%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP021^1 : 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.sUDpNUC2GW true
% Computer : n020.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 04:38:30 PM UTC 2025
% Result : Theorem 97.61s 13.34s
% Output : Refutation 97.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 109 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 63 equ; 39 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1720 ( 46 ~; 44 |; 26 &;1516 @)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 25 usr; 16 con; 0-6 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 167 ( 23 ^; 144 !; 0 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
thf(mono_2Etyop_2Eextreal_2Eextreal_type,type,
mono_2Etyop_2Eextreal_2Eextreal: $tType ).
thf(du_type,type,
du: $tType ).
thf(d_type,type,
d: $tType ).
thf(u_type,type,
u: $tType ).
thf(c_2Ebool_2ECOND_2E3_type,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf('#sk4_type',type,
'#sk4': mono_2Etyop_2Eextreal_2Eextreal ).
thf(tyop_2Eextreal_2Eextreal_type,type,
tyop_2Eextreal_2Eextreal: d ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eextreal_2Eextreal > $o ) > u ).
thf(mono_2Ec_2Eextreal_2Eextreal__max_type,type,
mono_2Ec_2Eextreal_2Eextreal__max: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
thf('#sk2_type',type,
'#sk2': mono_2Etyop_2Eextreal_2Eextreal ).
thf(app_2E2_type,type,
app_2E2: du > du > u ).
thf(mono_2Ec_2Eextreal_2Eextreal__le_type,type,
mono_2Ec_2Eextreal_2Eextreal__le: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: d > d > d ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ) > u ).
thf(s_type,type,
s: d > u > du ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_type,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eextreal_2Eextreal > $o ).
thf(i_mono_2Etyop_2Eextreal_2Eextreal_type,type,
i_mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Eextreal_2Eextreal > u ).
thf(i_mono_2Etyop_2Emin_2Ebool_type,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: d ).
thf(mono_2Ec_2Ebool_2ET_type,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal_type,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
thf('#sk3_type',type,
'#sk3': mono_2Etyop_2Eextreal_2Eextreal ).
thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(mono_2Ec_2Ebool_2EF_type,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(thm_2Eextreal_2Emax__le,conjecture,
! [V0z: mono_2Etyop_2Eextreal_2Eextreal,V1x: mono_2Etyop_2Eextreal_2Eextreal,V2y: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ V1x @ V2y ) @ V0z )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V2y @ V0z )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ V1x @ V0z ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [V0z: mono_2Etyop_2Eextreal_2Eextreal,V1x: mono_2Etyop_2Eextreal_2Eextreal,V2y: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ V1x @ V2y ) @ V0z )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V2y @ V0z )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ V1x @ V0z ) ) ),
inference('cnf.neg',[status(esa)],[thm_2Eextreal_2Emax__le]) ).
thf(zip_derived_cl78,plain,
~ ( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y2: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ Y1 @ Y2 ) @ Y0 )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ Y2 @ Y0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl79,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ mono_2Ec_2Eextreal_2Eextreal__le ) @ mono_2Ec_2Eextreal_2Eextreal__max ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ) ) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl144,plain,
~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ mono_2Ec_2Eextreal_2Eextreal__le ) @ mono_2Ec_2Eextreal_2Eextreal__max ) ) @ '#sk2' ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le @ '#sk2' ) ) ) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl145,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#C' @ ( '#B' @ mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' ) ) @ '#sk2' ) ) @ ( '#C' @ ( '#B' @ (&) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le @ '#sk2' ) ) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl146,plain,
~ ( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl147,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
!= ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl211,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
| ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl2343,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl211]) ).
thf(thm_2Eextreal_2Ele__trans,axiom,
! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal,V2z: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V2z )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) )
=> ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V2z ) ) ).
thf(zip_derived_cl64,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y2: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ Y1 @ Y2 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ Y1 ) )
=> ( mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Eextreal_2Ele__trans]) ).
thf(zip_derived_cl65,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ) ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl151,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal] : ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) ) ) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl152,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 ) ) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) ) ) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl153,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) )
=> ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl154,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl155,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl2709,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ X0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2343,zip_derived_cl155]) ).
thf(zip_derived_cl155_001,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl147_002,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
!= ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl280,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
!= ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& $true ) )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ X0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl155,zip_derived_cl147]) ).
thf(zip_derived_cl297,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
!= ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' ) )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ X0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl280]) ).
thf(zip_derived_cl391,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2' )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ X0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl297]) ).
thf(thm_2Eextreal_2Ele__total,axiom,
! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V0x ) ) ).
thf(zip_derived_cl66,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ Y1 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[thm_2Eextreal_2Ele__total]) ).
thf(zip_derived_cl67,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl128,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal] : ( !! @ ( '#S' @ ( '#B' @ (|) @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) @ ( '#C' @ mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl129,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl130,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl242,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] : ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ X0 ),
inference(eq_fact,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl147_003,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' )
!= ( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl146]) ).
thf(thm_2Eextreal_2Eextreal__max__def,axiom,
! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ V0x @ V1y )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) @ V1y @ V0x ) ) ).
thf(zip_derived_cl68,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ Y0 @ Y1 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ Y1 ) @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[thm_2Eextreal_2Eextreal__max__def]) ).
thf(zip_derived_cl69,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ mono_2Ec_2Eextreal_2Eextreal__max ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ) @ mono_2Ec_2Eextreal_2Eextreal__le ) ) @ '#I' ) ) @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl148,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( mono_2Ec_2Eextreal_2Eextreal__max @ X2 ) ) @ ( '#C' @ ( '#S' @ ( '#B' @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 ) ) @ '#I' ) @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl149,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl150,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl155_004,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl130_005,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl267,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal,X2: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X1 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl155,zip_derived_cl130]) ).
thf(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
( ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
= ( s @ A_27a @ V0t1_2E0 ) )
& ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
= ( s @ A_27a @ V1t2_2E0 ) ) ) ).
thf(zip_derived_cl62,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) )
= ( s @ Y0 @ Y1 ) )
& ( ( s @ Y0 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ Y0 @ Y1 ) @ ( s @ Y0 @ Y2 ) ) )
= ( s @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Ebool_2ECOND__CLAUSES]) ).
thf(zip_derived_cl63,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) ) @ s ) ) ) @ s ) ) ) ) ) @ s ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) ) ) @ s ) ) ) @ s ) ) ) ) ) @ s ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl201,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X2 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) @ ( s @ X2 ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X2 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) ) @ ( s @ X2 ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl202,plain,
! [X2: d,X4: u] : ( !! @ ( '#S' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X2 ) @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X2 @ X4 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 @ X4 ) ) ) @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X2 ) @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X2 @ X4 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl201]) ).
thf(zip_derived_cl203,plain,
! [X2: d,X4: u,X6: u] :
( ( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X4 ) )
& ( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl202]) ).
thf(thm_2Ebool_2ETRUTH,axiom,
mono_2Ec_2Ebool_2ET ).
thf(zip_derived_cl47,plain,
mono_2Ec_2Ebool_2ET,
inference(cnf,[status(esa)],[thm_2Ebool_2ETRUTH]) ).
thf(thm_2Ebool_2EIMP__F,axiom,
! [V0t: $o] :
( ( V0t
=> mono_2Ec_2Ebool_2EF )
=> ~ V0t ) ).
thf(zip_derived_cl50,plain,
( !!
@ ^ [Y0: $o] :
( ( Y0
=> mono_2Ec_2Ebool_2EF )
=> ( (~) @ Y0 ) ) ),
inference(cnf,[status(esa)],[thm_2Ebool_2EIMP__F]) ).
thf(zip_derived_cl51,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ (=>) @ mono_2Ec_2Ebool_2EF ) ) @ (~) ),
inference(lams2combs,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl83,plain,
! [X2: $o] :
( ( X2
=> mono_2Ec_2Ebool_2EF )
=> ( (~) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl84,plain,
! [X2: $o] :
( ~ ( X2
=> mono_2Ec_2Ebool_2EF )
| ~ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl86,plain,
! [X2: $o] :
( ~ mono_2Ec_2Ebool_2EF
| ~ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl87,plain,
~ mono_2Ec_2Ebool_2EF,
inference(condensation,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl204,plain,
! [X2: d,X4: u,X6: u] :
( ( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X4 ) )
& ( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X6 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl203,zip_derived_cl47,zip_derived_cl87]) ).
thf(zip_derived_cl206,plain,
! [X2: d,X4: u,X6: u] :
( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl204]) ).
thf(zip_derived_cl208,plain,
! [X2: d,X4: u,X6: u] :
( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl206]) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0: $o,V1: mono_2Etyop_2Eextreal_2Eextreal,V2: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V2 ) ) ) ) ) ).
thf(zip_derived_cl35,plain,
( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( !!
@ ^ [Y2: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ Y0 @ Y1 @ Y2 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ Y0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ Y1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal]) ).
thf(zip_derived_cl36,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Ebool_2ECOND_2E3 @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl197,plain,
! [X2: $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) ) @ ( '#B' @ ( '#B' @ i_mono_2Etyop_2Eextreal_2Eextreal ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl198,plain,
! [X2: $o,X4: mono_2Etyop_2Eextreal_2Eextreal] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ ( '#B' @ i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ X4 ) ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ ( '#B' @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl199,plain,
! [X2: $o,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X6 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl198]) ).
thf(zip_derived_cl200,plain,
! [X2: $o,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X6 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl2129,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $false @ X1 @ X0 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl208,zip_derived_cl200]) ).
thf(zip_derived_cl2343_006,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl155_007,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl2710,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2' )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2343,zip_derived_cl155]) ).
thf(zip_derived_cl155_008,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl130_009,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl150_010,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 ) @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl341,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X0 @ X1 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X1 @ X0 ) )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl130,zip_derived_cl150]) ).
thf(zip_derived_cl2342,plain,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) @ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl155_011,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl2346,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2' )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2' )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ ( mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2342,zip_derived_cl155]) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
thf(zip_derived_cl30,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( Y0 @ Y1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ Y0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29]) ).
thf(zip_derived_cl31,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl179,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ X2 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl180,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( X2 @ X4 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl179]) ).
thf(zip_derived_cl181,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( X2 @ X4 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl180]) ).
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_cl12,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_cl13,plain,
!! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool ) ) ) @ '#I' ),
inference(lams2combs,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl98,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_cl13]) ).
thf(zip_derived_cl99,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_cl98]) ).
thf(zip_derived_cl205,plain,
! [X2: d,X4: u,X6: u] :
( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl204]) ).
thf(zip_derived_cl207,plain,
! [X2: d,X4: u,X6: u] :
( ( s @ X2 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X2 @ X4 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl200_012,plain,
! [X2: $o,X4: mono_2Etyop_2Eextreal_2Eextreal,X6: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ X4 @ X6 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X6 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl2128,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X0 @ X1 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl207,zip_derived_cl200]) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
thf(zip_derived_cl26,plain,
( !!
@ ^ [Y0: mono_2Etyop_2Eextreal_2Eextreal > $o] :
( !!
@ ^ [Y1: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( Y0 @ Y1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ Y0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool]) ).
thf(zip_derived_cl27,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ i_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl166,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > $o] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ i_mono_2Etyop_2Emin_2Ebool @ X2 ) ) ) @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) ) @ ( '#B' @ ( s @ tyop_2Eextreal_2Eextreal ) @ i_mono_2Etyop_2Eextreal_2Eextreal ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl167,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > $o,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( X2 @ X4 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl166]) ).
thf(zip_derived_cl168,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > $o,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( X2 @ X4 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl167]) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ Y0 ) ) ),
inference(cnf,[status(esa)],[ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29]) ).
thf(zip_derived_cl7,plain,
!! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( '#B' @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl102,plain,
! [X2: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl103,plain,
! [X2: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl168_013,plain,
! [X2: mono_2Etyop_2Eextreal_2Eextreal > $o,X4: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( X2 @ X4 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X2 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X4 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl99_014,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_cl98]) ).
thf(zip_derived_cl1149,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal > $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X0 ) ) ) ) )
= ( X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl168,zip_derived_cl99]) ).
thf(zip_derived_cl1149_015,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal > $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X0 ) ) ) ) )
= ( X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl168,zip_derived_cl99]) ).
thf(zip_derived_cl2109,plain,
! [X0: mono_2Etyop_2Eextreal_2Eextreal,X1: mono_2Etyop_2Eextreal_2Eextreal > $o] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ X1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X0 ) ) ) ) )
| ( X1 @ X0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl1149]) ).
thf(zip_derived_cl6045,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl2709,zip_derived_cl391,zip_derived_cl242,zip_derived_cl147,zip_derived_cl150,zip_derived_cl267,zip_derived_cl2129,zip_derived_cl2710,zip_derived_cl155,zip_derived_cl341,zip_derived_cl2346,zip_derived_cl181,zip_derived_cl99,zip_derived_cl2128,zip_derived_cl168,zip_derived_cl103,zip_derived_cl1149,zip_derived_cl2109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP021^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sUDpNUC2GW true
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 15:28:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.58/0.69 % Total configuration time : 828
% 0.58/0.69 % Estimated wc time : 1656
% 0.58/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.86 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.61/0.90 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 97.61/13.34 % Solved by lams/40_b.comb.sh.
% 97.61/13.34 % done 426 iterations in 12.393s
% 97.61/13.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 97.61/13.34 % SZS output start Refutation
% See solution above
% 97.61/13.35
% 97.61/13.35
% 97.61/13.35 % Terminating...
% 97.98/13.47 % Runner terminated.
% 97.98/13.49 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------