%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP006^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 : Wed Feb 25 08:53:08 AM UTC 2026
% Result : Theorem 2.43s 1.84s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 790 ( 265 equ; 0 cnn)
% Maximal formula atoms : 32 ( 13 avg)
% Number of connectives : 4689 ( 186 ~; 103 |; 100 &;4239 @)
% ( 26 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 28 con; 0-4 aty)
% Number of variables : 361 ( 0 ^; 285 !; 76 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_4,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_5,type,
s: d > u > du ).
thf(func_def_6,type,
app_2E2: du > du > u ).
thf(func_def_7,type,
combin_i_2E0: u ).
thf(func_def_8,type,
combin_k_2E0: u ).
thf(func_def_9,type,
combin_s_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_11,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_14,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_16,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_18,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_20,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_21,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
thf(func_def_22,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u ).
thf(func_def_23,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
thf(func_def_24,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u ).
thf(func_def_25,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
thf(func_def_26,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u ).
thf(func_def_27,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
thf(func_def_28,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u ).
thf(func_def_29,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
thf(func_def_30,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u ).
thf(func_def_31,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
thf(func_def_32,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u ).
thf(func_def_33,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_34,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_35,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_36,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_37,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_38,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_39,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_40,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_41,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_44,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_46,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_47,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_48,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_49,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_50,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_51,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_58,type,
sK0: u ).
thf(func_def_59,type,
sK1: d ).
thf(func_def_60,type,
sK2: d ).
thf(func_def_61,type,
sK3: u ).
thf(func_def_62,type,
sK4: u ).
thf(func_def_63,type,
sK5: u > u > d > d > u ).
thf(func_def_64,type,
sK6: u > u > d > d > u ).
thf(func_def_65,type,
sK7: u > u > d > d > u ).
thf(func_def_66,type,
sK8: u > u > d > d > u ).
thf(func_def_67,type,
sK9: u > u > d > d > u ).
thf(func_def_68,type,
sK10: u > u > d > d > u ).
thf(func_def_69,type,
sK11: u > u > d > d > u ).
thf(func_def_70,type,
sK12: u > u > d > d > u ).
thf(func_def_71,type,
sK13: u > u > d > d > u ).
thf(func_def_72,type,
sK14: u > u > d > d > u ).
thf(func_def_73,type,
sK15: u > d > d > u > u ).
thf(f323,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f294,f315,f322]) ).
thf(f322,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[status(thm)],[f321]) ).
thf(f321,plain,
( $false
| ~ spl16_4 ),
inference(trivial_inequality_removal,[status(thm)],[f320]) ).
thf(f320,plain,
( ( $true = $false )
| ~ spl16_4 ),
inference(forward_demodulation,[status(thm)],[f318,f259]) ).
thf(f259,plain,
! [X0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ X0 ) ) ) ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f258]) ).
thf(f258,plain,
! [X0: u] :
( ( $true != $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ X0 ) ) ) ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f230,f155]) ).
thf(f155,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 ) @ sK0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true
!= ( 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 ) @ sK0 ) ) ) )
= $true )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X5 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f124,f125]) ).
thf(f125,plain,
( ? [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
& ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X1 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X1 @ X5 ) ) ) ) ) ) )
=> ( ( $true
!= ( 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 ) @ sK0 ) ) ) )
= $true )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f124,plain,
? [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
& ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X1 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X1 @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f119]) ).
thf(f119,plain,
? [X0: u,X2: d,X1: d,X4: u,X3: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) )
!= $true )
& ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X2 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ X2 @ X5 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f118]) ).
thf(f118,plain,
? [X2: d,X4: u,X1: d,X3: u,X0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) )
!= $true )
& ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
& ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X2 @ X5 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ X2 @ X5 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f91]) ).
thf(f91,plain,
~ ! [X2: d,X4: u,X1: d,X3: u,X0: u] :
( ! [X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ X2 @ X5 ) ) ) ) )
=> ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X2 @ X5 ) ) ) ) ) )
=> ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f90]) ).
thf(f90,plain,
~ ! [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ! [X5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ X2 @ X5 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X2 @ X5 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f52]) ).
thf(f52,negated_conjecture,
~ ! [X24: u,X1: d,X0: d,X51: u,X23: u] :
( ! [X52: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X51 ) @ ( s @ X0 @ X52 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X0 @ X52 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X51 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
thf(f51,conjecture,
! [X24: u,X1: d,X0: d,X51: u,X23: u] :
( ! [X52: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X51 ) @ ( s @ X0 @ X52 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X0 @ X52 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X51 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xApQoegLFN/DTF2THF_6174.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
thf(f230,plain,
! [X0: d,X1: d,X7: u,X4: u,X5: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X7 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X0: d,X1: d,X7: u,X4: u,X5: u] :
( ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X7 ) ) ) ) ) ) )
= $true )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ ( sK5 @ X5 @ X4 @ X1 @ X0 ) ) ) ) ) ) ) ) ) )
& ( ! [X7: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X7 ) ) ) ) ) ) )
= $true )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ) )
& ! [X8: u,X9: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) ) ) ) )
| ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ ( sK6 @ X9 @ X8 @ X1 @ X0 ) ) ) ) ) )
& ! [X11: u] :
( ( s @ X0 @ ( sK6 @ X9 @ X8 @ X1 @ X0 ) )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X11 ) ) ) ) ) )
& ( ! [X12: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ X12 ) ) ) ) )
| ( ( s @ X0 @ X12 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ ( sK7 @ X12 @ X8 @ X1 @ X0 ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) ) ) ) ) ) )
& ! [X14: u,X15: u] :
( ( ! [X16: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ X16 ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ ( sK8 @ X15 @ X14 @ X1 @ X0 ) ) ) ) ) ) )
!= $true ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
= $true )
& ! [X19: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X19 ) ) ) ) ) )
!= $true ) ) )
& ( ! [X20: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X20 ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ ( sK10 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) )
& ( ! [X22: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X22 ) ) ) ) ) )
| ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ ( sK11 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ( ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( sK12 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) )
= $true )
& ! [X25: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X25 ) ) ) ) ) ) ) ) ) )
& ! [X26: u,X27: u] :
( ( ! [X28: u] :
( ( ( s @ X0 @ X28 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ ( sK13 @ X28 @ X26 @ X1 @ X0 ) ) ) ) )
| ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ X28 ) ) ) ) )
!= $true ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) ) ) ) )
| ( ! [X31: u] :
( ( s @ X0 @ ( sK14 @ X27 @ X26 @ X1 @ X0 ) )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X31 ) ) ) )
& ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ ( sK14 @ X27 @ X26 @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f129,f139,f138,f137,f136,f135,f134,f133,f132,f131,f130]) ).
thf(f130,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ? [X6: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X6 ) ) ) ) ) ) ) )
=> ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ ( sK5 @ X5 @ X4 @ X1 @ X0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f131,plain,
! [X0: d,X1: d,X8: u,X9: u] :
( ? [X10: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ X10 ) ) ) ) )
& ! [X11: u] :
( ( s @ X0 @ X10 )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X11 ) ) ) ) )
=> ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ ( sK6 @ X9 @ X8 @ X1 @ X0 ) ) ) ) ) )
& ! [X11: u] :
( ( s @ X0 @ ( sK6 @ X9 @ X8 @ X1 @ X0 ) )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X11 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f132,plain,
! [X0: d,X1: d,X8: u,X12: u] :
( ? [X13: u] :
( ( s @ X0 @ X12 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X13 ) ) ) )
=> ( ( s @ X0 @ X12 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ ( sK7 @ X12 @ X8 @ X1 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f133,plain,
! [X0: d,X1: d,X14: u,X15: u] :
( ? [X17: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ X17 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ ( sK8 @ X15 @ X14 @ X1 @ X0 ) ) ) ) ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f134,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X18: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X18 ) ) ) ) )
& ! [X19: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X19 ) ) ) ) ) )
!= $true ) )
=> ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( sK9 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
= $true )
& ! [X19: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X19 ) ) ) ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f135,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X21: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X21 ) ) ) ) ) )
= $true )
=> ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ ( sK10 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f136,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X23: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X23 ) ) ) ) ) ) )
= $true )
=> ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ ( sK11 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f137,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X24: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X24 ) ) ) ) ) )
& ! [X25: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X25 ) ) ) ) ) ) ) ) )
=> ( ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( sK12 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) )
= $true )
& ! [X25: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X25 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f138,plain,
! [X0: d,X1: d,X26: u,X28: u] :
( ? [X29: u] :
( ( s @ X0 @ X28 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X29 ) ) ) )
=> ( ( s @ X0 @ X28 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ ( sK13 @ X28 @ X26 @ X1 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f139,plain,
! [X0: d,X1: d,X26: u,X27: u] :
( ? [X30: u] :
( ! [X31: u] :
( ( s @ X0 @ X30 )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X31 ) ) ) )
& ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ X30 ) ) ) ) )
= $true ) )
=> ( ! [X31: u] :
( ( s @ X0 @ ( sK14 @ X27 @ X26 @ X1 @ X0 ) )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X31 ) ) ) )
& ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ ( sK14 @ X27 @ X26 @ X1 @ X0 ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f129,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
| ? [X6: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X6 ) ) ) ) ) ) ) ) )
& ( ! [X7: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ X7 ) ) ) ) ) ) )
= $true )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ) )
& ! [X8: u,X9: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) ) ) ) )
| ? [X10: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ X10 ) ) ) ) )
& ! [X11: u] :
( ( s @ X0 @ X10 )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X11 ) ) ) ) ) )
& ( ! [X12: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) @ ( s @ X0 @ X12 ) ) ) ) )
| ? [X13: u] :
( ( s @ X0 @ X12 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ X1 @ X13 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X9 ) ) ) ) ) ) )
& ! [X14: u,X15: u] :
( ( ! [X16: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ X16 ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) )
| ? [X17: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X14 ) @ ( s @ X1 @ X17 ) ) ) ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ? [X18: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X18 ) ) ) ) )
& ! [X19: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X19 ) ) ) ) ) )
!= $true ) ) )
& ( ! [X20: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X20 ) ) ) ) )
| ? [X21: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X21 ) ) ) ) ) )
= $true ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) )
& ( ! [X22: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X22 ) ) ) ) ) )
| ? [X23: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X23 ) ) ) ) ) ) )
= $true ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ? [X24: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X24 ) ) ) ) ) )
& ! [X25: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X25 ) ) ) ) ) ) ) ) ) )
& ! [X26: u,X27: u] :
( ( ! [X28: u] :
( ? [X29: u] :
( ( s @ X0 @ X28 )
= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X29 ) ) ) )
| ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ X28 ) ) ) ) )
!= $true ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) ) ) ) )
| ? [X30: u] :
( ! [X31: u] :
( ( s @ X0 @ X30 )
!= ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X26 ) @ ( s @ X1 @ X31 ) ) ) )
& ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X27 ) @ ( s @ X0 @ X30 ) ) ) ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f128]) ).
thf(f128,plain,
! [X3: d,X0: d,X1: u,X2: u] :
( ! [X19: u,X20: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) )
| ? [X21: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) ) )
& ( ! [X21: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) ) ) )
& ! [X15: u,X16: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
= $true )
| ? [X17: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
& ! [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
!= ( s @ X3 @ X17 ) ) ) )
& ( ! [X17: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
| ? [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
= ( s @ X3 @ X17 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
!= $true ) ) )
& ! [X13: u,X12: u] :
( ( ! [X14: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
!= $true ) )
& ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
= $true )
| ? [X14: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ? [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
= $true )
& ! [X11: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) ) )
& ( ! [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
!= $true )
| ? [X11: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ( ! [X4: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
| ? [X5: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ? [X4: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
& ! [X5: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) ) )
& ! [X7: u,X6: u] :
( ( ! [X8: u] :
( ? [X9: u] :
( ( s @ X3 @ X8 )
= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) )
| ? [X8: u] :
( ! [X9: u] :
( ( s @ X3 @ X8 )
!= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) )
& ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f127]) ).
thf(f127,plain,
! [X3: d,X0: d,X1: u,X2: u] :
( ! [X19: u,X20: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) )
| ? [X21: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) ) )
& ( ! [X21: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) ) ) )
& ! [X15: u,X16: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
= $true )
| ? [X17: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
& ! [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
!= ( s @ X3 @ X17 ) ) ) )
& ( ! [X17: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
| ? [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
= ( s @ X3 @ X17 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
!= $true ) ) )
& ! [X13: u,X12: u] :
( ( ! [X14: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
!= $true ) )
& ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
= $true )
| ? [X14: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ? [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
= $true )
& ! [X11: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) ) )
& ( ! [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
!= $true )
| ? [X11: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ( ! [X4: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
| ? [X5: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ? [X4: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
& ! [X5: u] :
( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) ) )
& ! [X7: u,X6: u] :
( ( ! [X8: u] :
( ? [X9: u] :
( ( s @ X3 @ X8 )
= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) )
| ? [X8: u] :
( ! [X9: u] :
( ( s @ X3 @ X8 )
!= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) )
& ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f114]) ).
thf(f114,plain,
! [X3: d,X0: d,X1: u,X2: u] :
( ! [X19: u,X20: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) )
<=> ! [X21: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) ) )
& ! [X15: u,X16: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
= $true )
<=> ! [X17: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
| ? [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
= ( s @ X3 @ X17 ) ) ) )
& ! [X13: u,X12: u] :
( ! [X14: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
= $true ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
<=> ! [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
!= $true )
| ? [X11: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) ) )
& ( ! [X4: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
| ? [X5: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) )
<=> ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ! [X7: u,X6: u] :
( ! [X8: u] :
( ? [X9: u] :
( ( s @ X3 @ X8 )
= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) ) )
<=> ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: u,X2: u,X3: d,X0: d] :
( ( ! [X10: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
= $true )
=> ? [X11: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) ) )
<=> ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
& ! [X19: u,X20: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) ) )
<=> ! [X21: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) ) )
& ! [X16: u,X15: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
= $true )
<=> ! [X17: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) ) )
=> ? [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
= ( s @ X3 @ X17 ) ) ) )
& ! [X13: u,X12: u] :
( ! [X14: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) )
= $true ) )
& ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
<=> ! [X4: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) ) ) )
=> ? [X5: u] :
( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) ) ) ) )
& ! [X7: u,X6: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) ) )
<=> ! [X8: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) ) ) )
=> ? [X9: u] :
( ( s @ X3 @ X8 )
= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f84]) ).
thf(f84,plain,
! [X0: d,X1: u,X2: u,X3: d] :
( ( ! [X4: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X4 ) ) ) )
=> ? [X5: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X5 ) ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
& ! [X6: u,X7: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) ) ) )
<=> ! [X8: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X6 ) @ ( s @ X3 @ X8 ) ) ) )
=> ? [X9: u] :
( ( s @ X3 @ X8 )
= ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X7 ) @ ( s @ X0 @ X9 ) ) ) ) ) )
& ( ! [X10: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ X10 ) ) ) )
=> ? [X11: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ X0 @ X11 ) ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
& ! [X12: u,X13: u] :
( ! [X14: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ X0 @ X14 ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X13 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X12 ) ) ) ) )
& ! [X15: u,X16: u] :
( ! [X17: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ X3 @ X17 ) ) ) )
=> ? [X18: u] :
( ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ X0 @ X18 ) ) )
= ( s @ X3 @ X17 ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) ) )
& ! [X19: u,X20: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) ) ) )
<=> ! [X21: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X19 ) @ ( s @ X3 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X3 ) @ X20 ) @ ( s @ X0 @ X21 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,axiom,
! [X0: d,X24: u,X23: u,X1: d] :
( ( ! [X27: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X1 @ X27 ) ) ) )
=> ? [X28: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X23 ) @ ( s @ X0 @ X28 ) ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) ) )
& ! [X40: u,X39: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X39 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X40 ) ) ) )
<=> ! [X41: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X40 ) @ ( s @ X1 @ X41 ) ) ) )
=> ? [X42: u] :
( ( s @ X1 @ X41 )
= ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X39 ) @ ( s @ X0 @ X42 ) ) ) ) ) )
& ( ! [X25: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X1 @ X25 ) ) ) )
=> ? [X26: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) @ ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X23 ) @ ( s @ X0 @ X26 ) ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X23 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X24 ) ) ) ) )
& ! [X30: u,X29: u] :
( ! [X31: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X30 ) @ ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X29 ) @ ( s @ X0 @ X31 ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X29 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X30 ) ) ) ) )
& ! [X35: u,X36: u] :
( ! [X37: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X36 ) @ ( s @ X1 @ X37 ) ) ) )
=> ? [X38: u] :
( ( s @ X1 @ X37 )
= ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X35 ) @ ( s @ X0 @ X38 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X35 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X36 ) ) ) ) )
& ! [X33: u,X32: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X32 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X33 ) ) ) )
<=> ! [X34: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X33 ) @ ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X32 ) @ ( s @ X0 @ X34 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xApQoegLFN/DTF2THF_6174.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
thf(f318,plain,
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) ) )
| ~ spl16_4 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) ) )
| ( $true != $true )
| ~ spl16_4 ),
inference(superposition,[status(thm)],[f154,f293]) ).
thf(f293,plain,
( ( ( 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 @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) )
= $true )
| ~ spl16_4 ),
inference(avatar_component_clause,[status(thm)],[f291]) ).
thf(f291,definition,
( spl16_4
<=> ( ( 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 @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl16_4])],[avatar_definition]) ).
thf(f154,plain,
! [X5: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X5 ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK0 ) @ ( s @ sK1 @ X5 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
thf(f315,plain,
~ spl16_3,
inference(avatar_contradiction_clause,[status(thm)],[f314]) ).
thf(f314,plain,
( $false
| ~ spl16_3 ),
inference(trivial_inequality_removal,[status(thm)],[f311]) ).
thf(f311,plain,
( ( $true != $true )
| ~ spl16_3 ),
inference(superposition,[status(thm)],[f156,f301]) ).
thf(f301,plain,
( ! [X0: d,X1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ sK1 ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) ) ) )
= $true )
| ~ spl16_3 ),
inference(trivial_inequality_removal,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X0: d,X1: u] :
( ( $true != $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ sK1 ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) ) ) )
= $true ) )
| ~ spl16_3 ),
inference(superposition,[status(thm)],[f289,f234]) ).
thf(f234,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ ( sK5 @ X5 @ X4 @ X1 @ X0 ) ) ) ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ X1 @ ( sK5 @ X5 @ X4 @ X1 @ X0 ) ) ) ) ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X5 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
thf(f289,plain,
( ! [X0: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X0 ) ) ) ) )
| ~ spl16_3 ),
inference(avatar_component_clause,[status(thm)],[f288]) ).
thf(f288,definition,
( spl16_3
<=> ! [X0: u] :
( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl16_3])],[avatar_definition]) ).
thf(f156,plain,
( $true
!= ( 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(cnf_transformation,[status(thm)],[f126]) ).
thf(f294,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[status(thm)],[f286,f291,f288]) ).
thf(f286,plain,
! [X0: u] :
( ( ( 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 @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) )
= $true )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f285]) ).
thf(f285,plain,
! [X0: u] :
( ( ( 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 @ sK2 @ sK1 ) @ sK3 ) @ ( s @ sK2 @ ( sK10 @ sK3 @ sK4 @ sK2 @ sK1 ) ) ) ) ) ) )
= $true )
| ( $true != $true )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) @ ( s @ sK1 @ X0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f163,f284]) ).
thf(f284,plain,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f281]) ).
thf(f281,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ sK1 ) @ sK3 ) @ ( s @ ( tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool ) @ sK4 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f156,f278]) ).
thf(f278,plain,
! [X2: d,X3: u,X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f273]) ).
thf(f273,plain,
! [X2: d,X3: u,X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( $true != $true )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f164,f234]) ).
thf(f164,plain,
! [X2: u,X3: u,X0: d,X1: d,X19: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ X19 ) ) ) ) ) )
!= $true )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
thf(f163,plain,
! [X2: u,X3: u,X0: d,X1: d,X20: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ X20 ) ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ X0 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X0 ) @ X3 ) @ ( s @ X1 @ ( sK10 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP006^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.31 % Computer : n002.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue Feb 24 08:18:03 EST 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.42 ---- Original DTF file ---
% 0.18/0.42 thf(spec,logic,$$dhol).
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 % File : ITP006^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.18/0.42 % Domain : Interactive Theorem Proving
% 0.18/0.42 % Problem : HOL4 syntactic export of thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p, bushy mode
% 0.18/0.42 % Version : [BG+19] axioms.
% 0.18/0.42 % English :
% 0.18/0.42
% 0.18/0.42 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.18/0.42 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.18/0.42 % Source : [BG+19]
% 0.18/0.42 % Names : thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p [Gau19]
% 0.18/0.42 % : HL402501^1.p [TPAP]
% 0.18/0.42
% 0.18/0.42 % Status : Theorem
% 0.18/0.42 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0
% 0.18/0.42 % Syntax : Number of formulae : 103 ( 27 unt; 52 typ; 0 def)
% 0.18/0.42 % Number of atoms : 153 ( 37 equ; 39 cnn)
% 0.18/0.42 % Maximal formula atoms : 20 ( 3 avg)
% 0.18/0.42 % Number of connectives : 1157 ( 39 ~; 22 |; 25 &; 992 @)
% 0.18/0.42 % ( 40 <=>; 39 =>; 0 <=; 0 <~>)
% 0.18/0.42 % Maximal formula depth : 24 ( 6 avg)
% 0.18/0.42 % Number of types : 4 ( 3 usr)
% 0.18/0.42 % Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% 0.18/0.42 % Number of symbols : 51 ( 49 usr; 22 con; 0-3 aty)
% 0.18/0.42 % Number of variables : 145 ( 0 ^; 140 !; 5 ?; 145 :)
% 0.18/0.42 % SPC : TH0_THM_EQU_NAR
% 0.18/0.42
% 0.18/0.42 % Comments :
% 0.18/0.42 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 thf(u,type,
% 0.18/0.42 u: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(d,type,
% 0.18/0.42 d: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(du,type,
% 0.18/0.42 du: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(tyop_2Emin_2Ebool,type,
% 0.18/0.42 tyop_2Emin_2Ebool: d ).
% 0.18/0.42
% 0.18/0.42 thf(tyop_2Emin_2Efun,type,
% 0.18/0.42 tyop_2Emin_2Efun: d > d > d ).
% 0.18/0.42
% 0.18/0.42 thf(s,type,
% 0.18/0.42 s: d > u > du ).
% 0.18/0.42
% 0.18/0.42 thf(app_2E2,type,
% 0.18/0.42 app_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(combin_i_2E0,type,
% 0.18/0.42 combin_i_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(combin_k_2E0,type,
% 0.18/0.42 combin_k_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(combin_s_2E0,type,
% 0.18/0.42 combin_s_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_21_2E0,type,
% 0.18/0.42 c_2Ebool_2E_21_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_21_2E1,type,
% 0.18/0.42 c_2Ebool_2E_21_2E1: du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.18/0.42 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.18/0.42 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Emin_2E_3D_2E0,type,
% 0.18/0.42 c_2Emin_2E_3D_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Emin_2E_3D_2E2,type,
% 0.18/0.42 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.18/0.42 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.18/0.42 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_3F_2E0,type,
% 0.18/0.42 c_2Ebool_2E_3F_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_3F_2E1,type,
% 0.18/0.42 c_2Ebool_2E_3F_2E1: du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2EF_2E0,type,
% 0.18/0.42 c_2Ebool_2EF_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,type,
% 0.18/0.42 c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2ET_2E0,type,
% 0.18/0.42 c_2Ebool_2ET_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.18/0.42 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.18/0.42 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_7E_2E0,type,
% 0.18/0.42 c_2Ebool_2E_7E_2E0: u ).
% 0.18/0.42
% 0.18/0.42 thf(c_2Ebool_2E_7E_2E1,type,
% 0.18/0.42 c_2Ebool_2E_7E_2E1: du > u ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.18/0.42 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.18/0.42 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.18/0.42 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.18/0.42 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Ebool_2EF,type,
% 0.18/0.42 mono_2Ec_2Ebool_2EF: $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Ebool_2ET,type,
% 0.18/0.42 mono_2Ec_2Ebool_2ET: $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.18/0.42 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.18/0.42 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.18/0.42 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.18/0.42
% 0.18/0.42 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.18/0.42 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.18/0.42
% 0.18/0.42 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.18/0.42 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.18/0.42
% 0.18/0.42 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.18/0.42 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.18/0.42
% 0.18/0.42 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.18/0.42 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.18/0.42 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.18/0.42 ( ! [V2x_2E0: u] :
% 0.18/0.42 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.18/0.42 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.18/0.42 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.18/0.42 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.18/0.42 ! [A_27a: d,V0x_2E0: u] :
% 0.18/0.42 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.18/0.42 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.18/0.42 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.18/0.42 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Eho_2Es__thm,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.18/0.42 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.18/0.42 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.18/0.42 ! [V0: $o,V1: $o] :
% 0.18/0.42 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.18/0.42 <=> ( V0
% 0.18/0.42 & V1 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.18/0.42 ! [V0: $o,V1: $o] :
% 0.18/0.42 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.18/0.42 <=> ( V0
% 0.18/0.42 | V1 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Elogic_2E_7E,axiom,
% 0.18/0.42 ! [V0: $o] :
% 0.18/0.42 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.18/0.42 <=> ( (~) @ V0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.18/0.42 ! [V0: $o,V1: $o] :
% 0.18/0.42 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.18/0.42 <=> ( V0
% 0.18/0.42 => V1 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Elogic_2E_3D,axiom,
% 0.18/0.42 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.18/0.42 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.18/0.42 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Equant_2E_21,axiom,
% 0.18/0.42 ! [A_27a: d,V0f_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.18/0.42 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(reserved_2Equant_2E_3F,axiom,
% 0.18/0.42 ! [A_27a: d,V0f_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.18/0.42 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.18/0.42 ! [V0_2E0: u] :
% 0.18/0.42 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.18/0.42 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.18/0.42 ! [V0_2E0: u] :
% 0.18/0.42 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.18/0.42 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.18/0.42 ! [V0_2E0: u] :
% 0.18/0.42 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.18/0.42 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.18/0.42 ! [V0: $o] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.18/0.42 = V0 ) ).
% 0.18/0.42
% 0.18/0.42 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.18/0.42 ! [V0: $o > $o] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.18/0.42 = V0 ) ).
% 0.18/0.42
% 0.18/0.42 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.18/0.42 ! [V0: $o > $o > $o] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.18/0.42 = V0 ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.18/0.42 ! [A_27a: d,X0_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.18/0.42 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( ( s @ A_27a @ X0_2E0 )
% 0.18/0.42 = ( s @ A_27a @ X1_2E0 ) )
% 0.18/0.42 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.18/0.42 ! [A_27a: d,X0_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.18/0.42 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.18/0.42 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.18/0.42 ! [V0: $o > $o,V1: $o] :
% 0.18/0.42 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.18/0.42 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.18/0.42 ! [V0: $o > $o > $o,V1: $o] :
% 0.18/0.42 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.18/0.42 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.18/0.42 ! [V0: $o > $o,V1: $o] :
% 0.18/0.42 ( ( V0 @ V1 )
% 0.18/0.42 = ( V0 @ V1 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.18/0.42 ! [V0: $o > $o > $o,V1: $o] :
% 0.18/0.42 ( ( V0 @ V1 )
% 0.18/0.42 = ( V0 @ V1 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.18/0.42 mono_2Ec_2Ebool_2ET ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.18/0.42 ! [V0t: $o] :
% 0.18/0.42 ( ( ( mono_2Ec_2Ebool_2ET
% 0.18/0.42 => V0t )
% 0.18/0.42 <=> V0t )
% 0.18/0.42 & ( ( V0t
% 0.18/0.42 => mono_2Ec_2Ebool_2ET )
% 0.18/0.42 <=> mono_2Ec_2Ebool_2ET )
% 0.18/0.42 & ( ( mono_2Ec_2Ebool_2EF
% 0.18/0.42 => V0t )
% 0.18/0.42 <=> mono_2Ec_2Ebool_2ET )
% 0.18/0.42 & ( ( V0t
% 0.18/0.42 => V0t )
% 0.18/0.42 <=> mono_2Ec_2Ebool_2ET )
% 0.18/0.42 & ( ( V0t
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 <=> ( (~) @ V0t ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.18/0.42 ( ! [V0t: $o] :
% 0.18/0.42 ( ( (~) @ ( (~) @ V0t ) )
% 0.18/0.42 <=> V0t )
% 0.18/0.42 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.18/0.42 <=> mono_2Ec_2Ebool_2EF )
% 0.18/0.42 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.18/0.42 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.18/0.42 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 0.18/0.42 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.18/0.42 = ( s @ A_27a @ V1y_2E0 ) )
% 0.18/0.42 <=> ( ( s @ A_27a @ V1y_2E0 )
% 0.18/0.42 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.18/0.42 ! [V0t: $o] :
% 0.18/0.42 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.18/0.42 <=> V0t )
% 0.18/0.42 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.18/0.42 <=> V0t )
% 0.18/0.42 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.18/0.42 <=> ( (~) @ V0t ) )
% 0.18/0.42 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.18/0.42 <=> ( (~) @ V0t ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.18/0.42 ! [V0t1: $o,V1t2: $o,V2t3: $o] :
% 0.18/0.42 ( ( V0t1
% 0.18/0.42 => ( V1t2
% 0.18/0.42 => V2t3 ) )
% 0.18/0.42 <=> ( ( V0t1
% 0.18/0.42 & V1t2 )
% 0.18/0.42 => V2t3 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Ebool_2EIMP__CONG,axiom,
% 0.18/0.42 ! [V0x: $o,V1x_27: $o,V2y: $o,V3y_27: $o] :
% 0.18/0.42 ( ( ( V0x = V1x_27 )
% 0.18/0.42 & ( V1x_27
% 0.18/0.42 => ( V2y = V3y_27 ) ) )
% 0.18/0.42 => ( ( V0x
% 0.18/0.42 => V2y )
% 0.18/0.42 <=> ( V1x_27
% 0.18/0.42 => V3y_27 ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
% 0.18/0.42 ! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u] :
% 0.18/0.42 ( ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [V2v_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 => ? [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 ) ) ) ) ) ) ) )
% 0.18/0.42 & ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [V4v_2E0: u] :
% 0.18/0.42 ( ( (~) @ ( 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 ) ) ) ) )
% 0.18/0.42 => ? [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 ) ) ) ) ) ) ) ) )
% 0.18/0.42 & ! [V6i_2E0: u,V7P_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [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 ) ) ) ) ) ) )
% 0.18/0.42 & ! [V9i_2E0: u,V10P_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [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 ) ) ) ) ) ) ) )
% 0.18/0.42 & ! [V12i_2E0: u,V13P_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [V14v_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 => ? [V15fv_2E0: u] :
% 0.18/0.42 ( ( s @ A_27b @ V14v_2E0 )
% 0.18/0.42 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12i_2E0 ) @ ( s @ A_27a @ V15fv_2E0 ) ) ) ) ) )
% 0.18/0.42 & ! [V16i_2E0: u,V17P_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 <=> ! [V18v_2E0: u] :
% 0.18/0.42 ( ( (~) @ ( 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 ) ) ) ) )
% 0.18/0.42 => ? [V19fv_2E0: u] :
% 0.18/0.42 ( ( s @ A_27b @ V18v_2E0 )
% 0.18/0.42 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V16i_2E0 ) @ ( s @ A_27a @ V19fv_2E0 ) ) ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2ENOT__NOT,axiom,
% 0.18/0.42 ! [V0t: $o] :
% 0.18/0.42 ( ( (~) @ ( (~) @ V0t ) )
% 0.18/0.42 <=> V0t ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 0.18/0.42 ! [V0A: $o] :
% 0.18/0.42 ( V0A
% 0.18/0.42 => ( ( (~) @ V0A )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 0.18/0.42 ! [V0B: $o,V1A: $o] :
% 0.18/0.42 ( ( ( (~)
% 0.18/0.42 @ ( V1A
% 0.18/0.42 | V0B ) )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 <=> ( ( V1A
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 => ( ( (~) @ V0B )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 0.18/0.42 ! [V0B: $o,V1A: $o] :
% 0.18/0.42 ( ( ( (~)
% 0.18/0.42 @ ( ( (~) @ V1A )
% 0.18/0.42 | V0B ) )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 <=> ( V1A
% 0.18/0.42 => ( ( (~) @ V0B )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2EAND__INV2,axiom,
% 0.18/0.42 ! [V0A: $o] :
% 0.18/0.42 ( ( ( (~) @ V0A )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 => ( ( V0A
% 0.18/0.42 => mono_2Ec_2Ebool_2EF )
% 0.18/0.42 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Edc__eq,axiom,
% 0.18/0.42 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.18/0.42 ( ( V2p
% 0.18/0.42 <=> ( V1q = V0r ) )
% 0.18/0.42 <=> ( ( V2p
% 0.18/0.42 | V1q
% 0.18/0.42 | V0r )
% 0.18/0.42 & ( V2p
% 0.18/0.42 | ( (~) @ V0r )
% 0.18/0.42 | ( (~) @ V1q ) )
% 0.18/0.42 & ( V1q
% 0.18/0.42 | ( (~) @ V0r )
% 0.18/0.42 | ( (~) @ V2p ) )
% 0.18/0.42 & ( V0r
% 0.18/0.42 | ( (~) @ V1q )
% 0.18/0.42 | ( (~) @ V2p ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Edc__disj,axiom,
% 0.18/0.42 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.18/0.42 ( ( V2p
% 0.18/0.42 <=> ( V1q
% 0.18/0.42 | V0r ) )
% 0.18/0.42 <=> ( ( V2p
% 0.18/0.42 | ( (~) @ V1q ) )
% 0.18/0.42 & ( V2p
% 0.18/0.42 | ( (~) @ V0r ) )
% 0.18/0.42 & ( V1q
% 0.18/0.42 | V0r
% 0.18/0.42 | ( (~) @ V2p ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Edc__imp,axiom,
% 0.18/0.42 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.18/0.42 ( ( V2p
% 0.18/0.42 <=> ( V1q
% 0.18/0.42 => V0r ) )
% 0.18/0.42 <=> ( ( V2p
% 0.18/0.42 | V1q )
% 0.18/0.42 & ( V2p
% 0.18/0.42 | ( (~) @ V0r ) )
% 0.18/0.42 & ( ( (~) @ V1q )
% 0.18/0.42 | V0r
% 0.18/0.42 | ( (~) @ V2p ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Edc__neg,axiom,
% 0.18/0.42 ! [V0q: $o,V1p: $o] :
% 0.18/0.42 ( ( V1p
% 0.18/0.42 <=> ( (~) @ V0q ) )
% 0.18/0.42 <=> ( ( V1p
% 0.18/0.42 | V0q )
% 0.18/0.42 & ( ( (~) @ V0q )
% 0.18/0.42 | ( (~) @ V1p ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Epth__ni1,axiom,
% 0.18/0.42 ! [V0q: $o,V1p: $o] :
% 0.18/0.42 ( ( (~)
% 0.18/0.42 @ ( V1p
% 0.18/0.42 => V0q ) )
% 0.18/0.42 => V1p ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2Esat_2Epth__ni2,axiom,
% 0.18/0.42 ! [V0q: $o,V1p: $o] :
% 0.18/0.42 ( ( (~)
% 0.18/0.42 @ ( V1p
% 0.18/0.42 => V0q ) )
% 0.18/0.42 => ( (~) @ V0q ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
% 0.18/0.42 ! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
% 0.18/0.42 ( ! [V3x_2E0: u] :
% 0.18/0.42 ( ( 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 ) ) ) )
% 0.18/0.42 => ( 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 ) ) ) ) )
% 0.18/0.42 => ( ( 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 ) ) ) )
% 0.18/0.42 => ( 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 ) ) ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 ------------------------
% 2.27/1.65 ---- Embedded in THF ---
% 2.27/1.66 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.27/1.66 %%% Generated on Tue Feb 24 08:18:04 EST 2026
% 2.27/1.66 %%% using '$$dhol' embedding, version 1.3.0.
% 2.27/1.66 %%% Logic specification used:
% 2.27/1.66 %%% thf(spec, logic, $$dhol).
% 2.27/1.66
% 2.27/1.66 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xApQoegLFN/DTF2DTF6174.p
% See solution above
% 2.27/1.66 ------------------------
% 2.27/1.68 ---- Cleaned THF ---
% 2.27/1.68 thf(u,type,
% 2.27/1.68 u: $tType ).
% 2.27/1.68
% 2.27/1.68 thf(d,type,
% 2.27/1.68 d: $tType ).
% 2.27/1.68
% 2.27/1.68 thf(du,type,
% 2.27/1.68 du: $tType ).
% 2.27/1.68
% 2.27/1.68 thf(tyop_2Emin_2Ebool,type,
% 2.27/1.68 tyop_2Emin_2Ebool: d ).
% 2.27/1.68
% 2.27/1.68 thf(tyop_2Emin_2Efun,type,
% 2.27/1.68 tyop_2Emin_2Efun: d > d > d ).
% 2.27/1.68
% 2.27/1.68 thf(s,type,
% 2.27/1.68 s: d > u > du ).
% 2.27/1.68
% 2.27/1.68 thf(app_2E2,type,
% 2.27/1.68 app_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(combin_i_2E0,type,
% 2.27/1.68 combin_i_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(combin_k_2E0,type,
% 2.27/1.68 combin_k_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(combin_s_2E0,type,
% 2.27/1.68 combin_s_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_21_2E0,type,
% 2.27/1.68 c_2Ebool_2E_21_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_21_2E1,type,
% 2.27/1.68 c_2Ebool_2E_21_2E1: du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 2.27/1.68 c_2Ebool_2E_2F_5C_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 2.27/1.68 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Emin_2E_3D_2E0,type,
% 2.27/1.68 c_2Emin_2E_3D_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Emin_2E_3D_2E2,type,
% 2.27/1.68 c_2Emin_2E_3D_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 2.27/1.68 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 2.27/1.68 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_3F_2E0,type,
% 2.27/1.68 c_2Ebool_2E_3F_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_3F_2E1,type,
% 2.27/1.68 c_2Ebool_2E_3F_2E1: du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2EF_2E0,type,
% 2.27/1.68 c_2Ebool_2EF_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,type,
% 2.27/1.68 c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2ET_2E0,type,
% 2.27/1.68 c_2Ebool_2ET_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 2.27/1.68 c_2Ebool_2E_5C_2F_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 2.27/1.68 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_7E_2E0,type,
% 2.27/1.68 c_2Ebool_2E_7E_2E0: u ).
% 2.27/1.68
% 2.27/1.68 thf(c_2Ebool_2E_7E_2E1,type,
% 2.27/1.68 c_2Ebool_2E_7E_2E1: du > u ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 2.27/1.68 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.27/1.68 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 2.27/1.68 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 2.27/1.68 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Ebool_2EF,type,
% 2.27/1.68 mono_2Ec_2Ebool_2EF: $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Ebool_2ET,type,
% 2.27/1.68 mono_2Ec_2Ebool_2ET: $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 2.27/1.68 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(mono_2Ec_2Ebool_2E_7E,type,
% 2.27/1.68 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 2.27/1.68 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 2.27/1.68
% 2.27/1.68 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.27/1.68 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 2.27/1.68
% 2.27/1.68 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.27/1.68 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 2.27/1.68
% 2.27/1.68 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 2.27/1.68 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 2.27/1.68
% 2.27/1.68 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.27/1.68 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.27/1.68 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Eho_2Eeq__ext,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 2.27/1.68 ( ! [V2x_2E0: u] :
% 2.27/1.68 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.27/1.68 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.27/1.68 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 2.27/1.68 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Eho_2Ei__thm,axiom,
% 2.27/1.68 ! [A_27a: d,V0x_2E0: u] :
% 2.27/1.68 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 2.27/1.68 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Eho_2Ek__thm,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 2.27/1.68 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 2.27/1.68 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Eho_2Es__thm,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 2.27/1.68 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.27/1.68 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 2.27/1.68 ! [V0: $o,V1: $o] :
% 2.27/1.68 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 2.27/1.68 <=> ( V0
% 2.27/1.68 & V1 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 2.27/1.68 ! [V0: $o,V1: $o] :
% 2.27/1.68 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 2.27/1.68 <=> ( V0
% 2.27/1.68 | V1 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Elogic_2E_7E,axiom,
% 2.27/1.68 ! [V0: $o] :
% 2.27/1.68 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 2.27/1.68 <=> ( (~) @ V0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 2.27/1.68 ! [V0: $o,V1: $o] :
% 2.27/1.68 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 2.27/1.68 <=> ( V0
% 2.27/1.68 => V1 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Elogic_2E_3D,axiom,
% 2.27/1.68 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 2.27/1.68 <=> ( ( s @ A_27a @ V0_2E0 )
% 2.27/1.68 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Equant_2E_21,axiom,
% 2.27/1.68 ! [A_27a: d,V0f_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.27/1.68 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(reserved_2Equant_2E_3F,axiom,
% 2.27/1.68 ! [A_27a: d,V0f_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.27/1.68 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.27/1.68 ! [V0_2E0: u] :
% 2.27/1.68 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 2.27/1.68 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.27/1.68 ! [V0_2E0: u] :
% 2.27/1.68 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.27/1.68 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.27/1.68 ! [V0_2E0: u] :
% 2.27/1.68 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.27/1.68 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.27/1.68 ! [V0: $o] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 2.27/1.68 = V0 ) ).
% 2.27/1.68
% 2.27/1.68 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.27/1.68 ! [V0: $o > $o] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.27/1.68 = V0 ) ).
% 2.27/1.68
% 2.27/1.68 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.27/1.68 ! [V0: $o > $o > $o] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.27/1.68 = V0 ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 2.27/1.68 ! [A_27a: d,X0_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 2.27/1.68 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( ( s @ A_27a @ X0_2E0 )
% 2.27/1.68 = ( s @ A_27a @ X1_2E0 ) )
% 2.27/1.68 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 2.27/1.68 ! [A_27a: d,X0_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 2.27/1.68 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.27/1.68 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.27/1.68 ! [V0: $o > $o,V1: $o] :
% 2.27/1.68 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.27/1.68 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.27/1.68 ! [V0: $o > $o > $o,V1: $o] :
% 2.27/1.68 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.27/1.68 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.27/1.68 ! [V0: $o > $o,V1: $o] :
% 2.27/1.68 ( ( V0 @ V1 )
% 2.27/1.68 = ( V0 @ V1 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.27/1.68 ! [V0: $o > $o > $o,V1: $o] :
% 2.27/1.68 ( ( V0 @ V1 )
% 2.27/1.68 = ( V0 @ V1 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2ETRUTH,axiom,
% 2.27/1.68 mono_2Ec_2Ebool_2ET ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 2.27/1.68 ! [V0t: $o] :
% 2.27/1.68 ( ( ( mono_2Ec_2Ebool_2ET
% 2.27/1.68 => V0t )
% 2.27/1.68 <=> V0t )
% 2.27/1.68 & ( ( V0t
% 2.27/1.68 => mono_2Ec_2Ebool_2ET )
% 2.27/1.68 <=> mono_2Ec_2Ebool_2ET )
% 2.27/1.68 & ( ( mono_2Ec_2Ebool_2EF
% 2.27/1.68 => V0t )
% 2.27/1.68 <=> mono_2Ec_2Ebool_2ET )
% 2.27/1.68 & ( ( V0t
% 2.27/1.68 => V0t )
% 2.27/1.68 <=> mono_2Ec_2Ebool_2ET )
% 2.27/1.68 & ( ( V0t
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 <=> ( (~) @ V0t ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 2.27/1.68 ( ! [V0t: $o] :
% 2.27/1.68 ( ( (~) @ ( (~) @ V0t ) )
% 2.27/1.68 <=> V0t )
% 2.27/1.68 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 2.27/1.68 <=> mono_2Ec_2Ebool_2EF )
% 2.27/1.68 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 2.27/1.68 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 2.27/1.68 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 2.27/1.68 ( ( ( s @ A_27a @ V0x_2E0 )
% 2.27/1.68 = ( s @ A_27a @ V1y_2E0 ) )
% 2.27/1.68 <=> ( ( s @ A_27a @ V1y_2E0 )
% 2.27/1.68 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 2.27/1.68 ! [V0t: $o] :
% 2.27/1.68 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 2.27/1.68 <=> V0t )
% 2.27/1.68 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 2.27/1.68 <=> V0t )
% 2.27/1.68 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 2.27/1.68 <=> ( (~) @ V0t ) )
% 2.27/1.68 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 2.27/1.68 <=> ( (~) @ V0t ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 2.27/1.68 ! [V0t1: $o,V1t2: $o,V2t3: $o] :
% 2.27/1.68 ( ( V0t1
% 2.27/1.68 => ( V1t2
% 2.27/1.68 => V2t3 ) )
% 2.27/1.68 <=> ( ( V0t1
% 2.27/1.68 & V1t2 )
% 2.27/1.68 => V2t3 ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Ebool_2EIMP__CONG,axiom,
% 2.27/1.68 ! [V0x: $o,V1x_27: $o,V2y: $o,V3y_27: $o] :
% 2.27/1.68 ( ( ( V0x = V1x_27 )
% 2.27/1.68 & ( V1x_27
% 2.27/1.68 => ( V2y = V3y_27 ) ) )
% 2.27/1.68 => ( ( V0x
% 2.27/1.68 => V2y )
% 2.27/1.68 <=> ( V1x_27
% 2.27/1.68 => V3y_27 ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
% 2.27/1.68 ! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u] :
% 2.27/1.68 ( ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [V2v_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 => ? [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 ) ) ) ) ) ) ) )
% 2.27/1.68 & ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [V4v_2E0: u] :
% 2.27/1.68 ( ( (~) @ ( 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 ) ) ) ) )
% 2.27/1.68 => ? [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 ) ) ) ) ) ) ) ) )
% 2.27/1.68 & ! [V6i_2E0: u,V7P_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [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 ) ) ) ) ) ) )
% 2.27/1.68 & ! [V9i_2E0: u,V10P_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [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 ) ) ) ) ) ) ) )
% 2.27/1.68 & ! [V12i_2E0: u,V13P_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [V14v_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 => ? [V15fv_2E0: u] :
% 2.27/1.68 ( ( s @ A_27b @ V14v_2E0 )
% 2.27/1.68 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12i_2E0 ) @ ( s @ A_27a @ V15fv_2E0 ) ) ) ) ) )
% 2.27/1.68 & ! [V16i_2E0: u,V17P_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 <=> ! [V18v_2E0: u] :
% 2.27/1.68 ( ( (~) @ ( 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 ) ) ) ) )
% 2.27/1.68 => ? [V19fv_2E0: u] :
% 2.27/1.68 ( ( s @ A_27b @ V18v_2E0 )
% 2.27/1.68 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V16i_2E0 ) @ ( s @ A_27a @ V19fv_2E0 ) ) ) ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2ENOT__NOT,axiom,
% 2.27/1.68 ! [V0t: $o] :
% 2.27/1.68 ( ( (~) @ ( (~) @ V0t ) )
% 2.27/1.68 <=> V0t ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 2.27/1.68 ! [V0A: $o] :
% 2.27/1.68 ( V0A
% 2.27/1.68 => ( ( (~) @ V0A )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 2.27/1.68 ! [V0B: $o,V1A: $o] :
% 2.27/1.68 ( ( ( (~)
% 2.27/1.68 @ ( V1A
% 2.27/1.68 | V0B ) )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 <=> ( ( V1A
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 => ( ( (~) @ V0B )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 2.27/1.68 ! [V0B: $o,V1A: $o] :
% 2.27/1.68 ( ( ( (~)
% 2.27/1.68 @ ( ( (~) @ V1A )
% 2.27/1.68 | V0B ) )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 <=> ( V1A
% 2.27/1.68 => ( ( (~) @ V0B )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2EAND__INV2,axiom,
% 2.27/1.68 ! [V0A: $o] :
% 2.27/1.68 ( ( ( (~) @ V0A )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 => ( ( V0A
% 2.27/1.68 => mono_2Ec_2Ebool_2EF )
% 2.27/1.68 => mono_2Ec_2Ebool_2EF ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Edc__eq,axiom,
% 2.27/1.68 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.27/1.68 ( ( V2p
% 2.27/1.68 <=> ( V1q = V0r ) )
% 2.27/1.68 <=> ( ( V2p
% 2.27/1.68 | V1q
% 2.27/1.68 | V0r )
% 2.27/1.68 & ( V2p
% 2.27/1.68 | ( (~) @ V0r )
% 2.27/1.68 | ( (~) @ V1q ) )
% 2.27/1.68 & ( V1q
% 2.27/1.68 | ( (~) @ V0r )
% 2.27/1.68 | ( (~) @ V2p ) )
% 2.27/1.68 & ( V0r
% 2.27/1.68 | ( (~) @ V1q )
% 2.27/1.68 | ( (~) @ V2p ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Edc__disj,axiom,
% 2.27/1.68 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.27/1.68 ( ( V2p
% 2.27/1.68 <=> ( V1q
% 2.27/1.68 | V0r ) )
% 2.27/1.68 <=> ( ( V2p
% 2.27/1.68 | ( (~) @ V1q ) )
% 2.27/1.68 & ( V2p
% 2.27/1.68 | ( (~) @ V0r ) )
% 2.27/1.68 & ( V1q
% 2.27/1.68 | V0r
% 2.27/1.68 | ( (~) @ V2p ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Edc__imp,axiom,
% 2.27/1.68 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.27/1.68 ( ( V2p
% 2.27/1.68 <=> ( V1q
% 2.27/1.68 => V0r ) )
% 2.27/1.68 <=> ( ( V2p
% 2.27/1.68 | V1q )
% 2.27/1.68 & ( V2p
% 2.27/1.68 | ( (~) @ V0r ) )
% 2.27/1.68 & ( ( (~) @ V1q )
% 2.27/1.68 | V0r
% 2.27/1.68 | ( (~) @ V2p ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Edc__neg,axiom,
% 2.27/1.68 ! [V0q: $o,V1p: $o] :
% 2.27/1.68 ( ( V1p
% 2.27/1.68 <=> ( (~) @ V0q ) )
% 2.27/1.68 <=> ( ( V1p
% 2.27/1.68 | V0q )
% 2.27/1.68 & ( ( (~) @ V0q )
% 2.27/1.68 | ( (~) @ V1p ) ) ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Epth__ni1,axiom,
% 2.27/1.68 ! [V0q: $o,V1p: $o] :
% 2.27/1.68 ( ( (~)
% 2.27/1.68 @ ( V1p
% 2.27/1.68 => V0q ) )
% 2.27/1.68 => V1p ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2Esat_2Epth__ni2,axiom,
% 2.27/1.68 ! [V0q: $o,V1p: $o] :
% 2.27/1.68 ( ( (~)
% 2.27/1.68 @ ( V1p
% 2.27/1.68 => V0q ) )
% 2.27/1.68 => ( (~) @ V0q ) ) ).
% 2.27/1.68
% 2.27/1.68 thf(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
% 2.27/1.68 ! [A_27a: d,A_27b: d,V0i_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
% 2.27/1.68 ( ! [V3x_2E0: u] :
% 2.27/1.68 ( ( 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 ) ) ) )
% 2.27/1.68 => ( 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 ) ) ) ) )
% 2.27/1.68 => ( ( 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 ) ) ) )
% 2.27/1.68 => ( 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 ) ) ) ) ) ) ).
% 2.27/1.68 ------------------------
% 2.43/1.71 % (6276)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/2Mi)
% 2.43/1.71 % (6272)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/183Mi)
% 2.43/1.71 % (6273)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/4Mi)
% 2.43/1.71 % (6274)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/27Mi)
% 2.43/1.71 % (6277)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/275Mi)
% 2.43/1.71 % (6278)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/18Mi)
% 2.43/1.71 % (6275)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/2Mi)
% 2.43/1.71 % (6275)Instruction limit reached!
% 2.43/1.71 % (6275)------------------------------
% 2.43/1.71 % (6275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.71 % (6275)Termination reason: Unknown
% 2.43/1.71 % (6275)Termination phase: shuffling
% 2.43/1.71 % (6276)Instruction limit reached!
% 2.43/1.71 % (6276)------------------------------
% 2.43/1.71 % (6276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.71
% 2.43/1.71 % (6275)Memory used [KB]: 1023
% 2.43/1.71 % (6275)Time elapsed: 0.003 s
% 2.43/1.71 % (6275)Instructions burned: 2 (million)
% 2.43/1.71 % (6275)------------------------------
% 2.43/1.71 % (6275)------------------------------
% 2.43/1.71 % (6276)Termination reason: Unknown
% 2.43/1.71 % (6276)Termination phase: shuffling
% 2.43/1.71
% 2.43/1.71 % (6276)Memory used [KB]: 1023
% 2.43/1.71 % (6276)Time elapsed: 0.003 s
% 2.43/1.71 % (6276)Instructions burned: 2 (million)
% 2.43/1.71 % (6276)------------------------------
% 2.43/1.71 % (6276)------------------------------
% 2.43/1.71 % (6273)Instruction limit reached!
% 2.43/1.71 % (6273)------------------------------
% 2.43/1.71 % (6273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.71 % (6273)Termination reason: Unknown
% 2.43/1.71 % (6273)Termination phase: shuffling
% 2.43/1.71
% 2.43/1.71 % (6273)Memory used [KB]: 1151
% 2.43/1.71 % (6273)Time elapsed: 0.005 s
% 2.43/1.71 % (6273)Instructions burned: 5 (million)
% 2.43/1.71 % (6273)------------------------------
% 2.43/1.71 % (6273)------------------------------
% 2.43/1.72 % (6278)Instruction limit reached!
% 2.43/1.72 % (6278)------------------------------
% 2.43/1.72 % (6278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.72 % (6278)Termination reason: Unknown
% 2.43/1.72 % (6278)Termination phase: Preprocessing 3
% 2.43/1.72
% 2.43/1.72 % (6278)Memory used [KB]: 1279
% 2.43/1.72 % (6278)Time elapsed: 0.011 s
% 2.43/1.72 % (6278)Instructions burned: 18 (million)
% 2.43/1.72 % (6278)------------------------------
% 2.43/1.72 % (6278)------------------------------
% 2.43/1.72 % (6277)Refutation not found, incomplete strategy
% 2.43/1.72 % (6277)------------------------------
% 2.43/1.72 % (6277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.72 % (6277)Termination reason: Refutation not found, incomplete strategy
% 2.43/1.72
% 2.43/1.72
% 2.43/1.72 % (6277)Memory used [KB]: 5756
% 2.43/1.72 % (6277)Time elapsed: 0.011 s
% 2.43/1.72 % (6277)Instructions burned: 16 (million)
% 2.43/1.72 % (6277)------------------------------
% 2.43/1.72 % (6277)------------------------------
% 2.43/1.72 % (6274)Instruction limit reached!
% 2.43/1.72 % (6274)------------------------------
% 2.43/1.72 % (6274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.72 % (6274)Termination reason: Unknown
% 2.43/1.72 % (6274)Termination phase: Property scanning
% 2.43/1.72
% 2.43/1.72 % (6274)Memory used [KB]: 1407
% 2.43/1.72 % (6274)Time elapsed: 0.016 s
% 2.43/1.72 % (6274)Instructions burned: 28 (million)
% 2.43/1.72 % (6274)------------------------------
% 2.43/1.72 % (6274)------------------------------
% 2.43/1.73 % (6279)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/3Mi)
% 2.43/1.73 % (6280)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/37Mi)
% 2.43/1.73 % (6281)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/15Mi)
% 2.43/1.73 % (6279)Instruction limit reached!
% 2.43/1.73 % (6279)------------------------------
% 2.43/1.73 % (6279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.73 % (6279)Termination reason: Unknown
% 2.43/1.73 % (6279)Termination phase: shuffling
% 2.43/1.73
% 2.43/1.73 % (6279)Memory used [KB]: 1151
% 2.43/1.73 % (6279)Time elapsed: 0.004 s
% 2.43/1.73 % (6279)Instructions burned: 4 (million)
% 2.43/1.73 % (6279)------------------------------
% 2.43/1.73 % (6279)------------------------------
% 2.43/1.74 % (6281)Instruction limit reached!
% 2.43/1.74 % (6281)------------------------------
% 2.43/1.74 % (6281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.74 % (6281)Termination reason: Unknown
% 2.43/1.74 % (6281)Termination phase: Preprocessing 3
% 2.43/1.74
% 2.43/1.74 % (6281)Memory used [KB]: 1279
% 2.43/1.74 % (6281)Time elapsed: 0.009 s
% 2.43/1.74 % (6281)Instructions burned: 15 (million)
% 2.43/1.74 % (6281)------------------------------
% 2.43/1.74 % (6281)------------------------------
% 2.43/1.74 % (6283)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/1041Mi)
% 2.43/1.74 % (6282)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/3Mi)
% 2.43/1.74 % (6282)Instruction limit reached!
% 2.43/1.74 % (6282)------------------------------
% 2.43/1.74 % (6282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.74 % (6282)Termination reason: Unknown
% 2.43/1.74 % (6282)Termination phase: shuffling
% 2.43/1.74
% 2.43/1.74 % (6282)Memory used [KB]: 1151
% 2.43/1.74 % (6282)Time elapsed: 0.004 s
% 2.43/1.74 % (6282)Instructions burned: 3 (million)
% 2.43/1.74 % (6282)------------------------------
% 2.43/1.74 % (6282)------------------------------
% 2.43/1.74 % (6284)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/7Mi)
% 2.43/1.74 % (6284)Instruction limit reached!
% 2.43/1.74 % (6284)------------------------------
% 2.43/1.74 % (6284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.74 % (6284)Termination reason: Unknown
% 2.43/1.74 % (6284)Termination phase: Property scanning
% 2.43/1.74
% 2.43/1.74 % (6284)Memory used [KB]: 1151
% 2.43/1.74 % (6284)Time elapsed: 0.005 s
% 2.43/1.74 % (6284)Instructions burned: 7 (million)
% 2.43/1.74 % (6284)------------------------------
% 2.43/1.74 % (6284)------------------------------
% 2.43/1.75 % (6280)Instruction limit reached!
% 2.43/1.75 % (6280)------------------------------
% 2.43/1.75 % (6280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.75 % (6280)Termination reason: Unknown
% 2.43/1.75 % (6280)Termination phase: Property scanning
% 2.43/1.75
% 2.43/1.75 % (6280)Memory used [KB]: 1407
% 2.43/1.75 % (6280)Time elapsed: 0.020 s
% 2.43/1.75 % (6280)Instructions burned: 38 (million)
% 2.43/1.75 % (6280)------------------------------
% 2.43/1.75 % (6280)------------------------------
% 2.43/1.75 % (6285)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/16Mi)
% 2.43/1.75 % (6286)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/3Mi)
% 2.43/1.76 % (6285)Instruction limit reached!
% 2.43/1.76 % (6285)------------------------------
% 2.43/1.76 % (6285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.76 % (6285)Termination reason: Unknown
% 2.43/1.76 % (6285)Termination phase: Preprocessing 3
% 2.43/1.76
% 2.43/1.76 % (6285)Memory used [KB]: 1279
% 2.43/1.76 % (6285)Time elapsed: 0.010 s
% 2.43/1.76 % (6285)Instructions burned: 16 (million)
% 2.43/1.76 % (6285)------------------------------
% 2.43/1.76 % (6285)------------------------------
% 2.43/1.76 % (6286)Instruction limit reached!
% 2.43/1.76 % (6286)------------------------------
% 2.43/1.76 % (6286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.76 % (6286)Termination reason: Unknown
% 2.43/1.76 % (6286)Termination phase: shuffling
% 2.43/1.76
% 2.43/1.76 % (6286)Memory used [KB]: 1151
% 2.43/1.76 % (6286)Time elapsed: 0.004 s
% 2.43/1.76 % (6286)Instructions burned: 4 (million)
% 2.43/1.76 % (6286)------------------------------
% 2.43/1.76 % (6286)------------------------------
% 2.43/1.76 % (6287)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/3Mi)
% 2.43/1.76 % (6287)Instruction limit reached!
% 2.43/1.76 % (6287)------------------------------
% 2.43/1.76 % (6287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.76 % (6287)Termination reason: Unknown
% 2.43/1.76 % (6287)Termination phase: shuffling
% 2.43/1.76
% 2.43/1.76 % (6287)Memory used [KB]: 1151
% 2.43/1.76 % (6287)Time elapsed: 0.003 s
% 2.43/1.76 % (6287)Instructions burned: 3 (million)
% 2.43/1.76 % (6287)------------------------------
% 2.43/1.76 % (6287)------------------------------
% 2.43/1.76 % (6288)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/7Mi)
% 2.43/1.76 % (6289)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/3Mi)
% 2.43/1.77 % (6289)Instruction limit reached!
% 2.43/1.77 % (6289)------------------------------
% 2.43/1.77 % (6289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.77 % (6289)Termination reason: Unknown
% 2.43/1.77 % (6289)Termination phase: shuffling
% 2.43/1.77
% 2.43/1.77 % (6289)Memory used [KB]: 1151
% 2.43/1.77 % (6289)Time elapsed: 0.003 s
% 2.43/1.77 % (6289)Instructions burned: 4 (million)
% 2.43/1.77 % (6289)------------------------------
% 2.43/1.77 % (6289)------------------------------
% 2.43/1.77 % (6288)Instruction limit reached!
% 2.43/1.77 % (6288)------------------------------
% 2.43/1.77 % (6288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.77 % (6288)Termination reason: Unknown
% 2.43/1.77 % (6288)Termination phase: shuffling
% 2.43/1.77
% 2.43/1.77 % (6288)Memory used [KB]: 1151
% 2.43/1.77 % (6288)Time elapsed: 0.006 s
% 2.43/1.77 % (6288)Instructions burned: 8 (million)
% 2.43/1.77 % (6288)------------------------------
% 2.43/1.77 % (6288)------------------------------
% 2.43/1.77 % (6290)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/4Mi)
% 2.43/1.77 % (6291)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/18Mi)
% 2.43/1.77 % (6290)Instruction limit reached!
% 2.43/1.77 % (6290)------------------------------
% 2.43/1.77 % (6290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.77 % (6290)Termination reason: Unknown
% 2.43/1.77 % (6290)Termination phase: shuffling
% 2.43/1.77
% 2.43/1.77 % (6290)Memory used [KB]: 1151
% 2.43/1.77 % (6290)Time elapsed: 0.004 s
% 2.43/1.77 % (6290)Instructions burned: 4 (million)
% 2.43/1.77 % (6290)------------------------------
% 2.43/1.77 % (6290)------------------------------
% 2.43/1.78 % (6292)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/710Mi)
% 2.43/1.78 % (6291)Instruction limit reached!
% 2.43/1.78 % (6291)------------------------------
% 2.43/1.78 % (6291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.78 % (6291)Termination reason: Unknown
% 2.43/1.78 % (6291)Termination phase: Preprocessing 3
% 2.43/1.78
% 2.43/1.78 % (6291)Memory used [KB]: 1279
% 2.43/1.78 % (6291)Time elapsed: 0.011 s
% 2.43/1.78 % (6291)Instructions burned: 18 (million)
% 2.43/1.78 % (6291)------------------------------
% 2.43/1.78 % (6291)------------------------------
% 2.43/1.78 % (6294)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/902Mi)
% 2.43/1.78 % (6293)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/6Mi)
% 2.43/1.79 % (6293)Instruction limit reached!
% 2.43/1.79 % (6293)------------------------------
% 2.43/1.79 % (6293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.79 % (6293)Termination reason: Unknown
% 2.43/1.79 % (6293)Termination phase: shuffling
% 2.43/1.79
% 2.43/1.79 % (6293)Memory used [KB]: 1151
% 2.43/1.79 % (6293)Time elapsed: 0.004 s
% 2.43/1.79 % (6293)Instructions burned: 6 (million)
% 2.43/1.79 % (6293)------------------------------
% 2.43/1.79 % (6293)------------------------------
% 2.43/1.79 % (6295)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/21Mi)
% 2.43/1.80 % (6296)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/5Mi)
% 2.43/1.80 % (6297)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_6174 for (2999ds/6Mi)
% 2.43/1.80 % (6296)Instruction limit reached!
% 2.43/1.80 % (6296)------------------------------
% 2.43/1.80 % (6296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.80 % (6296)Termination reason: Unknown
% 2.43/1.80 % (6296)Termination phase: shuffling
% 2.43/1.80
% 2.43/1.80 % (6296)Memory used [KB]: 1151
% 2.43/1.80 % (6296)Time elapsed: 0.005 s
% 2.43/1.80 % (6296)Instructions burned: 7 (million)
% 2.43/1.80 % (6296)------------------------------
% 2.43/1.80 % (6296)------------------------------
% 2.43/1.80 % (6295)Instruction limit reached!
% 2.43/1.80 % (6295)------------------------------
% 2.43/1.80 % (6295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.80 % (6295)Termination reason: Unknown
% 2.43/1.80 % (6295)Termination phase: Preprocessing 3
% 2.43/1.80
% 2.43/1.80 % (6295)Memory used [KB]: 1279
% 2.43/1.80 % (6295)Time elapsed: 0.013 s
% 2.43/1.80 % (6295)Instructions burned: 22 (million)
% 2.43/1.80 % (6295)------------------------------
% 2.43/1.80 % (6295)------------------------------
% 2.43/1.81 % (6297)Instruction limit reached!
% 2.43/1.81 % (6297)------------------------------
% 2.43/1.81 % (6297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.81 % (6297)Termination reason: Unknown
% 2.43/1.81 % (6297)Termination phase: shuffling
% 2.43/1.81
% 2.43/1.81 % (6297)Memory used [KB]: 1151
% 2.43/1.81 % (6297)Time elapsed: 0.004 s
% 2.43/1.81 % (6297)Instructions burned: 6 (million)
% 2.43/1.81 % (6297)------------------------------
% 2.43/1.81 % (6297)------------------------------
% 2.43/1.81 % (6272)Instruction limit reached!
% 2.43/1.81 % (6272)------------------------------
% 2.43/1.81 % (6272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.81 % (6272)Termination reason: Unknown
% 2.43/1.81 % (6272)Termination phase: Saturation
% 2.43/1.81
% 2.43/1.81 % (6272)Memory used [KB]: 6780
% 2.43/1.81 % (6272)Time elapsed: 0.101 s
% 2.43/1.81 % (6272)Instructions burned: 184 (million)
% 2.43/1.81 % (6272)------------------------------
% 2.43/1.81 % (6272)------------------------------
% 2.43/1.82 % (6299)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_6174 for (2998ds/779Mi)
% 2.43/1.82 % (6298)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6174 for (2998ds/377Mi)
% 2.43/1.82 % (6300)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_6174 for (2998ds/19Mi)
% 2.43/1.83 % (6301)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6174 for (2998ds/879Mi)
% 2.43/1.83 % (6292)First to succeed.
% 2.43/1.83 % (6300)Instruction limit reached!
% 2.43/1.83 % (6300)------------------------------
% 2.43/1.83 % (6300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.83 % (6300)Termination reason: Unknown
% 2.43/1.83 % (6300)Termination phase: Property scanning
% 2.43/1.83
% 2.43/1.83 % (6300)Memory used [KB]: 1279
% 2.43/1.83 % (6300)Time elapsed: 0.011 s
% 2.43/1.83 % (6300)Instructions burned: 20 (million)
% 2.43/1.83 % (6300)------------------------------
% 2.43/1.83 % (6300)------------------------------
% 2.43/1.84 % (6292)Refutation found. Thanks to Tanya!
% 2.43/1.84 % SZS status Theorem for DTF2THF_6174
% 2.43/1.84 % SZS output start Proof for DTF2THF_6174
% 2.43/1.84 thf(type_def_5, type, d: $tType).
% 2.43/1.84 thf(type_def_7, type, u: $tType).
% 2.43/1.84 thf(type_def_8, type, du: $tType).
% 2.43/1.84 thf(func_def_0, type, u: $tType).
% 2.43/1.84 thf(func_def_1, type, d: $tType).
% 2.43/1.84 thf(func_def_2, type, du: $tType).
% 2.43/1.84 thf(func_def_3, type, tyop_2Emin_2Ebool: d).
% 2.43/1.84 thf(func_def_4, type, tyop_2Emin_2Efun: d > d > d).
% 2.43/1.84 thf(func_def_5, type, s: d > u > du).
% 2.43/1.84 thf(func_def_6, type, app_2E2: du > du > u).
% 2.43/1.84 thf(func_def_7, type, combin_i_2E0: u).
% 2.43/1.84 thf(func_def_8, type, combin_k_2E0: u).
% 2.43/1.84 thf(func_def_9, type, combin_s_2E0: u).
% 2.43/1.84 thf(func_def_10, type, c_2Ebool_2E_21_2E0: u).
% 2.43/1.84 thf(func_def_11, type, c_2Ebool_2E_21_2E1: du > u).
% 2.43/1.84 thf(func_def_12, type, c_2Ebool_2E_2F_5C_2E0: u).
% 2.43/1.84 thf(func_def_13, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 2.43/1.84 thf(func_def_14, type, c_2Emin_2E_3D_2E0: u).
% 2.43/1.84 thf(func_def_15, type, c_2Emin_2E_3D_2E2: du > du > u).
% 2.43/1.84 thf(func_def_16, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 2.43/1.84 thf(func_def_17, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 2.43/1.84 thf(func_def_18, type, c_2Ebool_2E_3F_2E0: u).
% 2.43/1.84 thf(func_def_19, type, c_2Ebool_2E_3F_2E1: du > u).
% 2.43/1.84 thf(func_def_20, type, c_2Ebool_2EF_2E0: u).
% 2.43/1.84 thf(func_def_21, type, c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u).
% 2.43/1.84 thf(func_def_22, type, c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u).
% 2.43/1.84 thf(func_def_23, type, c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u).
% 2.43/1.84 thf(func_def_24, type, c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u).
% 2.43/1.84 thf(func_def_25, type, c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u).
% 2.43/1.84 thf(func_def_26, type, c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u).
% 2.43/1.84 thf(func_def_27, type, c_2EquantHeuristics_2EGUESS__FORALL_2E0: u).
% 2.43/1.84 thf(func_def_28, type, c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u).
% 2.43/1.84 thf(func_def_29, type, c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u).
% 2.43/1.84 thf(func_def_30, type, c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u).
% 2.43/1.84 thf(func_def_31, type, c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u).
% 2.43/1.84 thf(func_def_32, type, c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u).
% 2.43/1.84 thf(func_def_33, type, c_2Ebool_2ET_2E0: u).
% 2.43/1.84 thf(func_def_34, type, c_2Ebool_2E_5C_2F_2E0: u).
% 2.43/1.84 thf(func_def_35, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 2.43/1.84 thf(func_def_36, type, c_2Ebool_2E_7E_2E0: u).
% 2.43/1.84 thf(func_def_37, type, c_2Ebool_2E_7E_2E1: du > u).
% 2.43/1.84 thf(func_def_38, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 2.43/1.84 thf(func_def_39, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 2.43/1.84 thf(func_def_40, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 2.43/1.84 thf(func_def_41, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 2.43/1.84 thf(func_def_44, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 2.43/1.84 thf(func_def_45, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 2.43/1.84 thf(func_def_46, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 2.43/1.84 thf(func_def_47, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 2.43/1.84 thf(func_def_48, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 2.43/1.84 thf(func_def_49, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 2.43/1.84 thf(func_def_50, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 2.43/1.84 thf(func_def_51, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 2.43/1.84 thf(func_def_58, type, sK0: u).
% 2.43/1.84 thf(func_def_59, type, sK1: d).
% 2.43/1.84 thf(func_def_60, type, sK2: d).
% 2.43/1.84 thf(func_def_61, type, sK3: u).
% 2.43/1.84 thf(func_def_62, type, sK4: u).
% 2.43/1.84 thf(func_def_63, type, sK5: u > u > d > d > u).
% 2.43/1.84 thf(func_def_64, type, sK6: u > u > d > d > u).
% 2.43/1.84 thf(func_def_65, type, sK7: u > u > d > d > u).
% 2.43/1.84 thf(func_def_66, type, sK8: u > u > d > d > u).
% 2.43/1.84 thf(func_def_67, type, sK9: u > u > d > d > u).
% 2.43/1.84 thf(func_def_68, type, sK10: u > u > d > d > u).
% 2.43/1.84 thf(func_def_69, type, sK11: u > u > d > d > u).
% 2.43/1.84 thf(func_def_70, type, sK12: u > u > d > d > u).
% 2.43/1.84 thf(func_def_71, type, sK13: u > u > d > d > u).
% 2.43/1.84 thf(func_def_72, type, sK14: u > u > d > d > u).
% 2.43/1.84 thf(func_def_73, type, sK15: u > d > d > u > u).
% 2.43/1.84 thf(f323,plain,(
% 2.43/1.84 $false),
% 2.43/1.84 inference(avatar_sat_refutation,[status(thm)],[f294,f315,f322])).
% 2.43/1.84 thf(f322,plain,(
% 2.43/1.84 ~spl16_4),
% 2.43/1.84 inference(avatar_contradiction_clause,[status(thm)],[f321])).
% 2.43/1.84 thf(f321,plain,(
% 2.43/1.84 $false | ~spl16_4),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f320])).
% 2.43/1.84 thf(f320,plain,(
% 2.43/1.84 ($true = $false) | ~spl16_4),
% 2.43/1.84 inference(forward_demodulation,[status(thm)],[f318,f259])).
% 2.43/1.84 thf(f259,plain,(
% 2.43/1.84 ( ! [X0 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ X0)))))) = $false)) )),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f258])).
% 2.43/1.84 thf(f258,plain,(
% 2.43/1.84 ( ! [X0 : u] : (($true != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ X0)))))) = $false)) )),
% 2.43/1.84 inference(superposition,[status(thm)],[f230,f155])).
% 2.43/1.84 thf(f155,plain,(
% 2.43/1.84 ((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) @ sK0)))) = $true)),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f126])).
% 2.43/1.84 thf(f126,plain,(
% 2.43/1.84 ($true != (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) @ sK0)))) = $true) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X5))))))),
% 2.43/1.84 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f124,f125])).
% 2.43/1.84 thf(f125,plain,(
% 2.43/1.84 ? [X0 : u,X1 : d,X2 : d,X3 : u,X4 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X1) @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X4))))) & ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X1) @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X1 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X1 @ X5))))))) => (($true != (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) @ sK0)))) = $true) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X5)))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f124,plain,(
% 2.43/1.84 ? [X0 : u,X1 : d,X2 : d,X3 : u,X4 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X1) @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X4))))) & ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X1) @ X3) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0))))) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X1 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X1 @ X5)))))))),
% 2.43/1.84 inference(rectify,[status(thm)],[f119])).
% 2.43/1.84 thf(f119,plain,(
% 2.43/1.84 ? [X0 : u,X2 : d,X1 : d,X4 : u,X3 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))) != $true) & ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0))))) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X2 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X5)))))))),
% 2.43/1.84 inference(flattening,[status(thm)],[f118])).
% 2.43/1.84 thf(f118,plain,(
% 2.43/1.84 ? [X2 : d,X4 : u,X1 : d,X3 : u,X0 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))) != $true) & ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0)))))) & ! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X2 @ X5))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X5)))))))),
% 2.43/1.84 inference(ennf_transformation,[status(thm)],[f91])).
% 2.43/1.84 thf(f91,plain,(
% 2.43/1.84 ~! [X2 : d,X4 : u,X1 : d,X3 : u,X0 : u] : (! [X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X5))))) => ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X2 @ X5)))))) => (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))) = $true)))),
% 2.43/1.84 inference(fool_elimination,[status(thm)],[f90])).
% 2.43/1.84 thf(f90,plain,(
% 2.43/1.84 ~! [X0 : u,X1 : d,X2 : d,X3 : u,X4 : u] : (! [X5 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3) @ (s @ X2 @ X5)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X2 @ X5))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X2) @ X4) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))))),
% 2.43/1.84 inference(rectify,[status(thm)],[f52])).
% 2.43/1.84 thf(f52,negated_conjecture,(
% 2.43/1.84 ~! [X24 : u,X1 : d,X0 : d,X51 : u,X23 : u] : (! [X52 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X51) @ (s @ X0 @ X52)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X0 @ X52))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X23) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X24)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X23) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X51))))))),
% 2.43/1.84 inference(negated_conjecture,[status(cth)],[f51])).
% 2.43/1.84 thf(f51,conjecture,(
% 2.43/1.84 ! [X24 : u,X1 : d,X0 : d,X51 : u,X23 : u] : (! [X52 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X51) @ (s @ X0 @ X52)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X0 @ X52))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X23) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X24)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X23) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X51))))))),
% 2.43/1.84 file('/export/starexec/sandbox/tmp/tmp.xApQoegLFN/DTF2THF_6174.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT)).
% 2.43/1.84 thf(f230,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : d,X7 : u,X4 : u,X5 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X7)))))) = $false)) )),
% 2.43/1.84 inference(not_proxy_clausification,[status(thm)],[f171])).
% 2.43/1.84 thf(f171,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : d,X7 : u,X4 : u,X5 : u] : (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X7))))))) = $true) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4)))))) )),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f140])).
% 2.43/1.84 thf(f140,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (! [X4 : u,X5 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4))))) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ (sK5 @ X5 @ X4 @ X1 @ X0)))))))))) & (! [X7 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X7))))))) = $true) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4))))))) & ! [X8 : u,X9 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9))))) | (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ (sK6 @ X9 @ X8 @ X1 @ X0)))))) & ! [X11 : u] : ((s @ X0 @ (sK6 @ X9 @ X8 @ X1 @ X0)) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X11)))))) & (! [X12 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ X12))))) | ((s @ X0 @ X12) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ (sK7 @ X12 @ X8 @ X1 @ X0)))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9))))))) & ! [X14 : u,X15 : u] : ((! [X16 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ X16))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ (sK8 @ X15 @ X14 @ X1 @ X0))))))) != $true))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (sK9 @ X3 @ X2 @ X1 @ X0))))) = $true) & ! [X19 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X19)))))) != $true))) & (! [X20 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X20))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (sK10 @ X3 @ X2 @ X1 @ X0))))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) & (! [X22 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X22)))))) | ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (sK11 @ X3 @ X2 @ X1 @ X0)))))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) | (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (sK12 @ X3 @ X2 @ X1 @ X0)))))) = $true) & ! [X25 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X25)))))))))) & ! [X26 : u,X27 : u] : ((! [X28 : u] : (((s @ X0 @ X28) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ (sK13 @ X28 @ X26 @ X1 @ X0))))) | ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ X28))))) != $true)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27))))) | (! [X31 : u] : ((s @ X0 @ (sK14 @ X27 @ X26 @ X1 @ X0)) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X31)))) & ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ (sK14 @ X27 @ X26 @ X1 @ X0)))))))))))),
% 2.43/1.84 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f129,f139,f138,f137,f136,f135,f134,f133,f132,f131,f130])).
% 2.43/1.84 thf(f130,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X4 : u,X5 : u] : (? [X6 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X6)))))))) => ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ (sK5 @ X5 @ X4 @ X1 @ X0))))))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f131,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X8 : u,X9 : u] : (? [X10 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ X10))))) & ! [X11 : u] : ((s @ X0 @ X10) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X11))))) => (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ (sK6 @ X9 @ X8 @ X1 @ X0)))))) & ! [X11 : u] : ((s @ X0 @ (sK6 @ X9 @ X8 @ X1 @ X0)) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X11))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f132,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X8 : u,X12 : u] : (? [X13 : u] : ((s @ X0 @ X12) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X13)))) => ((s @ X0 @ X12) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ (sK7 @ X12 @ X8 @ X1 @ X0))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f133,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X14 : u,X15 : u] : (? [X17 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ X17))))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ (sK8 @ X15 @ X14 @ X1 @ X0))))))) != $true))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f134,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (? [X18 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X18))))) & ! [X19 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X19)))))) != $true)) => (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (sK9 @ X3 @ X2 @ X1 @ X0))))) = $true) & ! [X19 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X19)))))) != $true)))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f135,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (? [X21 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X21)))))) = $true) => ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (sK10 @ X3 @ X2 @ X1 @ X0)))))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f136,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (? [X23 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X23))))))) = $true) => ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (sK11 @ X3 @ X2 @ X1 @ X0))))))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f137,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (? [X24 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X24)))))) & ! [X25 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X25))))))))) => (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (sK12 @ X3 @ X2 @ X1 @ X0)))))) = $true) & ! [X25 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X25))))))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f138,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X26 : u,X28 : u] : (? [X29 : u] : ((s @ X0 @ X28) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X29)))) => ((s @ X0 @ X28) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ (sK13 @ X28 @ X26 @ X1 @ X0))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f139,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X26 : u,X27 : u] : (? [X30 : u] : (! [X31 : u] : ((s @ X0 @ X30) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X31)))) & ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ X30))))) = $true)) => (! [X31 : u] : ((s @ X0 @ (sK14 @ X27 @ X26 @ X1 @ X0)) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X31)))) & ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ (sK14 @ X27 @ X26 @ X1 @ X0)))))))))),
% 2.43/1.84 introduced(definition,[],[choice_axiom])).
% 2.43/1.84 thf(f129,plain,(
% 2.43/1.84 ! [X0 : d,X1 : d,X2 : u,X3 : u] : (! [X4 : u,X5 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4))))) | ? [X6 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X6))))))))) & (! [X7 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ X7))))))) = $true) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4))))))) & ! [X8 : u,X9 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9))))) | ? [X10 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ X10))))) & ! [X11 : u] : ((s @ X0 @ X10) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X11)))))) & (! [X12 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9) @ (s @ X0 @ X12))))) | ? [X13 : u] : ((s @ X0 @ X12) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ X1 @ X13))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X8) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X9))))))) & ! [X14 : u,X15 : u] : ((! [X16 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ X16))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))) | ? [X17 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X14) @ (s @ X1 @ X17))))))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) | ? [X18 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X18))))) & ! [X19 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X19)))))) != $true))) & (! [X20 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X20))))) | ? [X21 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X21)))))) = $true)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) & (! [X22 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X22)))))) | ? [X23 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X23))))))) = $true)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) | ? [X24 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X24)))))) & ! [X25 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X25)))))))))) & ! [X26 : u,X27 : u] : ((! [X28 : u] : (? [X29 : u] : ((s @ X0 @ X28) = (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X29)))) | ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ X28))))) != $true)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27))))) | ? [X30 : u] : (! [X31 : u] : ((s @ X0 @ X30) != (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X26) @ (s @ X1 @ X31)))) & ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X27) @ (s @ X0 @ X30))))) = $true)))))),
% 2.43/1.84 inference(rectify,[status(thm)],[f128])).
% 2.43/1.84 thf(f128,plain,(
% 2.43/1.84 ! [X3 : d,X0 : d,X1 : u,X2 : u] : (! [X19 : u,X20 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))) | ? [X21 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21))))))))) & (! [X21 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21)))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))))) & ! [X15 : u,X16 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) = $true) | ? [X17 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) & ! [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) != (s @ X3 @ X17)))) & (! [X17 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) | ? [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) = (s @ X3 @ X17))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) != $true))) & ! [X13 : u,X12 : u] : ((! [X14 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) != $true)) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) = $true) | ? [X14 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) | ? [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) = $true) & ! [X11 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11))))))))) & (! [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) != $true) | ? [X11 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11)))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))))) & (! [X4 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) | ? [X5 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5))))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) | ? [X4 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) & ! [X5 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5)))))))))) & ! [X7 : u,X6 : u] : ((! [X8 : u] : (? [X9 : u] : ((s @ X3 @ X8) = (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6))))) | ? [X8 : u] : (! [X9 : u] : ((s @ X3 @ X8) != (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))) & ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))))))))),
% 2.43/1.84 inference(flattening,[status(thm)],[f127])).
% 2.43/1.84 thf(f127,plain,(
% 2.43/1.84 ! [X3 : d,X0 : d,X1 : u,X2 : u] : (! [X19 : u,X20 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))) | ? [X21 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21))))))))) & (! [X21 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21)))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))))) & ! [X15 : u,X16 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) = $true) | ? [X17 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) & ! [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) != (s @ X3 @ X17)))) & (! [X17 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) | ? [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) = (s @ X3 @ X17))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) != $true))) & ! [X13 : u,X12 : u] : ((! [X14 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) != $true)) & (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) = $true) | ? [X14 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))))) & ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) | ? [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) = $true) & ! [X11 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11))))))))) & (! [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) != $true) | ? [X11 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11)))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))))) & ((! [X4 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) | ? [X5 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5))))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) | ? [X4 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) & ! [X5 : u] : ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5))))))))))) & ! [X7 : u,X6 : u] : ((! [X8 : u] : (? [X9 : u] : ((s @ X3 @ X8) = (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6)))))) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6))))) | ? [X8 : u] : (! [X9 : u] : ((s @ X3 @ X8) != (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))) & ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))))))))),
% 2.43/1.84 inference(nnf_transformation,[status(thm)],[f114])).
% 2.43/1.84 thf(f114,plain,(
% 2.43/1.84 ! [X3 : d,X0 : d,X1 : u,X2 : u] : (! [X19 : u,X20 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))) <=> ! [X21 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21))))))))) & ! [X15 : u,X16 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) = $true) <=> ! [X17 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) | ? [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) = (s @ X3 @ X17)))) & ! [X13 : u,X12 : u] : (! [X14 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))) <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) = $true)) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) <=> ! [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) != $true) | ? [X11 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11))))))))) & (! [X4 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) | ? [X5 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5))))))))) <=> ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))))) & ! [X7 : u,X6 : u] : (! [X8 : u] : (? [X9 : u] : ((s @ X3 @ X8) = (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))))) <=> ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6)))))))),
% 2.43/1.84 inference(ennf_transformation,[status(thm)],[f85])).
% 2.43/1.84 thf(f85,plain,(
% 2.43/1.84 ! [X1 : u,X2 : u,X3 : d,X0 : d] : ((! [X10 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) = $true) => ? [X11 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11)))))))) <=> ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))))) & ! [X19 : u,X20 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19))))) <=> ! [X21 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21))))))))) & ! [X16 : u,X15 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16)))) = $true) <=> ! [X17 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17))))) => ? [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) = (s @ X3 @ X17)))) & ! [X13 : u,X12 : u] : (! [X14 : u] : ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14))))))) <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12)))) = $true)) & (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) <=> ! [X4 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4)))))) => ? [X5 : u] : ($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5)))))))))) & ! [X7 : u,X6 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6))))) <=> ! [X8 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8)))))) => ? [X9 : u] : ((s @ X3 @ X8) = (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))))))),
% 2.43/1.84 inference(fool_elimination,[status(thm)],[f84])).
% 2.43/1.84 thf(f84,plain,(
% 2.43/1.84 ! [X0 : d,X1 : u,X2 : u,X3 : d] : ((! [X4 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X4))))) => ? [X5 : u] : (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X5)))))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) & ! [X6 : u,X7 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6)))) <=> ! [X8 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X6) @ (s @ X3 @ X8))))) => ? [X9 : u] : ((s @ X3 @ X8) = (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X7) @ (s @ X0 @ X9)))))) & (! [X10 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ X10)))) => ? [X11 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ X0 @ X11))))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X2) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1))))) & ! [X12 : u,X13 : u] : (! [X14 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ X0 @ X14)))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X13) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X12))))) & ! [X15 : u,X16 : u] : (! [X17 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16) @ (s @ X3 @ X17)))) => ? [X18 : u] : ((s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ X0 @ X18))) = (s @ X3 @ X17))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X15) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X16))))) & ! [X19 : u,X20 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19)))) <=> ! [X21 : u] : (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X19) @ (s @ X3 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X3) @ X20) @ (s @ X0 @ X21)))))))))),
% 2.43/1.84 inference(rectify,[status(thm)],[f39])).
% 2.43/1.84 thf(f39,axiom,(
% 2.43/1.84 ! [X0 : d,X24 : u,X23 : u,X1 : d] : ((! [X27 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X1 @ X27))))) => ? [X28 : u] : (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X23) @ (s @ X0 @ X28)))))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X23) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24))))) & ! [X40 : u,X39 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X39) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X40)))) <=> ! [X41 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X40) @ (s @ X1 @ X41))))) => ? [X42 : u] : ((s @ X1 @ X41) = (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X39) @ (s @ X0 @ X42)))))) & (! [X25 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X1 @ X25)))) => ? [X26 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24) @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X23) @ (s @ X0 @ X26))))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X23) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X24))))) & ! [X30 : u,X29 : u] : (! [X31 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X30) @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X29) @ (s @ X0 @ X31)))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X29) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X30))))) & ! [X35 : u,X36 : u] : (! [X37 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X36) @ (s @ X1 @ X37)))) => ? [X38 : u] : ((s @ X1 @ X37) = (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X35) @ (s @ X0 @ X38))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X35) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X36))))) & ! [X33 : u,X32 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X32) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X33)))) <=> ! [X34 : u] : (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X33) @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X32) @ (s @ X0 @ X34)))))))))),
% 2.43/1.84 file('/export/starexec/sandbox/tmp/tmp.xApQoegLFN/DTF2THF_6174.p',thm_2EquantHeuristics_2EGUESS__REWRITES)).
% 2.43/1.84 thf(f318,plain,(
% 2.43/1.84 ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1)))))))) | ~spl16_4),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 2.43/1.84 thf(f317,plain,(
% 2.43/1.84 ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1)))))))) | ($true != $true) | ~spl16_4),
% 2.43/1.84 inference(superposition,[status(thm)],[f154,f293])).
% 2.43/1.84 thf(f293,plain,(
% 2.43/1.84 ((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 @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1))))))) = $true) | ~spl16_4),
% 2.43/1.84 inference(avatar_component_clause,[status(thm)],[f291])).
% 2.43/1.84 thf(f291,definition,(
% 2.43/1.84 spl16_4 <=> ((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 @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1))))))) = $true)),
% 2.43/1.84 introduced(definition,[new_symbols(naming,[spl16_4])],[avatar_definition])).
% 2.43/1.84 thf(f154,plain,(
% 2.43/1.84 ( ! [X5 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X5))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK0) @ (s @ sK1 @ X5)))))) )),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f126])).
% 2.43/1.84 thf(f315,plain,(
% 2.43/1.84 ~spl16_3),
% 2.43/1.84 inference(avatar_contradiction_clause,[status(thm)],[f314])).
% 2.43/1.84 thf(f314,plain,(
% 2.43/1.84 $false | ~spl16_3),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f311])).
% 2.43/1.84 thf(f311,plain,(
% 2.43/1.84 ($true != $true) | ~spl16_3),
% 2.43/1.84 inference(superposition,[status(thm)],[f156,f301])).
% 2.43/1.84 thf(f301,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ sK1) @ X1) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4)))) = $true)) ) | ~spl16_3),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f300])).
% 2.43/1.84 thf(f300,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : u] : (($true != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ sK1) @ X1) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4)))) = $true)) ) | ~spl16_3),
% 2.43/1.84 inference(superposition,[status(thm)],[f289,f234])).
% 2.43/1.84 thf(f234,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : d,X4 : u,X5 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ (sK5 @ X5 @ X4 @ X1 @ X0)))))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4)))))) )),
% 2.43/1.84 inference(not_proxy_clausification,[status(thm)],[f172])).
% 2.43/1.84 thf(f172,plain,(
% 2.43/1.84 ( ! [X0 : d,X1 : d,X4 : u,X5 : u] : (($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ X1 @ (sK5 @ X5 @ X4 @ X1 @ X0))))))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X5) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X4)))))) )),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f140])).
% 2.43/1.84 thf(f289,plain,(
% 2.43/1.84 ( ! [X0 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X0)))))) ) | ~spl16_3),
% 2.43/1.84 inference(avatar_component_clause,[status(thm)],[f288])).
% 2.43/1.84 thf(f288,definition,(
% 2.43/1.84 spl16_3 <=> ! [X0 : u] : ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X0)))))),
% 2.43/1.84 introduced(definition,[new_symbols(naming,[spl16_3])],[avatar_definition])).
% 2.43/1.84 thf(f156,plain,(
% 2.43/1.84 ($true != (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)))))),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f126])).
% 2.43/1.84 thf(f294,plain,(
% 2.43/1.84 spl16_3 | spl16_4),
% 2.43/1.84 inference(avatar_split_clause,[status(thm)],[f286,f291,f288])).
% 2.43/1.84 thf(f286,plain,(
% 2.43/1.84 ( ! [X0 : u] : (((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 @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1))))))) = $true) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X0)))))) )),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 2.43/1.84 thf(f285,plain,(
% 2.43/1.84 ( ! [X0 : u] : (((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 @ sK2 @ sK1) @ sK3) @ (s @ sK2 @ (sK10 @ sK3 @ sK4 @ sK2 @ sK1))))))) = $true) | ($true != $true) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4) @ (s @ sK1 @ X0)))))) )),
% 2.43/1.84 inference(superposition,[status(thm)],[f163,f284])).
% 2.43/1.84 thf(f284,plain,(
% 2.43/1.84 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4)))) = $true)),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f281])).
% 2.43/1.84 thf(f281,plain,(
% 2.43/1.84 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ sK1) @ sK3) @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ sK4)))) = $true) | ($true != $true)),
% 2.43/1.84 inference(superposition,[status(thm)],[f156,f278])).
% 2.43/1.84 thf(f278,plain,(
% 2.43/1.84 ( ! [X2 : d,X3 : u,X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) )),
% 2.43/1.84 inference(trivial_inequality_removal,[status(thm)],[f273])).
% 2.43/1.84 thf(f273,plain,(
% 2.43/1.84 ( ! [X2 : d,X3 : u,X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ($true != $true) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) )),
% 2.43/1.84 inference(superposition,[status(thm)],[f164,f234])).
% 2.43/1.84 thf(f164,plain,(
% 2.43/1.84 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X19 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ X19)))))) != $true) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))))) )),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f140])).
% 2.43/1.84 thf(f163,plain,(
% 2.43/1.84 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X20 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2EquantHeuristics_2EGUESS__EXISTS_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ X20))))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ X0 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ X0) @ X3) @ (s @ X1 @ (sK10 @ X3 @ X2 @ X1 @ X0))))))))) )),
% 2.43/1.84 inference(cnf_transformation,[status(thm)],[f140])).
% 2.43/1.84 % SZS output end Proof for DTF2THF_6174
% 2.43/1.84 % (6292)------------------------------
% 2.43/1.84 % (6292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.84 % (6292)Termination reason: Refutation
% 2.43/1.84
% 2.43/1.84 % (6292)Memory used [KB]: 6524
% 2.43/1.84 % (6292)Time elapsed: 0.064 s
% 2.43/1.84 % (6292)Instructions burned: 98 (million)
% 2.43/1.84 % (6292)------------------------------
% 2.43/1.84 % (6292)------------------------------
% 2.43/1.84 % (6271)Success in time 0.145 s
%------------------------------------------------------------------------------