%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP012^2 : 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.bqo5Ngud2l true
% Computer : n031.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 04:38:19 PM UTC 2025
% Result : Theorem 48.03s 8.26s
% Output : Refutation 48.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 17 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 544 ( 7 ~; 5 |; 2 &; 465 @)
% ( 11 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-2 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 85 ( 33 ^; 52 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp__ty_2Einteger_2Eint_type,type,
tp__ty_2Einteger_2Eint: $tType ).
thf(del_type,type,
del: $tType ).
thf(mem_type,type,
mem: $i > del > $o ).
thf(inj__o_type,type,
inj__o: $o > $i ).
thf(c_2Einteger_2Eint__sub_type,type,
c_2Einteger_2Eint__sub: $i ).
thf(fo__c_2Einteger_2Eint__add_type,type,
fo__c_2Einteger_2Eint__add: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(p_type,type,
p: $i > $o ).
thf(inj__ty_2Einteger_2Eint_type,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
thf(fo__c_2Einteger_2Eint__neg_type,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(c_2Einteger_2Eint__add_type,type,
c_2Einteger_2Eint__add: $i ).
thf(arr_type,type,
arr: del > del > del ).
thf(c_2Einteger_2Eint__neg_type,type,
c_2Einteger_2Eint__neg: $i ).
thf(bool_type,type,
bool: del ).
thf(surj__ty_2Einteger_2Eint_type,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
thf(ty_2Einteger_2Eint_type,type,
ty_2Einteger_2Eint: del ).
thf(c_2Einteger_2Eint__divides_type,type,
c_2Einteger_2Eint__divides: $i ).
thf(fo__c_2Einteger_2Eint__sub_type,type,
fo__c_2Einteger_2Eint__sub: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
thf(stp_inj_mem_ty_2Einteger_2Eint,axiom,
! [X: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X ) @ ty_2Einteger_2Eint ) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ Y0 ) @ ty_2Einteger_2Eint ) ),
inference(cnf,[status(esa)],[stp_inj_mem_ty_2Einteger_2Eint]) ).
thf(stp_eq_fo_c_2Einteger_2Eint__neg,axiom,
! [X0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) ) ).
thf(zip_derived_cl19,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ Y0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Einteger_2Eint__neg]) ).
thf(zip_derived_cl1337,plain,
! [X2: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X2 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl1338,plain,
! [X2: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ X2 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1337]) ).
thf(zip_derived_cl12_001,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ Y0 ) @ ty_2Einteger_2Eint ) ),
inference(cnf,[status(esa)],[stp_inj_mem_ty_2Einteger_2Eint]) ).
thf(zip_derived_cl110,plain,
! [X2: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X2 ) @ ty_2Einteger_2Eint ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl1344,plain,
! [X0: tp__ty_2Einteger_2Eint] : ( mem @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ty_2Einteger_2Eint ),
inference('sup+',[status(thm)],[zip_derived_cl1338,zip_derived_cl110]) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0p ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) ) ) ).
thf(zip_derived_cl49,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG]) ).
thf(stp_inj_surj_o,axiom,
! [X: $o] :
( ( p @ ( inj__o @ X ) )
<=> X ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $o] :
( ( p @ ( inj__o @ Y0 ) )
<=> Y0 ) ),
inference(cnf,[status(esa)],[stp_inj_surj_o]) ).
thf(stp_iso_mem_ty_2Einteger_2Eint,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Einteger_2Eint )
=> ( X
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: $i] :
( ( mem @ Y0 @ ty_2Einteger_2Eint )
=> ( Y0
= ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[stp_iso_mem_ty_2Einteger_2Eint]) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V2r ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V2r ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V2r ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V2r ) ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__RSUB]) ).
thf(zip_derived_cl60,plain,
~ ( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y2: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ Y2 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(conj_thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
! [V0p: tp__ty_2Einteger_2Eint,V1q: tp__ty_2Einteger_2Eint,V2r: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V2r ) ) @ ( inj__ty_2Einteger_2Eint @ V1q ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ V0p ) ) @ ( inj__ty_2Einteger_2Eint @ V2r ) ) ) ) ) ).
thf(zip_derived_cl48,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y2: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ Y2 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__RADD]) ).
thf(mem_c_2Einteger_2Eint__divides,axiom,
mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).
thf(zip_derived_cl20,plain,
mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__divides]) ).
thf(stp_iso_mem_o,axiom,
! [X: $i] :
( ( mem @ X @ bool )
=> ( X
= ( inj__o @ ( p @ X ) ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( ( mem @ Y0 @ bool )
=> ( Y0
= ( inj__o @ ( p @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[stp_iso_mem_o]) ).
thf(stp_inj_surj_ty_2Einteger_2Eint,axiom,
! [X: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ X ) )
= X ) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( inj__ty_2Einteger_2Eint @ Y0 ) )
= Y0 ) ),
inference(cnf,[status(esa)],[stp_inj_surj_ty_2Einteger_2Eint]) ).
thf(stp_eq_fo_c_2Einteger_2Eint__sub,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ( inj__ty_2Einteger_2Eint @ X1 ) ) ) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__sub @ Y0 @ Y1 ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Einteger_2Eint__sub]) ).
thf(ax_thm_2Einteger_2Eint__sub,axiom,
! [V0x: tp__ty_2Einteger_2Eint,V1y: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( inj__ty_2Einteger_2Eint @ V1y ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0x ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V1y ) ) ) ) ) ).
thf(zip_derived_cl47,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[ax_thm_2Einteger_2Eint__sub]) ).
thf(zip_derived_cl19_002,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__neg @ Y0 ) )
= ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Einteger_2Eint__neg]) ).
thf(stp_eq_fo_c_2Einteger_2Eint__add,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ ( inj__ty_2Einteger_2Eint @ X1 ) ) ) ).
thf(zip_derived_cl17,plain,
( !!
@ ^ [Y0: tp__ty_2Einteger_2Eint] :
( !!
@ ^ [Y1: tp__ty_2Einteger_2Eint] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger_2Eint__add @ Y0 @ Y1 ) )
= ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ Y0 ) ) @ ( inj__ty_2Einteger_2Eint @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[stp_eq_fo_c_2Einteger_2Eint__add]) ).
thf(zip_derived_cl110_003,plain,
! [X2: tp__ty_2Einteger_2Eint] : ( mem @ ( inj__ty_2Einteger_2Eint @ X2 ) @ ty_2Einteger_2Eint ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
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_cl3,plain,
( !!
@ ^ [Y0: del] :
( !!
@ ^ [Y1: del] :
( !!
@ ^ [Y2: $i] :
( ( mem @ Y2 @ ( arr @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( mem @ Y3 @ Y0 )
=> ( mem @ ( ap @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[ap_tp]) ).
thf(zip_derived_cl271,plain,
! [X2: del] :
( !!
@ ^ [Y0: del] :
( !!
@ ^ [Y1: $i] :
( ( mem @ Y1 @ ( arr @ X2 @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( mem @ Y2 @ X2 )
=> ( mem @ ( ap @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl272,plain,
! [X2: del,X4: del] :
( !!
@ ^ [Y0: $i] :
( ( mem @ Y0 @ ( arr @ X2 @ X4 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( mem @ Y1 @ X2 )
=> ( mem @ ( ap @ Y0 @ Y1 ) @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl273,plain,
! [X2: del,X4: del,X6: $i] :
( ( mem @ X6 @ ( arr @ X2 @ X4 ) )
=> ( !!
@ ^ [Y0: $i] :
( ( mem @ Y0 @ X2 )
=> ( mem @ ( ap @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl272]) ).
thf(zip_derived_cl274,plain,
! [X2: del,X4: del,X6: $i] :
( ~ ( mem @ X6 @ ( arr @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( mem @ Y0 @ X2 )
=> ( mem @ ( ap @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl273]) ).
thf(zip_derived_cl275,plain,
! [X2: del,X4: del,X6: $i,X8: $i] :
( ( ( mem @ X8 @ X2 )
=> ( mem @ ( ap @ X6 @ X8 ) @ X4 ) )
| ~ ( mem @ X6 @ ( arr @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl274]) ).
thf(zip_derived_cl276,plain,
! [X2: del,X4: del,X6: $i,X8: $i] :
( ~ ( mem @ X8 @ X2 )
| ( mem @ ( ap @ X6 @ X8 ) @ X4 )
| ~ ( mem @ X6 @ ( arr @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl275]) ).
thf(zip_derived_cl291,plain,
! [X0: tp__ty_2Einteger_2Eint,X1: del,X2: $i] :
( ~ ( mem @ X2 @ ( arr @ ty_2Einteger_2Eint @ X1 ) )
| ( mem @ ( ap @ X2 @ ( inj__ty_2Einteger_2Eint @ X0 ) ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl276]) ).
thf(zip_derived_cl1729,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl12,zip_derived_cl1344,zip_derived_cl49,zip_derived_cl0,zip_derived_cl13,zip_derived_cl60,zip_derived_cl48,zip_derived_cl20,zip_derived_cl2,zip_derived_cl11,zip_derived_cl15,zip_derived_cl47,zip_derived_cl19,zip_derived_cl17,zip_derived_cl291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.19 % Problem : ITP012^2 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.10/0.20 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bqo5Ngud2l true
% 0.12/0.42 % Computer : n031.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8042.1875MB
% 0.12/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Wed Oct 1 15:28:23 EDT 2025
% 0.12/0.42 % CPUTime :
% 0.17/0.42 % Running portfolio for 300 s
% 0.17/0.42 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Number of cores: 8
% 0.17/0.42 % Python version: Python 3.6.8
% 0.17/0.42 % Running in HO mode
% 0.43/0.69 % Total configuration time : 828
% 0.43/0.69 % Estimated wc time : 1656
% 0.43/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.44/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.44/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.44/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.45/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.45/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.45/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.45/0.85 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.45/0.85 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.46/0.99 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 48.03/8.26 % Solved by lams/15_e_short1.sh.
% 48.03/8.26 % done 166 iterations in 7.433s
% 48.03/8.26 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 48.03/8.26 % SZS output start Refutation
% See solution above
% 48.03/8.27
% 48.03/8.27
% 48.03/8.27 % Terminating...
% 48.42/8.44 % Runner terminated.
% 48.42/8.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------