ap @ X5 @ X0 ) @ ( ap @ ( c_2Eoption_2ETHE @ X3 ) @ X2 ) ) ) ) @ ( c_2Eoption_2ENONE @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl300]) ).
thf(zip_derived_cl7016_023,plain,
! [X0: $i,X1: del,X2: del,X3: $i,X4: del,X5: $i] :
( ~ ( mem @ X3 @ ( ty_2Eoption_2Eoption @ X4 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ ( arr @ X2 @ X1 ) ) )
| ~ ( mem @ X0 @ X2 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ X1 @ X4 @ X2 ) @ X5 ) @ X3 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ X1 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ X4 ) @ X3 ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ X2 ) @ ( ap @ ( c_2Eoption_2ESOME @ X2 ) @ X0 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ X1 ) @ ( ap @ ( ap @ X5 @ ( ap @ ( c_2Eoption_2ETHE @ X4 ) @ X3 ) ) @ X0 ) ) ) @ ( c_2Eoption_2ENONE @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl519,zip_derived_cl300]) ).
thf(zip_derived_cl47,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7023,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ sk__7 @ sk__4 )
| ~ ( mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl7016,zip_derived_cl47]) ).
thf(zip_derived_cl46,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl45_024,plain,
mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7048,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl7023,zip_derived_cl46,zip_derived_cl45]) ).
thf(zip_derived_cl9406,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ sk__6 @ sk__3 )
| ~ ( mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__4 ) @ ( ty_2Eoption_2Eoption @ sk__4 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl9381,zip_derived_cl7048]) ).
thf(zip_derived_cl48,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl45_025,plain,
mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mem_c_2Eoption_2ENONE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ).
thf(zip_derived_cl16,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl9462,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9406,zip_derived_cl48,zip_derived_cl45,zip_derived_cl16]) ).
thf(zip_derived_cl9468,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ sk__7 @ sk__4 )
| ~ ( mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__3 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl7016,zip_derived_cl9462]) ).
thf(zip_derived_cl46_026,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl45_027,plain,
mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_028,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl9470,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk__2 @ sk__3 @ sk__4 ) @ sk__5 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ ( c_2Eoption_2ENONE @ sk__4 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9468,zip_derived_cl46,zip_derived_cl45,zip_derived_cl16]) ).
thf(zip_derived_cl9488,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__4 ) @ ( ty_2Eoption_2Eoption @ sk__4 ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__3 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl44,zip_derived_cl9470]) ).
thf(zip_derived_cl45_029,plain,
mem @ sk__5 @ ( arr @ sk__3 @ ( arr @ sk__4 @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_030,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl16_031,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl9489,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9488,zip_derived_cl45,zip_derived_cl16,zip_derived_cl16]) ).
thf(zip_derived_cl10301,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ sk__6 @ sk__3 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl9489]) ).
thf(zip_derived_cl48_032,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10302,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl10301,zip_derived_cl48]) ).
thf(zip_derived_cl42,plain,
! [X0: del] :
~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) ) ),
inference(cnf,[status(esa)],[ax_thm_2Eoption_2EIS__SOME__DEF]) ).
thf(zip_derived_cl339_033,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ X1 ) @ bool )
| ~ ( mem @ X1 @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl0]) ).
thf(mem_c_2Ebool_2EF,axiom,
mem @ c_2Ebool_2EF @ bool ).
thf(zip_derived_cl10,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl2,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_cl312,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ c_2Ebool_2EF )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl2]) ).
thf(ax_false_p,axiom,
~ ( p @ c_2Ebool_2EF ) ).
thf(zip_derived_cl12,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl316,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl312,zip_derived_cl12]) ).
thf(zip_derived_cl1416,plain,
! [X0: $i,X1: del] :
( ~ ( mem @ X0 @ ( ty_2Eoption_2Eoption @ X1 ) )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl339,zip_derived_cl316]) ).
thf(zip_derived_cl21224,plain,
! [X0: del] :
( ( ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) )
= c_2Ebool_2EF )
| ~ ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl1416]) ).
thf(zip_derived_cl16_034,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl21226,plain,
! [X0: del] :
( ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl21224,zip_derived_cl16]) ).
thf(zip_derived_cl21226_035,plain,
! [X0: del] :
( ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl21224,zip_derived_cl16]) ).
thf(zip_derived_cl21226_036,plain,
! [X0: del] :
( ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl21224,zip_derived_cl16]) ).
thf(zip_derived_cl21226_037,plain,
! [X0: del] :
( ( ap @ ( c_2Eoption_2EIS__SOME @ X0 ) @ ( c_2Eoption_2ENONE @ X0 ) )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl21224,zip_derived_cl16]) ).
thf(zip_derived_cl21264,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl10302,zip_derived_cl21226,zip_derived_cl21226,zip_derived_cl21226,zip_derived_cl21226]) ).
thf(zip_derived_cl27172,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ sk__7 @ sk__4 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl27090,zip_derived_cl21264]) ).
thf(zip_derived_cl46_038,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl27233,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27172,zip_derived_cl46]) ).
thf(zip_derived_cl27238,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ sk__6 @ sk__3 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl27090,zip_derived_cl27233]) ).
thf(zip_derived_cl48_039,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl27241,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27238,zip_derived_cl48]) ).
thf(zip_derived_cl27244,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ sk__6 @ sk__3 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl27090,zip_derived_cl27241]) ).
thf(zip_derived_cl48_040,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl27247,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27244,zip_derived_cl48]) ).
thf(zip_derived_cl27248,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ c_2Ebool_2ET @ bool )
| ~ ( p @ c_2Ebool_2ET )
| ~ ( p @ c_2Ebool_2ET )
| ~ ( mem @ c_2Ebool_2ET @ bool )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl20194,zip_derived_cl27247]) ).
thf(zip_derived_cl13_041,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl15_042,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl15_043,plain,
p @ c_2Ebool_2ET,
inference(cnf,[status(esa)],[ax_true_p]) ).
thf(zip_derived_cl13_044,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl27249,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27248,zip_derived_cl13,zip_derived_cl15,zip_derived_cl15,zip_derived_cl13]) ).
thf(zip_derived_cl22,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 ) )
| ( p @ X1 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[ax_and_p]) ).
thf(zip_derived_cl11_045,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2EF]) ).
thf(zip_derived_cl11_046,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2EF]) ).
thf(stp_eq_fo_c_2Ebool_2E_2F_5C,axiom,
! [X0: tp__o,X1: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ ( inj__o @ X1 ) ) ) ).
thf(zip_derived_cl21,plain,
! [X0: tp__o,X1: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ ( inj__o @ X1 ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2E_2F_5C]) ).
thf(zip_derived_cl21_047,plain,
! [X0: tp__o,X1: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ ( inj__o @ X1 ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2E_2F_5C]) ).
thf(stp_inj_surj_o,axiom,
! [X: tp__o] :
( ( surj__o @ ( inj__o @ X ) )
= X ) ).
thf(zip_derived_cl7,plain,
! [X0: tp__o] :
( ( surj__o @ ( inj__o @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[stp_inj_surj_o]) ).
thf(zip_derived_cl342,plain,
! [X0: tp__o,X1: tp__o] :
( ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X1 ) ) @ ( inj__o @ X0 ) ) )
= ( fo__c_2Ebool_2E_2F_5C @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl7]) ).
thf(zip_derived_cl1455,plain,
! [X0: tp__o,X1: tp__o] :
( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ ( inj__o @ X1 ) ) ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ ( inj__o @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl342]) ).
thf(stp_inj_mem_o,axiom,
! [X: tp__o] : ( mem @ ( inj__o @ X ) @ bool ) ).
thf(zip_derived_cl8,plain,
! [X0: tp__o] : ( mem @ ( inj__o @ X0 ) @ bool ),
inference(cnf,[status(esa)],[stp_inj_mem_o]) ).
thf(zip_derived_cl27430,plain,
! [X0: tp__o,X1: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X1 ) ) @ ( inj__o @ X0 ) ) @ bool ),
inference('sup+',[status(thm)],[zip_derived_cl1455,zip_derived_cl8]) ).
thf(zip_derived_cl29482,plain,
! [X0: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ c_2Ebool_2EF ) @ bool ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl27430]) ).
thf(zip_derived_cl29569,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) @ bool,
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl29482]) ).
thf(zip_derived_cl316_048,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl312,zip_derived_cl12]) ).
thf(zip_derived_cl29584,plain,
( ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl29569,zip_derived_cl316]) ).
thf(zip_derived_cl50806,plain,
( ~ ( mem @ c_2Ebool_2EF @ bool )
| ( p @ c_2Ebool_2EF )
| ~ ( mem @ c_2Ebool_2EF @ bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference('sup+',[status(thm)],[zip_derived_cl22,zip_derived_cl29584]) ).
thf(zip_derived_cl10_049,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl12_050,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl10_051,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl50811,plain,
( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl50806,zip_derived_cl10,zip_derived_cl12,zip_derived_cl10]) ).
thf(zip_derived_cl50854,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27249,zip_derived_cl50811]) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 ) )
| ( p @ X0 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[ax_and_p]) ).
thf(zip_derived_cl14_052,plain,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2ET]) ).
thf(zip_derived_cl29482_053,plain,
! [X0: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ c_2Ebool_2EF ) @ bool ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl27430]) ).
thf(zip_derived_cl29570,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) @ bool,
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl29482]) ).
thf(zip_derived_cl316_054,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl312,zip_derived_cl12]) ).
thf(zip_derived_cl29600,plain,
( ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl29570,zip_derived_cl316]) ).
thf(zip_derived_cl51402,plain,
( ~ ( mem @ c_2Ebool_2ET @ bool )
| ( p @ c_2Ebool_2EF )
| ~ ( mem @ c_2Ebool_2EF @ bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference('sup+',[status(thm)],[zip_derived_cl23,zip_derived_cl29600]) ).
thf(zip_derived_cl13_055,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl12_056,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl10_057,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl51407,plain,
( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl51402,zip_derived_cl13,zip_derived_cl12,zip_derived_cl10]) ).
thf(zip_derived_cl78564,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk__4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__4 ) @ sk__7 ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl50854,zip_derived_cl51407]) ).
thf(zip_derived_cl78567,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ sk__7 @ sk__4 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl27090,zip_derived_cl78564]) ).
thf(zip_derived_cl22_058,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ X1 ) @ X0 ) )
| ( p @ X1 )
| ~ ( mem @ X1 @ bool ) ),
inference(cnf,[status(esa)],[ax_and_p]) ).
thf(zip_derived_cl11_059,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2EF]) ).
thf(zip_derived_cl14_060,plain,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Ebool_2ET]) ).
thf(zip_derived_cl27430_061,plain,
! [X0: tp__o,X1: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X1 ) ) @ ( inj__o @ X0 ) ) @ bool ),
inference('sup+',[status(thm)],[zip_derived_cl1455,zip_derived_cl8]) ).
thf(zip_derived_cl29483,plain,
! [X0: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ X0 ) ) @ c_2Ebool_2ET ) @ bool ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl27430]) ).
thf(zip_derived_cl29654,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) @ bool,
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl29483]) ).
thf(zip_derived_cl316_062,plain,
! [X0: $i] :
( ~ ( mem @ X0 @ bool )
| ( p @ X0 )
| ( X0 = c_2Ebool_2EF ) ),
inference(demod,[status(thm)],[zip_derived_cl312,zip_derived_cl12]) ).
thf(zip_derived_cl29796,plain,
( ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET )
= c_2Ebool_2EF )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl29654,zip_derived_cl316]) ).
thf(zip_derived_cl52170,plain,
( ~ ( mem @ c_2Ebool_2EF @ bool )
| ( p @ c_2Ebool_2EF )
| ~ ( mem @ c_2Ebool_2ET @ bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET )
= c_2Ebool_2EF ) ),
inference('sup+',[status(thm)],[zip_derived_cl22,zip_derived_cl29796]) ).
thf(zip_derived_cl10_063,plain,
mem @ c_2Ebool_2EF @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).
thf(zip_derived_cl12_064,plain,
~ ( p @ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[ax_false_p]) ).
thf(zip_derived_cl13_065,plain,
mem @ c_2Ebool_2ET @ bool,
inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).
thf(zip_derived_cl52175,plain,
( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET )
= c_2Ebool_2EF ),
inference(demod,[status(thm)],[zip_derived_cl52170,zip_derived_cl10,zip_derived_cl12,zip_derived_cl13]) ).
thf(zip_derived_cl46_066,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl78570,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78567,zip_derived_cl52175,zip_derived_cl46]) ).
thf(zip_derived_cl78571,plain,
( ( ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__2 ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl78570]) ).
thf(zip_derived_cl16_067,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl78572,plain,
( ( ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78571,zip_derived_cl16]) ).
thf(zip_derived_cl78573,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl78572]) ).
thf(zip_derived_cl78574,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__2 ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl484,zip_derived_cl78573]) ).
thf(zip_derived_cl16_068,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl78575,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78574,zip_derived_cl16]) ).
thf(zip_derived_cl78576,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl78575]) ).
thf(zip_derived_cl78577,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__2 ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl484,zip_derived_cl78576]) ).
thf(zip_derived_cl16_069,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl78578,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78577,zip_derived_cl16]) ).
thf(zip_derived_cl78579,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ sk__2 ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ sk__2 ) )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl78578]) ).
thf(zip_derived_cl78580,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( c_2Eoption_2ENONE @ sk__2 ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl484,zip_derived_cl78579]) ).
thf(zip_derived_cl16_070,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl78581,plain,
( ( ( c_2Eoption_2ENONE @ sk__2 )
!= ( c_2Eoption_2ENONE @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78580,zip_derived_cl16]) ).
thf(zip_derived_cl78582,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl78581]) ).
thf(zip_derived_cl300_071,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl78584,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl78582,zip_derived_cl300]) ).
thf(zip_derived_cl405_072,plain,
! [X0: $i,X1: $i] :
( ~ ( mem @ X0 @ sk__3 )
| ( mem @ ( ap @ ( ap @ sk__5 @ X0 ) @ X1 ) @ sk__2 )
| ~ ( mem @ X1 @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl345,zip_derived_cl0]) ).
thf(zip_derived_cl78586,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference('sup+',[status(thm)],[zip_derived_cl78584,zip_derived_cl405]) ).
thf(zip_derived_cl300_073,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl78588,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( ap @ sk__5 @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) ) @ sk__7 ) @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl78586,zip_derived_cl300]) ).
thf(zip_derived_cl78591,plain,
( ~ ( mem @ sk__7 @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl405,zip_derived_cl78588]) ).
thf(zip_derived_cl46_074,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl78592,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl78591,zip_derived_cl46]) ).
thf(zip_derived_cl78593,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference(simplify,[status(thm)],[zip_derived_cl78592]) ).
thf(zip_derived_cl300_075,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl78596,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) ) @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl78593,zip_derived_cl300]) ).
thf(zip_derived_cl80208,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ sk__6 @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl405,zip_derived_cl78596]) ).
thf(zip_derived_cl48_076,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl80209,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl80208,zip_derived_cl48]) ).
thf(zip_derived_cl80210,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__2 ) @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) ) @ ( ty_2Eoption_2Eoption @ sk__2 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 ) ),
inference(simplify,[status(thm)],[zip_derived_cl80209]) ).
thf(zip_derived_cl300_077,plain,
! [X0: del,X1: $i] :
( ( mem @ ( ap @ ( c_2Eoption_2ESOME @ X0 ) @ X1 ) @ ( ty_2Eoption_2Eoption @ X0 ) )
| ~ ( mem @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl0]) ).
thf(zip_derived_cl80213,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( ap @ sk__5 @ sk__6 ) @ sk__7 ) @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl80210,zip_derived_cl300]) ).
thf(zip_derived_cl80216,plain,
( ~ ( mem @ sk__7 @ sk__4 )
| ~ ( mem @ sk__6 @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl405,zip_derived_cl80213]) ).
thf(zip_derived_cl46_078,plain,
mem @ sk__7 @ sk__4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl48_079,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl80217,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ESOME @ sk__3 ) @ sk__6 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 ) ),
inference(demod,[status(thm)],[zip_derived_cl80216,zip_derived_cl46,zip_derived_cl48]) ).
thf(zip_derived_cl80220,plain,
( ~ ( mem @ sk__6 @ sk__3 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl300,zip_derived_cl80217]) ).
thf(zip_derived_cl48_080,plain,
mem @ sk__6 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl80221,plain,
( ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__4 ) @ ( c_2Eoption_2ENONE @ sk__4 ) ) @ sk__4 )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl80220,zip_derived_cl48]) ).
thf(zip_derived_cl80224,plain,
( ~ ( mem @ ( c_2Eoption_2ENONE @ sk__4 ) @ ( ty_2Eoption_2Eoption @ sk__4 ) )
| ~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl322,zip_derived_cl80221]) ).
thf(zip_derived_cl16_081,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl80225,plain,
~ ( mem @ ( ap @ ( c_2Eoption_2ETHE @ sk__3 ) @ ( c_2Eoption_2ENONE @ sk__3 ) ) @ sk__3 ),
inference(demod,[status(thm)],[zip_derived_cl80224,zip_derived_cl16]) ).
thf(zip_derived_cl80228,plain,
~ ( mem @ ( c_2Eoption_2ENONE @ sk__3 ) @ ( ty_2Eoption_2Eoption @ sk__3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl322,zip_derived_cl80225]) ).
thf(zip_derived_cl16_082,plain,
! [X0: del] : ( mem @ ( c_2Eoption_2ENONE @ X0 ) @ ( ty_2Eoption_2Eoption @ X0 ) ),
inference(cnf,[status(esa)],[mem_c_2Eoption_2ENONE]) ).
thf(zip_derived_cl80229,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl80228,zip_derived_cl16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ITP002_2 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.02/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2zgIVI2q8E true
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 15:26:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.47/0.59 % Total configuration time : 435
% 0.47/0.59 % Estimated wc time : 1092
% 0.47/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.51/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.51/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 114.08/16.88 % Solved by fo/fo3_bce.sh.
% 114.08/16.88 % BCE start: 49
% 114.08/16.88 % BCE eliminated: 2
% 114.08/16.88 % PE start: 47
% 114.08/16.88 logic: eq
% 114.08/16.88 % PE eliminated: 0
% 114.08/16.88 % done 4236 iterations in 16.159s
% 114.08/16.88 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 114.08/16.88 % SZS output start Refutation
% See solution above
% 114.08/16.88
% 114.08/16.88
% 114.08/16.88 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 114.08/16.88 % Terminating...
% 114.42/16.95 % Runner terminated.
% 114.42/16.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------