TSTP Solution File: ITP006^1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP006^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xQRr2N53g3 true
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:20:49 EDT 2023
% Result : Theorem 2.11s 0.97s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 53 ( 6 unt; 20 typ; 0 def)
% Number of atoms : 323 ( 14 equ; 27 cnn)
% Maximal formula atoms : 42 ( 9 avg)
% Number of connectives : 2665 ( 46 ~; 7 |; 30 &;2360 @)
% ( 39 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 17 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 10 con; 0-4 aty)
% ( 112 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 132 ^; 80 !; 4 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(du_type,type,
du: $tType ).
thf(d_type,type,
d: $tType ).
thf(u_type,type,
u: $tType ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: d > d > d ).
thf('#sk1_type',type,
'#sk1': d ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_type,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u ).
thf('#sk4_type',type,
'#sk4': u ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2_type,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u ).
thf(app_2E2_type,type,
app_2E2: du > du > u ).
thf('#sk2_type',type,
'#sk2': d ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2_type,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u ).
thf('#sk5_type',type,
'#sk5': u ).
thf(c_2EquantHeuristics_2EGUESS__FORALL_2E2_type,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u ).
thf(s_type,type,
s: d > u > du ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: d ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS_2E2_type,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u ).
thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2_type,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u ).
thf('#sk8_type',type,
'#sk8': d > d > u > u > u ).
thf('#sk3_type',type,
'#sk3': u ).
thf(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
( ! [V3x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
( ! [V3x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) @ ( s @ Y0 @ Y5 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y0 @ Y5 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y0 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y0 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ '#sk1' @ Y4 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ '#sk1' @ Y4 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ '#sk1' ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ '#sk1' ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
~ ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ '#sk1' @ Y3 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ '#sk1' @ Y3 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
~ ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ '#sk1' @ Y2 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ '#sk1' @ Y2 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: u] :
( ( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ '#sk1' @ Y1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ Y1 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
~ ( ( !!
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) @ ( s @ '#sk1' @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ Y0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl16,plain,
~ ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl18,plain,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) )
<=> ! [V2v_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) )
=> ? [V3fv_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0i_2E0 ) @ ( s @ A_27a @ V3fv_2E0 ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) )
<=> ! [V4v_2E0: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) )
=> ? [V5fv_2E0: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0i_2E0 ) @ ( s @ A_27a @ V5fv_2E0 ) ) ) ) ) ) ) )
& ! [V6i_2E0: u,V7P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V7P_2E0 ) ) ) )
<=> ! [V8fv_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V7P_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6i_2E0 ) @ ( s @ A_27a @ V8fv_2E0 ) ) ) ) ) ) )
& ! [V9i_2E0: u,V10P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V9i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V10P_2E0 ) ) ) )
<=> ! [V11fv_2E0: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V10P_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V9i_2E0 ) @ ( s @ A_27a @ V11fv_2E0 ) ) ) ) ) ) )
& ! [V12i_2E0: u,V13P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V13P_2E0 ) ) ) )
<=> ! [V14v_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V13P_2E0 ) @ ( s @ A_27b @ V14v_2E0 ) ) ) )
=> ? [V15fv_2E0: u] :
( ( s @ A_27b @ V14v_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12i_2E0 ) @ ( s @ A_27a @ V15fv_2E0 ) ) ) ) ) )
& ! [V16i_2E0: u,V17P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V16i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V17P_2E0 ) ) ) )
<=> ! [V18v_2E0: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V17P_2E0 ) @ ( s @ A_27b @ V18v_2E0 ) ) ) )
=> ? [V19fv_2E0: u] :
( ( s @ A_27b @ V18v_2E0 )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V16i_2E0 ) @ ( s @ A_27a @ V19fv_2E0 ) ) ) ) ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ Y4 ) ) ) )
=> ( ??
@ ^ [Y5: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y2 ) @ ( s @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ Y4 ) ) ) ) )
=> ( ??
@ ^ [Y5: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y2 ) @ ( s @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) ) ) )
<=> ( !!
@ ^ [Y6: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) @ ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ Y0 @ Y6 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) ) ) )
<=> ( !!
@ ^ [Y6: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) @ ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) ) ) )
<=> ( !!
@ ^ [Y6: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) @ ( s @ Y1 @ Y6 ) ) ) )
=> ( ??
@ ^ [Y7: u] :
( ( s @ Y1 @ Y6 )
= ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ Y0 @ Y7 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) ) ) )
<=> ( !!
@ ^ [Y6: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y5 ) @ ( s @ Y1 @ Y6 ) ) ) ) )
=> ( ??
@ ^ [Y7: u] :
( ( s @ Y1 @ Y6 )
= ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ Y0 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2EquantHeuristics_2EGUESS__REWRITES]) ).
thf(zip_derived_cl39,plain,
! [X2: d] :
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ Y3 ) ) ) )
=> ( ??
@ ^ [Y4: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y1 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ Y3 ) ) ) ) )
=> ( ??
@ ^ [Y4: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y1 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) ) ) )
<=> ( !!
@ ^ [Y5: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) @ ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ X2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) ) ) )
<=> ( !!
@ ^ [Y5: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) @ ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ X2 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) ) ) )
<=> ( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) @ ( s @ Y0 @ Y5 ) ) ) )
=> ( ??
@ ^ [Y6: u] :
( ( s @ Y0 @ Y5 )
= ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ X2 @ Y6 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) ) ) )
<=> ( !!
@ ^ [Y5: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y4 ) @ ( s @ Y0 @ Y5 ) ) ) ) )
=> ( ??
@ ^ [Y6: u] :
( ( s @ Y0 @ Y5 )
= ( s @ Y0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ Y0 ) @ Y3 ) @ ( s @ X2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl40,plain,
! [X2: d,X4: d] :
( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ Y2 ) ) ) )
=> ( ??
@ ^ [Y3: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ Y2 ) ) ) ) )
=> ( ??
@ ^ [Y3: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ X4 @ Y4 ) ) ) )
=> ( ??
@ ^ [Y5: u] :
( ( s @ X4 @ Y4 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ X2 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
<=> ( !!
@ ^ [Y4: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ X4 @ Y4 ) ) ) ) )
=> ( ??
@ ^ [Y5: u] :
( ( s @ X4 @ Y4 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y2 ) @ ( s @ X2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: d,X4: d,X6: u] :
( !!
@ ^ [Y0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
<=> ( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X4 @ Y1 ) ) ) )
=> ( ??
@ ^ [Y2: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
<=> ( !!
@ ^ [Y1: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X4 @ Y1 ) ) ) ) )
=> ( ??
@ ^ [Y2: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ X4 @ Y3 ) ) ) )
=> ( ??
@ ^ [Y4: u] :
( ( s @ X4 @ Y3 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: u] :
( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
<=> ( !!
@ ^ [Y3: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ X4 @ Y3 ) ) ) ) )
=> ( ??
@ ^ [Y4: u] :
( ( s @ X4 @ Y3 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y1 ) @ ( s @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
<=> ( !!
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ Y0 ) ) ) )
=> ( ??
@ ^ [Y1: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
<=> ( !!
@ ^ [Y0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ Y0 ) ) ) ) )
=> ( ??
@ ^ [Y1: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ Y2 ) ) ) )
=> ( ??
@ ^ [Y3: u] :
( ( s @ X4 @ Y2 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ Y2 ) ) ) ) )
=> ( ??
@ ^ [Y3: u] :
( ( s @ X4 @ Y2 )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl46,plain,
! [X2: d,X4: d] :
( !!
@ ^ [Y0: u] :
( !!
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
<=> ( !!
@ ^ [Y2: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ Y0 ) @ ( s @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl52,plain,
! [X2: d,X4: d,X6: u] :
( !!
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
<=> ( !!
@ ^ [Y1: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl56,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
<=> ( !!
@ ^ [Y0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl60,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
= ( !!
@ ^ [Y0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl91,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
| ~ ( !!
@ ^ [Y0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl95,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) @ ( s @ '#sk1' @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl17,plain,
! [X2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) @ ( s @ '#sk1' @ X2 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
! [X2: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) @ ( s @ '#sk1' @ X2 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl97,plain,
! [X0: u,X1: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ '#sk1' ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) @ ( s @ '#sk1' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ '#sk1' ) @ X0 ) @ ( s @ X1 @ ( '#sk8' @ X1 @ '#sk1' @ X0 @ '#sk5' ) ) ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl95,zip_derived_cl20]) ).
thf(zip_derived_cl60_001,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
= ( !!
@ ^ [Y0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl92,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) )
| ( !!
@ ^ [Y0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl112,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ X2 @ X10 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) @ X8 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl143,plain,
! [X0: u,X1: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ '#sk1' ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ '#sk1' ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk4' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl97,zip_derived_cl112]) ).
thf(zip_derived_cl147,plain,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk1' ) @ '#sk3' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk1' @ tyop_2Emin_2Ebool ) @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl143]) ).
thf(zip_derived_cl149,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl19,zip_derived_cl147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP006^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xQRr2N53g3 true
% 0.17/0.35 % Computer : n026.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 15:03:49 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.17/0.36 % Running portfolio for 300 s
% 0.17/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.36 % Number of cores: 8
% 0.17/0.36 % Python version: Python 3.6.8
% 0.17/0.36 % Running in HO mode
% 0.21/0.66 % Total configuration time : 828
% 0.21/0.66 % Estimated wc time : 1656
% 0.21/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.57/0.86 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 2.11/0.97 % Solved by lams/30_sp5.sh.
% 2.11/0.97 % done 40 iterations in 0.119s
% 2.11/0.97 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.11/0.97 % SZS output start Refutation
% See solution above
% 2.11/0.97
% 2.11/0.97
% 2.11/0.97 % Terminating...
% 2.46/1.08 % Runner terminated.
% 2.46/1.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------