%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP020^1 : 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.ZP5QfnuaPk true
% Computer : n001.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 04:38:29 PM UTC 2025
% Result : Theorem 115.81s 15.22s
% Output : Refutation 115.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 25 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1205 ( 12 ~; 9 |; 0 &;1125 @)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 6 con; 0-4 aty)
% ( 25 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 140 ( 48 ^; 87 !; 5 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(du_type,type,
du: $tType ).
thf(d_type,type,
d: $tType ).
thf(u_type,type,
u: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(i_mono_2Etyop_2Emin_2Ebool_type,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum_type,type,
mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(tyop_2Epair_2Eprod_type,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: d > d > d ).
thf(s_type,type,
s: d > u > du ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: d ).
thf(c_2Epred__set_2EUNIV_2E0_type,type,
c_2Epred__set_2EUNIV_2E0: u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > u ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: d ).
thf('#sk2_type',type,
'#sk2': mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(mono_2Etyop_2Enum_2Enum_type,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_type,type,
mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf('#form224_type',type,
'#form224': d > d > u > u > $o ).
thf('#sk225_type',type,
'#sk225': d > d > u > u > u ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(c_2Epred__set_2EBIJ_2E3_type,type,
c_2Epred__set_2EBIJ_2E3: du > du > du > u ).
thf(mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum_type,type,
mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $o ).
thf(thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture,
? [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0f @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ? [V0f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0f @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ),
inference('cnf.neg',[status(esa)],[thm_2Eutil__prob_2ENUM__2D__BIJ__INV]) ).
thf(zip_derived_cl67,plain,
~ ( ??
@ ^ [Y0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ Y0 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl70,plain,
! [X2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
~ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X2 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ Y0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ Y0 ) ) ),
inference(cnf,[status(esa)],[ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29]) ).
thf(zip_derived_cl118,plain,
! [X2: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ X2 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl119,plain,
! [X2: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ X2 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl118]) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).
thf(zip_derived_cl45,plain,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Enum_2Enum]) ).
thf(thm_2Eutil__prob_2ENUM__2D__BIJ,axiom,
? [V0f: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ V0f @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ).
thf(zip_derived_cl66,plain,
( ??
@ ^ [Y0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ Y0 @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ),
inference(cnf,[status(esa)],[thm_2Eutil__prob_2ENUM__2D__BIJ]) ).
thf(zip_derived_cl71,plain,
mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ '#sk2' @ ( mono_2Ec_2Epred__set_2ECROSS_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum,
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ Y0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ Y0 ) ) ),
inference(cnf,[status(esa)],[ij_2Emono_2Etyop_2Emin_2Ebool]) ).
thf(zip_derived_cl74,plain,
! [X2: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X2 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl75,plain,
! [X2: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X2 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl74]) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > $o,V2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V2 ) ) ) ) ) ).
thf(zip_derived_cl40,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( !!
@ ^ [Y1: mono_2Etyop_2Enum_2Enum > $o] :
( !!
@ ^ [Y2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ Y0 @ Y1 @ Y2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ Y0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ Y1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29]) ).
thf(zip_derived_cl171,plain,
! [X2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( !!
@ ^ [Y0: mono_2Etyop_2Enum_2Enum > $o] :
( !!
@ ^ [Y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X2 @ Y0 @ Y1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ Y0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl172,plain,
! [X2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X4: mono_2Etyop_2Enum_2Enum > $o] :
( !!
@ ^ [Y0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X2 @ X4 @ Y0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl173,plain,
! [X2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X4: mono_2Etyop_2Enum_2Enum > $o,X6: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ X6 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl172]) ).
thf(zip_derived_cl174,plain,
! [X2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X4: mono_2Etyop_2Enum_2Enum > $o,X6: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ X6 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl173]) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
<=> V0 ) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ Y0 ) ) )
<=> Y0 ) ),
inference(cnf,[status(esa)],[ji_2Emono_2Etyop_2Emin_2Ebool]) ).
thf(zip_derived_cl72,plain,
! [X2: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) )
<=> X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl73,plain,
! [X2: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl72]) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V2: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V2 ) ) ) ) ) ).
thf(zip_derived_cl42,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] :
( !!
@ ^ [Y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( !!
@ ^ [Y2: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ Y0 @ Y1 @ Y2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ Y0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ Y1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum]) ).
thf(zip_derived_cl175,plain,
! [X2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] :
( !!
@ ^ [Y0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( !!
@ ^ [Y1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ X2 @ Y0 @ Y1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ Y0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl176,plain,
! [X2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,X4: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( !!
@ ^ [Y0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ X2 @ X4 @ Y0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl175]) ).
thf(zip_derived_cl177,plain,
! [X2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,X4: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,X6: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X6 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl176]) ).
thf(zip_derived_cl178,plain,
! [X2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,X4: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,X6: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ X4 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ X6 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl177]) ).
thf(thm_2Epred__set_2EBIJ__SYM,axiom,
! [A_27a: d,A_27b: d,V0s_2E0: u,V1t_2E0: u] :
( ? [V2f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) )
<=> ? [V3g_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V3g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ).
thf(zip_derived_cl65,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( ??
@ ^ [Y4: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) ) )
<=> ( ??
@ ^ [Y4: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y0 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Epred__set_2EBIJ__SYM]) ).
thf(zip_derived_cl293,plain,
! [X2: d] :
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( ??
@ ^ [Y3: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) ) )
<=> ( ??
@ ^ [Y3: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ X2 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl294,plain,
! [X2: d,X4: d] :
( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( ??
@ ^ [Y2: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) )
<=> ( ??
@ ^ [Y2: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl293]) ).
thf(zip_derived_cl295,plain,
! [X2: d,X4: d,X6: u] :
( !!
@ ^ [Y0: u] :
( ( ??
@ ^ [Y1: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) )
<=> ( ??
@ ^ [Y1: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl294]) ).
thf(zip_derived_cl296,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
<=> ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl295]) ).
thf(zip_derived_cl297,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
= ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl296]) ).
thf(zip_derived_cl298,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ~ ( '#form224' @ X2 @ X4 @ X6 @ X8 )
| ( ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
<=> ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl300,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ~ ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
| ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) )
| ~ ( '#form224' @ X2 @ X4 @ X6 @ X8 ) ),
inference(lazy_cnf_equiv,[status(thm)],[zip_derived_cl298]) ).
thf(zip_derived_cl302,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
| ~ ( '#form224' @ X2 @ X4 @ X6 @ X8 )
| ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl300]) ).
thf(zip_derived_cl304,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ ( '#sk225' @ X4 @ X2 @ X8 @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) )
| ~ ( '#form224' @ X2 @ X4 @ X6 @ X8 )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl302]) ).
thf(zip_derived_cl297_001,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
= ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl296]) ).
thf(zip_derived_cl298_002,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ~ ( '#form224' @ X2 @ X4 @ X6 @ X8 )
| ( ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) )
<=> ( ??
@ ^ [Y0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl301,plain,
! [X2: d,X4: d,X6: u,X8: u] : ( '#form224' @ X2 @ X4 @ X6 @ X8 ),
inference(renaming,[status(thm)],[zip_derived_cl297,zip_derived_cl298]) ).
thf(zip_derived_cl314,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ ( '#sk225' @ X4 @ X2 @ X8 @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl304,zip_derived_cl301]) ).
thf(zip_derived_cl6266,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl70,zip_derived_cl119,zip_derived_cl45,zip_derived_cl71,zip_derived_cl75,zip_derived_cl174,zip_derived_cl73,zip_derived_cl178,zip_derived_cl314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP020^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.04/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ZP5QfnuaPk true
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 15:29:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.46/0.61 % Total configuration time : 828
% 0.46/0.61 % Estimated wc time : 1656
% 0.46/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.51/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 115.81/15.22 % Solved by lams/30_b.l.sh.
% 115.81/15.22 % done 274 iterations in 14.436s
% 115.81/15.22 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 115.81/15.22 % SZS output start Refutation
% See solution above
% 115.81/15.23
% 115.81/15.23
% 115.81/15.23 % Terminating...
% 116.10/15.33 % Runner terminated.
% 116.10/15.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------