%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL941^5 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:43 AM UTC 2026
% Result : Theorem 50.06s 7.65s
% Output : Refutation 51.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_18,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_19,type,
inv: $i > $i ).
thf(func_def_20,type,
op: $i > $i > $i ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vAND: $o > $o > $o ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
vIFF: $o > $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
sK0: mworld ).
thf(func_def_40,type,
sK1: mworld > mworld ).
thf(func_def_41,type,
sK2: mworld > mworld ).
thf(func_def_42,type,
sK3: mworld > mworld ).
thf(func_def_43,type,
sK4: mworld ).
thf(func_def_44,type,
sK5: mworld > mworld ).
thf(func_def_45,type,
sK6: mworld > mworld ).
thf(func_def_46,type,
sK7: mworld > mworld ).
thf(func_def_47,type,
sK8: mworld > mworld ).
thf(func_def_48,type,
sK9: mworld ).
thf(func_def_49,type,
sK10: mworld > mworld ).
thf(func_def_50,type,
sK11: mworld > mworld ).
thf(func_def_51,type,
sK12: mworld > mworld ).
thf(func_def_52,type,
sK13: mworld > mworld ).
thf(func_def_53,type,
sK14: mworld ).
thf(func_def_54,type,
sK15: mworld ).
thf(func_def_55,type,
sK16: mworld ).
thf(func_def_56,type,
sK17: mworld > mworld ).
thf(func_def_57,type,
sK18: mworld > mworld ).
thf(func_def_58,type,
sK19: mworld > mworld ).
thf(func_def_59,type,
sK20: mworld > mworld ).
thf(func_def_60,type,
sK21: mworld ).
thf(func_def_61,type,
sK22: mworld > mworld ).
thf(func_def_62,type,
sK23: mworld > mworld ).
thf(func_def_63,type,
sK24: mworld > mworld ).
thf(func_def_64,type,
sK25: mworld > mworld ).
thf(func_def_65,type,
sK26: mworld > mworld ).
thf(func_def_66,type,
sK27: mworld ).
thf(func_def_67,type,
sK28: mworld ).
thf(func_def_68,type,
sK29: mworld > mworld ).
thf(func_def_69,type,
sK30: mworld ).
thf(func_def_70,type,
sK31: mworld ).
thf(func_def_71,type,
sK32: mworld ).
thf(func_def_72,type,
sK33: mworld > mworld ).
thf(func_def_73,type,
sK34: mworld > mworld ).
thf(func_def_74,type,
sK35: mworld ).
thf(func_def_75,type,
sK36: mworld ).
thf(func_def_76,type,
sK37: $i > mworld > $i > mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f10,axiom,
! [X2: mworld,X1: mworld,X0: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f30,conjecture,
mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(f31,negated_conjecture,
~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f51,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f57,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f65,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
& ( mrel @ X2 @ X0 ) )
=> ( mrel @ X0 @ X1 ) ),
inference(rectify,[],[f10]) ).
thf(f66,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f75,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f76,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f83,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f84,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f87,plain,
~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f88,plain,
( ( ~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f94,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f97,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f107,plain,
( ( ~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f110,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f66]) ).
thf(f115,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f117,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f131,plain,
( $true
= ( ~ ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f107,f117,f94,f115,f97,f115,f97,f115,f97,f97,f94,f115,f97,f115,f97,f115,f97,f97,f94,f115,f97,f115,f97,f115,f97,f97,f94,f115,f97,f115,f97,f115,f97,f97,f97,f95,f94,f115,f97,f115,f97,f115,f97,f97,f94,f115,f97,f115,f97,f115,f97,f97,f94,f115,f97,f115,f97,f115,f97,f97,f115,f97,f115,f97,f115,f97,f97]) ).
thf(f162,plain,
( $true
= ( ~ ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f185,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f186,plain,
! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( ( mrel @ X1 @ Y1 )
& ( mrel @ X1 @ Y0 ) )
=> ( mrel @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f197,plain,
( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f229,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( ( mrel @ X1 @ Y1 )
& ( mrel @ X1 @ Y0 ) )
=> ( mrel @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f230,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( ( mrel @ X1 @ Y0 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f244,plain,
( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f245,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f284,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( ( mrel @ X1 @ Y0 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f285,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( $true
= ( ( ( mrel @ X1 @ X3 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f302,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f245]) ).
thf(f303,plain,
( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f304,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f347,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ X1 @ X3 )
& ( mrel @ X1 @ X2 ) ) )
| ( $true
= ( mrel @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f367,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f368,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f304]) ).
thf(f370,plain,
( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f371,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f412,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( mrel @ X3 @ X2 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f347]) ).
thf(f435,plain,
( ( $false
= ( ( mrel @ mactual @ sK0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f368]) ).
thf(f436,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f369]) ).
thf(f437,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( mrel @ mactual @ sK4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f436]) ).
thf(f438,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f371]) ).
thf(f439,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f440,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f513,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f435]) ).
thf(f514,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f435]) ).
thf(f515,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f437]) ).
thf(f516,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f438]) ).
thf(f517,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f440]) ).
thf(f518,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) ) ) )
@ sK9 )
= $false ),
inference(sigma_proxy_clausification,[],[f439]) ).
thf(f519,plain,
( $false
= ( ( mrel @ mactual @ sK9 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f518]) ).
thf(f588,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f514]) ).
thf(f589,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f588]) ).
thf(f590,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f513]) ).
thf(f591,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ sK15 ) )
| ( $false
= ( ( mrel @ mactual @ sK4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f515]) ).
thf(f593,plain,
( ( $false
= ( ( mrel @ mactual @ sK4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f592]) ).
thf(f594,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f516]) ).
thf(f595,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ sK16 ) ) ),
inference(sigma_proxy_clausification,[],[f517]) ).
thf(f596,plain,
( ( ( ( mrel @ mactual @ sK16 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f595]) ).
thf(f597,plain,
( $false
= ( ~ ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f519]) ).
thf(f598,plain,
( $true
= ( mrel @ mactual @ sK9 ) ),
inference(imp_proxy_clausification,[],[f519]) ).
thf(f666,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f589]) ).
thf(f667,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f591]) ).
thf(f668,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f669,plain,
( ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f670,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ sK21 ) ) ),
inference(sigma_proxy_clausification,[],[f594]) ).
thf(f671,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(beta-eta_normalization,[],[f670]) ).
thf(f672,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f596]) ).
thf(f673,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f596]) ).
thf(f674,plain,
( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f597]) ).
thf(f749,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ sK27 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f666]) ).
thf(f750,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ) ),
inference(beta-eta_normalization,[],[f749]) ).
thf(f751,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f752,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f753,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f669]) ).
thf(f754,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f669]) ).
thf(f755,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f668]) ).
thf(f756,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ sK28 ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f671]) ).
thf(f757,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( ( mrel @ mactual @ sK28 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ) ),
inference(beta-eta_normalization,[],[f756]) ).
thf(f758,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f672]) ).
thf(f759,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f673]) ).
thf(f760,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f674]) ).
thf(f825,plain,
( ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ sK30 ) )
| ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f750]) ).
thf(f826,plain,
( ( $false
= ( ( mrel @ mactual @ sK14 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ) ),
inference(beta-eta_normalization,[],[f825]) ).
thf(f827,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ sK27 ) ) ),
inference(sigma_proxy_clausification,[],[f752]) ).
thf(f828,plain,
( ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f827]) ).
thf(f829,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ sK30 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f751]) ).
thf(f830,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f829]) ).
thf(f831,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f754]) ).
thf(f832,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f753]) ).
thf(f833,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ sK31 )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f755]) ).
thf(f834,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f833]) ).
thf(f835,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( ( mrel @ mactual @ sK28 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f757]) ).
thf(f836,plain,
( ( $false
= ( ( mrel @ mactual @ sK28 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(beta-eta_normalization,[],[f835]) ).
thf(f837,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f758]) ).
thf(f838,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f759]) ).
thf(f839,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f760]) ).
thf(f840,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f760]) ).
thf(f897,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ) ),
inference(imp_proxy_clausification,[],[f826]) ).
thf(f898,plain,
( ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f826]) ).
thf(f899,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ),
inference(imp_proxy_clausification,[],[f828]) ).
thf(f900,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f828]) ).
thf(f901,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f830]) ).
thf(f902,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( ( mrel @ mactual @ sK30 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f830]) ).
thf(f903,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f831]) ).
thf(f904,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $false
= ( ( mrel @ mactual @ sK35 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f903]) ).
thf(f905,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ sK31 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f832]) ).
thf(f906,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f905]) ).
thf(f907,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ sK35 ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f834]) ).
thf(f908,plain,
( ( $false
= ( ( mrel @ mactual @ sK35 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f907]) ).
thf(f909,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f836]) ).
thf(f910,plain,
( ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f836]) ).
thf(f911,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ sK36 ) ) ),
inference(sigma_proxy_clausification,[],[f837]) ).
thf(f912,plain,
( ( $false
= ( ( mrel @ mactual @ sK36 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f911]) ).
thf(f913,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ sK36 ) ) ),
inference(sigma_proxy_clausification,[],[f838]) ).
thf(f914,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK36 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(beta-eta_normalization,[],[f913]) ).
thf(f915,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f840]) ).
thf(f916,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f840]) ).
thf(f917,plain,
! [X1: mworld] :
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f839]) ).
thf(f918,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f917]) ).
thf(f977,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) ),
inference(imp_proxy_clausification,[],[f898]) ).
thf(f978,plain,
( ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( ( mrel @ mactual @ sK30 )
= $true )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f898]) ).
thf(f979,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f897]) ).
thf(f980,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( ( mrel @ mactual @ sK30 )
= $true )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f897]) ).
thf(f981,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f899]) ).
thf(f982,plain,
( ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f981]) ).
thf(f983,plain,
( ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ sK30 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f900]) ).
thf(f984,plain,
( ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( ( mrel @ mactual @ sK30 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f983]) ).
thf(f985,plain,
( ( ( mrel @ mactual @ sK30 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f902]) ).
thf(f986,plain,
( ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( ( mrel @ mactual @ sK30 )
= $true ) ),
inference(beta-eta_normalization,[],[f985]) ).
thf(f987,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ sK27 ) ) ),
inference(sigma_proxy_clausification,[],[f901]) ).
thf(f988,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( ( mrel @ mactual @ sK27 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) ),
inference(beta-eta_normalization,[],[f987]) ).
thf(f989,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) ),
inference(imp_proxy_clausification,[],[f904]) ).
thf(f990,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK35 ) ) ),
inference(imp_proxy_clausification,[],[f904]) ).
thf(f991,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(sigma_proxy_clausification,[],[f906]) ).
thf(f992,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( ( mrel @ mactual @ sK35 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) ) ),
inference(beta-eta_normalization,[],[f991]) ).
thf(f993,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f908]) ).
thf(f994,plain,
( ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f908]) ).
thf(f995,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f909]) ).
thf(f996,plain,
( ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f909]) ).
thf(f997,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f910]) ).
thf(f998,plain,
( ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f910]) ).
thf(f999,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f912]) ).
thf(f1000,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true ) ),
inference(imp_proxy_clausification,[],[f912]) ).
thf(f1001,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK36 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f914]) ).
thf(f1002,plain,
( ( $false
= ( ( mrel @ mactual @ sK36 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1001]) ).
thf(f1003,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f916]) ).
thf(f1004,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f915]) ).
thf(f1005,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f918]) ).
thf(f1082,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ),
inference(imp_proxy_clausification,[],[f977]) ).
thf(f1083,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f977]) ).
thf(f1084,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( ( mrel @ mactual @ sK30 )
= $true )
| ( $true
= ( mrel @ mactual @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f1085,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( ( mrel @ mactual @ sK30 )
= $true ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f1086,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( ( mrel @ mactual @ sK30 )
= $true ) ),
inference(imp_proxy_clausification,[],[f980]) ).
thf(f1087,plain,
( ( ( mrel @ mactual @ sK30 )
= $true )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f980]) ).
thf(f1088,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ),
inference(imp_proxy_clausification,[],[f979]) ).
thf(f1089,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $true
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $true
= ( mrel @ mactual @ sK27 ) ) ),
inference(imp_proxy_clausification,[],[f979]) ).
thf(f1090,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ),
inference(imp_proxy_clausification,[],[f982]) ).
thf(f1091,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) )
| ( ( mrel @ mactual @ sK30 )
= $true ) ),
inference(imp_proxy_clausification,[],[f982]) ).
thf(f1092,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f984]) ).
thf(f1093,plain,
( ( ( mrel @ mactual @ sK30 )
= $true )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ( $true
= ( mrel @ mactual @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f984]) ).
thf(f1094,plain,
( ( ( mrel @ mactual @ sK30 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f986]) ).
thf(f1095,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( ( mrel @ mactual @ sK30 )
= $true )
| ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f986]) ).
thf(f1096,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f988]) ).
thf(f1097,plain,
( ( $true
= ( mrel @ mactual @ sK27 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f988]) ).
thf(f1098,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ sK31 )
= $false )
| ( $true
= ( mrel @ mactual @ sK35 ) ) ),
inference(sigma_proxy_clausification,[],[f990]) ).
thf(f1099,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(beta-eta_normalization,[],[f1098]) ).
thf(f1100,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ sK31 )
= $false )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(sigma_proxy_clausification,[],[f989]) ).
thf(f1101,plain,
( ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f1100]) ).
thf(f1102,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $false
= ( ( mrel @ mactual @ sK35 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) ) ),
inference(imp_proxy_clausification,[],[f992]) ).
thf(f1103,plain,
( ( $false
= ( ( mrel @ mactual @ sK35 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( ( mrel @ mactual @ sK31 )
= $true ) ),
inference(imp_proxy_clausification,[],[f992]) ).
thf(f1104,plain,
( ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) ) ),
inference(imp_proxy_clausification,[],[f994]) ).
thf(f1105,plain,
( ( $true
= ( mrel @ mactual @ sK35 ) )
| ( ( mrel @ mactual @ sK31 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( ( mrel @ mactual @ sK15 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ) ),
inference(imp_proxy_clausification,[],[f994]) ).
thf(f1106,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f993]) ).
thf(f1107,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( ( ( mrel @ mactual @ sK31 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f993]) ).
thf(f1108,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(sigma_proxy_clausification,[],[f995]) ).
thf(f1109,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(beta-eta_normalization,[],[f1108]) ).
thf(f1110,plain,
( ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(sigma_proxy_clausification,[],[f996]) ).
thf(f1111,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(beta-eta_normalization,[],[f1110]) ).
thf(f1112,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f998]) ).
thf(f1113,plain,
( ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f998]) ).
thf(f1114,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(sigma_proxy_clausification,[],[f997]) ).
thf(f1115,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(beta-eta_normalization,[],[f1114]) ).
thf(f1116,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1000]) ).
thf(f1117,plain,
( ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1116]) ).
thf(f1118,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(sigma_proxy_clausification,[],[f999]) ).
thf(f1119,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1118]) ).
thf(f1120,plain,
( ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1002]) ).
thf(f1121,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1002]) ).
thf(f1122,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1003]) ).
thf(f1123,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1003]) ).
thf(f1124,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1004]) ).
thf(f1125,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1004]) ).
thf(f1126,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f1005]) ).
thf(f1196,definition,
( spl38_9
<=> ( $true
= ( mrel @ mactual @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_9])],[avatar_definition]) ).
thf(f1197,plain,
( ( $true
= ( mrel @ mactual @ sK14 ) )
| ~ spl38_9 ),
inference(avatar_component_clause,[],[f1196]) ).
thf(f1199,definition,
( spl38_10
<=> ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_10])],[avatar_definition]) ).
thf(f1200,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK30 ) )
| ~ spl38_10 ),
inference(avatar_component_clause,[],[f1199]) ).
thf(f1202,definition,
( spl38_11
<=> ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_11])],[avatar_definition]) ).
thf(f1203,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK27 ) )
| ~ spl38_11 ),
inference(avatar_component_clause,[],[f1202]) ).
thf(f1205,definition,
( spl38_12
<=> ( $true
= ( mrel @ mactual @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_12])],[avatar_definition]) ).
thf(f1206,plain,
( ( $true
= ( mrel @ mactual @ sK0 ) )
| ~ spl38_12 ),
inference(avatar_component_clause,[],[f1205]) ).
thf(f1207,plain,
( spl38_9
| spl38_10
| spl38_11
| spl38_12 ),
inference(avatar_split_clause,[],[f1082,f1205,f1202,f1199,f1196]) ).
thf(f1209,definition,
( spl38_13
<=> ( $true
= ( mrel @ mactual @ sK27 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_13])],[avatar_definition]) ).
thf(f1210,plain,
( ( $true
= ( mrel @ mactual @ sK27 ) )
| ~ spl38_13 ),
inference(avatar_component_clause,[],[f1209]) ).
thf(f1211,plain,
( spl38_13
| spl38_9
| spl38_12
| spl38_10 ),
inference(avatar_split_clause,[],[f1083,f1199,f1205,f1196,f1209]) ).
thf(f1213,definition,
( spl38_14
<=> ( ( mrel @ mactual @ sK30 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl38_14])],[avatar_definition]) ).
thf(f1214,plain,
( ( ( mrel @ mactual @ sK30 )
= $true )
| ~ spl38_14 ),
inference(avatar_component_clause,[],[f1213]) ).
thf(f1215,plain,
( spl38_14
| spl38_12
| spl38_9
| spl38_13 ),
inference(avatar_split_clause,[],[f1085,f1209,f1196,f1205,f1213]) ).
thf(f1216,plain,
( spl38_12
| spl38_11
| spl38_9
| spl38_14 ),
inference(avatar_split_clause,[],[f1084,f1213,f1196,f1202,f1205]) ).
thf(f1218,definition,
( spl38_15
<=> ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_15])],[avatar_definition]) ).
thf(f1219,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK14 ) )
| ~ spl38_15 ),
inference(avatar_component_clause,[],[f1218]) ).
thf(f1220,plain,
( spl38_12
| spl38_14
| spl38_11
| spl38_15 ),
inference(avatar_split_clause,[],[f1086,f1218,f1202,f1213,f1205]) ).
thf(f1221,plain,
( spl38_12
| spl38_14
| spl38_15
| spl38_13 ),
inference(avatar_split_clause,[],[f1087,f1209,f1218,f1213,f1205]) ).
thf(f1222,plain,
( spl38_11
| spl38_15
| spl38_10
| spl38_12 ),
inference(avatar_split_clause,[],[f1088,f1205,f1199,f1218,f1202]) ).
thf(f1223,plain,
( spl38_13
| spl38_15
| spl38_10
| spl38_12 ),
inference(avatar_split_clause,[],[f1089,f1205,f1199,f1218,f1209]) ).
thf(f1225,definition,
( spl38_16
<=> ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_16])],[avatar_definition]) ).
thf(f1226,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK0 ) )
| ~ spl38_16 ),
inference(avatar_component_clause,[],[f1225]) ).
thf(f1227,plain,
( spl38_11
| spl38_16
| spl38_14
| spl38_9 ),
inference(avatar_split_clause,[],[f1091,f1196,f1213,f1225,f1202]) ).
thf(f1228,plain,
( spl38_11
| spl38_16
| spl38_9
| spl38_10 ),
inference(avatar_split_clause,[],[f1090,f1199,f1196,f1225,f1202]) ).
thf(f1229,plain,
( spl38_14
| spl38_16
| spl38_9
| spl38_13 ),
inference(avatar_split_clause,[],[f1093,f1209,f1196,f1225,f1213]) ).
thf(f1230,plain,
( spl38_9
| spl38_16
| spl38_13
| spl38_10 ),
inference(avatar_split_clause,[],[f1092,f1199,f1209,f1225,f1196]) ).
thf(f1231,plain,
( spl38_16
| spl38_13
| spl38_15
| spl38_14 ),
inference(avatar_split_clause,[],[f1095,f1213,f1218,f1209,f1225]) ).
thf(f1232,plain,
( spl38_11
| spl38_16
| spl38_14
| spl38_15 ),
inference(avatar_split_clause,[],[f1094,f1218,f1213,f1225,f1202]) ).
thf(f1233,plain,
( spl38_11
| spl38_16
| spl38_10
| spl38_15 ),
inference(avatar_split_clause,[],[f1096,f1218,f1199,f1225,f1202]) ).
thf(f1234,plain,
( spl38_15
| spl38_13
| spl38_16
| spl38_10 ),
inference(avatar_split_clause,[],[f1097,f1199,f1225,f1209,f1218]) ).
thf(f1235,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) ) ),
inference(imp_proxy_clausification,[],[f1099]) ).
thf(f1236,plain,
( ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( ( mrel @ mactual @ sK31 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1099]) ).
thf(f1237,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1101]) ).
thf(f1238,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( ( mrel @ mactual @ sK31 )
= $true )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f1101]) ).
thf(f1239,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1102]) ).
thf(f1240,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f1102]) ).
thf(f1241,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( ( mrel @ mactual @ sK31 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1103]) ).
thf(f1242,plain,
( ( ( mrel @ mactual @ sK31 )
= $true )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1103]) ).
thf(f1243,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1104]) ).
thf(f1244,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) ) ),
inference(imp_proxy_clausification,[],[f1104]) ).
thf(f1245,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( ( mrel @ mactual @ sK31 )
= $true )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1105]) ).
thf(f1246,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( ( mrel @ mactual @ sK31 )
= $true )
| ( $true
= ( mrel @ mactual @ sK35 ) )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1105]) ).
thf(f1247,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) ) ),
inference(imp_proxy_clausification,[],[f1106]) ).
thf(f1248,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( ( mrel @ mactual @ sK31 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1106]) ).
thf(f1249,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f1107]) ).
thf(f1250,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ( ( mrel @ mactual @ sK31 )
= $true )
| ( $true
= ( mrel @ mactual @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f1107]) ).
thf(f1251,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f1109]) ).
thf(f1252,plain,
( ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1109]) ).
thf(f1253,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(imp_proxy_clausification,[],[f1111]) ).
thf(f1254,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( ( mrel @ mactual @ sK21 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ) ),
inference(imp_proxy_clausification,[],[f1111]) ).
thf(f1255,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(sigma_proxy_clausification,[],[f1112]) ).
thf(f1256,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(beta-eta_normalization,[],[f1255]) ).
thf(f1257,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK32 ) ) ),
inference(sigma_proxy_clausification,[],[f1113]) ).
thf(f1258,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) )
| ( $true
= ( mrel @ mactual @ sK32 ) ) ),
inference(beta-eta_normalization,[],[f1257]) ).
thf(f1259,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1115]) ).
thf(f1260,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( ( ( mrel @ mactual @ sK32 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1115]) ).
thf(f1261,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1117]) ).
thf(f1262,plain,
( ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true ) ),
inference(beta-eta_normalization,[],[f1261]) ).
thf(f1263,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1119]) ).
thf(f1264,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1263]) ).
thf(f1265,plain,
( ( ( mrel @ mactual @ sK36 )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1121]) ).
thf(f1266,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1121]) ).
thf(f1267,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1120]) ).
thf(f1268,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f1120]) ).
thf(f1269,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1122]) ).
thf(f1270,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1123]) ).
thf(f1271,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1123]) ).
thf(f1272,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1124]) ).
thf(f1273,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1272]) ).
thf(f1274,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1125]) ).
thf(f1275,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1126]) ).
thf(f1351,definition,
( spl38_21
<=> ( $true
= ( mrel @ mactual @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_21])],[avatar_definition]) ).
thf(f1352,plain,
( ( $true
= ( mrel @ mactual @ sK15 ) )
| ~ spl38_21 ),
inference(avatar_component_clause,[],[f1351]) ).
thf(f1354,definition,
( spl38_22
<=> ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_22])],[avatar_definition]) ).
thf(f1355,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
| ~ spl38_22 ),
inference(avatar_component_clause,[],[f1354]) ).
thf(f1357,definition,
( spl38_23
<=> ( $true
= ( mrel @ mactual @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_23])],[avatar_definition]) ).
thf(f1358,plain,
( ( $true
= ( mrel @ mactual @ sK4 ) )
| ~ spl38_23 ),
inference(avatar_component_clause,[],[f1357]) ).
thf(f1360,definition,
( spl38_24
<=> ( $true
= ( mrel @ mactual @ sK35 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_24])],[avatar_definition]) ).
thf(f1361,plain,
( ( $true
= ( mrel @ mactual @ sK35 ) )
| ~ spl38_24 ),
inference(avatar_component_clause,[],[f1360]) ).
thf(f1362,plain,
( spl38_21
| spl38_22
| spl38_23
| spl38_24 ),
inference(avatar_split_clause,[],[f1235,f1360,f1357,f1354,f1351]) ).
thf(f1364,definition,
( spl38_25
<=> ( ( mrel @ mactual @ sK31 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl38_25])],[avatar_definition]) ).
thf(f1365,plain,
( ( ( mrel @ mactual @ sK31 )
= $true )
| ~ spl38_25 ),
inference(avatar_component_clause,[],[f1364]) ).
thf(f1366,plain,
( spl38_24
| spl38_21
| spl38_25
| spl38_23 ),
inference(avatar_split_clause,[],[f1236,f1357,f1364,f1351,f1360]) ).
thf(f1368,definition,
( spl38_26
<=> ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_26])],[avatar_definition]) ).
thf(f1369,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK35 ) )
| ~ spl38_26 ),
inference(avatar_component_clause,[],[f1368]) ).
thf(f1370,plain,
( spl38_21
| spl38_23
| spl38_25
| spl38_26 ),
inference(avatar_split_clause,[],[f1238,f1368,f1364,f1357,f1351]) ).
thf(f1371,plain,
( spl38_23
| spl38_22
| spl38_21
| spl38_26 ),
inference(avatar_split_clause,[],[f1237,f1368,f1351,f1354,f1357]) ).
thf(f1373,definition,
( spl38_27
<=> ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_27])],[avatar_definition]) ).
thf(f1374,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK15 ) )
| ~ spl38_27 ),
inference(avatar_component_clause,[],[f1373]) ).
thf(f1375,plain,
( spl38_23
| spl38_27
| spl38_22
| spl38_24 ),
inference(avatar_split_clause,[],[f1240,f1360,f1354,f1373,f1357]) ).
thf(f1376,plain,
( spl38_27
| spl38_23
| spl38_26
| spl38_22 ),
inference(avatar_split_clause,[],[f1239,f1354,f1368,f1357,f1373]) ).
thf(f1377,plain,
( spl38_24
| spl38_23
| spl38_25
| spl38_27 ),
inference(avatar_split_clause,[],[f1242,f1373,f1364,f1357,f1360]) ).
thf(f1378,plain,
( spl38_26
| spl38_27
| spl38_25
| spl38_23 ),
inference(avatar_split_clause,[],[f1241,f1357,f1364,f1373,f1368]) ).
thf(f1380,definition,
( spl38_28
<=> ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_28])],[avatar_definition]) ).
thf(f1381,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK4 ) )
| ~ spl38_28 ),
inference(avatar_component_clause,[],[f1380]) ).
thf(f1382,plain,
( spl38_22
| spl38_24
| spl38_28
| spl38_27 ),
inference(avatar_split_clause,[],[f1243,f1373,f1380,f1360,f1354]) ).
thf(f1383,plain,
( spl38_28
| spl38_22
| spl38_21
| spl38_24 ),
inference(avatar_split_clause,[],[f1244,f1360,f1351,f1354,f1380]) ).
thf(f1384,plain,
( spl38_28
| spl38_21
| spl38_25
| spl38_24 ),
inference(avatar_split_clause,[],[f1246,f1360,f1364,f1351,f1380]) ).
thf(f1385,plain,
( spl38_25
| spl38_24
| spl38_28
| spl38_27 ),
inference(avatar_split_clause,[],[f1245,f1373,f1380,f1360,f1364]) ).
thf(f1386,plain,
( spl38_26
| spl38_22
| spl38_27
| spl38_28 ),
inference(avatar_split_clause,[],[f1247,f1380,f1373,f1354,f1368]) ).
thf(f1387,plain,
( spl38_25
| spl38_27
| spl38_26
| spl38_28 ),
inference(avatar_split_clause,[],[f1248,f1380,f1368,f1373,f1364]) ).
thf(f1388,plain,
( spl38_26
| spl38_25
| spl38_28
| spl38_21 ),
inference(avatar_split_clause,[],[f1250,f1351,f1380,f1364,f1368]) ).
thf(f1389,plain,
( spl38_26
| spl38_22
| spl38_28
| spl38_21 ),
inference(avatar_split_clause,[],[f1249,f1351,f1380,f1354,f1368]) ).
thf(f1390,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
inference(imp_proxy_clausification,[],[f1252]) ).
thf(f1391,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1252]) ).
thf(f1392,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1251]) ).
thf(f1393,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1251]) ).
thf(f1394,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
inference(imp_proxy_clausification,[],[f1254]) ).
thf(f1395,plain,
( ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1254]) ).
thf(f1396,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f1253]) ).
thf(f1397,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) ) ),
inference(imp_proxy_clausification,[],[f1253]) ).
thf(f1398,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1256]) ).
thf(f1399,plain,
( ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) ) ),
inference(imp_proxy_clausification,[],[f1256]) ).
thf(f1400,plain,
( ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1258]) ).
thf(f1401,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f1258]) ).
thf(f1402,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
inference(imp_proxy_clausification,[],[f1260]) ).
thf(f1403,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
inference(imp_proxy_clausification,[],[f1260]) ).
thf(f1404,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f1259]) ).
thf(f1405,plain,
( ( $true
= ( mrel @ mactual @ sK32 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ( $true
= ( mrel @ mactual @ sK28 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1259]) ).
thf(f1406,plain,
( ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1262]) ).
thf(f1407,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1262]) ).
thf(f1408,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f1264]) ).
thf(f1409,plain,
( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1264]) ).
thf(f1410,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1265]) ).
thf(f1411,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true ) ),
inference(beta-eta_normalization,[],[f1410]) ).
thf(f1412,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1266]) ).
thf(f1413,plain,
( ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(beta-eta_normalization,[],[f1412]) ).
thf(f1414,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1267]) ).
thf(f1415,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(beta-eta_normalization,[],[f1414]) ).
thf(f1416,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f1268]) ).
thf(f1417,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
= $false )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(beta-eta_normalization,[],[f1416]) ).
thf(f1418,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1269]) ).
thf(f1419,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1269]) ).
thf(f1420,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1270]) ).
thf(f1421,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1420]) ).
thf(f1422,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1271]) ).
thf(f1423,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1422]) ).
thf(f1424,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1273]) ).
thf(f1425,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1274]) ).
thf(f1426,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1274]) ).
thf(f1427,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1275]) ).
thf(f1428,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1275]) ).
thf(f1502,definition,
( spl38_33
<=> ( $true
= ( mrel @ mactual @ sK21 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_33])],[avatar_definition]) ).
thf(f1503,plain,
( ( $true
= ( mrel @ mactual @ sK21 ) )
| ~ spl38_33 ),
inference(avatar_component_clause,[],[f1502]) ).
thf(f1505,definition,
( spl38_34
<=> ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_34])],[avatar_definition]) ).
thf(f1506,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ~ spl38_34 ),
inference(avatar_component_clause,[],[f1505]) ).
thf(f1508,definition,
( spl38_35
<=> ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_35])],[avatar_definition]) ).
thf(f1509,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK28 ) )
| ~ spl38_35 ),
inference(avatar_component_clause,[],[f1508]) ).
thf(f1511,definition,
( spl38_36
<=> ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_36])],[avatar_definition]) ).
thf(f1512,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK32 ) )
| ~ spl38_36 ),
inference(avatar_component_clause,[],[f1511]) ).
thf(f1513,plain,
( spl38_33
| spl38_34
| spl38_35
| spl38_36 ),
inference(avatar_split_clause,[],[f1391,f1511,f1508,f1505,f1502]) ).
thf(f1515,definition,
( spl38_37
<=> ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_37])],[avatar_definition]) ).
thf(f1516,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
| ~ spl38_37 ),
inference(avatar_component_clause,[],[f1515]) ).
thf(f1517,plain,
( spl38_34
| spl38_35
| spl38_36
| spl38_37 ),
inference(avatar_split_clause,[],[f1390,f1515,f1511,f1508,f1505]) ).
thf(f1519,definition,
( spl38_38
<=> ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_38])],[avatar_definition]) ).
thf(f1520,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ~ spl38_38 ),
inference(avatar_component_clause,[],[f1519]) ).
thf(f1521,plain,
( spl38_35
| spl38_36
| spl38_38
| spl38_37 ),
inference(avatar_split_clause,[],[f1392,f1515,f1519,f1511,f1508]) ).
thf(f1522,plain,
( spl38_36
| spl38_33
| spl38_35
| spl38_38 ),
inference(avatar_split_clause,[],[f1393,f1519,f1508,f1502,f1511]) ).
thf(f1524,definition,
( spl38_39
<=> ( $true
= ( mrel @ mactual @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_39])],[avatar_definition]) ).
thf(f1525,plain,
( ( $true
= ( mrel @ mactual @ sK32 ) )
| ~ spl38_39 ),
inference(avatar_component_clause,[],[f1524]) ).
thf(f1526,plain,
( spl38_34
| spl38_39
| spl38_33
| spl38_35 ),
inference(avatar_split_clause,[],[f1395,f1508,f1502,f1524,f1505]) ).
thf(f1527,plain,
( spl38_39
| spl38_37
| spl38_35
| spl38_34 ),
inference(avatar_split_clause,[],[f1394,f1505,f1508,f1515,f1524]) ).
thf(f1528,plain,
( spl38_39
| spl38_38
| spl38_35
| spl38_37 ),
inference(avatar_split_clause,[],[f1396,f1515,f1508,f1519,f1524]) ).
thf(f1529,plain,
( spl38_33
| spl38_39
| spl38_38
| spl38_35 ),
inference(avatar_split_clause,[],[f1397,f1508,f1519,f1524,f1502]) ).
thf(f1531,definition,
( spl38_40
<=> ( $true
= ( mrel @ mactual @ sK28 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_40])],[avatar_definition]) ).
thf(f1532,plain,
( ( $true
= ( mrel @ mactual @ sK28 ) )
| ~ spl38_40 ),
inference(avatar_component_clause,[],[f1531]) ).
thf(f1533,plain,
( spl38_40
| spl38_38
| spl38_33
| spl38_36 ),
inference(avatar_split_clause,[],[f1398,f1511,f1502,f1519,f1531]) ).
thf(f1534,plain,
( spl38_40
| spl38_36
| spl38_34
| spl38_33 ),
inference(avatar_split_clause,[],[f1399,f1502,f1505,f1511,f1531]) ).
thf(f1535,plain,
( spl38_39
| spl38_40
| spl38_38
| spl38_33 ),
inference(avatar_split_clause,[],[f1400,f1502,f1519,f1531,f1524]) ).
thf(f1536,plain,
( spl38_39
| spl38_33
| spl38_40
| spl38_34 ),
inference(avatar_split_clause,[],[f1401,f1505,f1531,f1502,f1524]) ).
thf(f1537,plain,
( spl38_37
| spl38_34
| spl38_39
| spl38_40 ),
inference(avatar_split_clause,[],[f1403,f1531,f1524,f1505,f1515]) ).
thf(f1538,plain,
( spl38_40
| spl38_34
| spl38_37
| spl38_36 ),
inference(avatar_split_clause,[],[f1402,f1511,f1515,f1505,f1531]) ).
thf(f1539,plain,
( spl38_39
| spl38_37
| spl38_40
| spl38_38 ),
inference(avatar_split_clause,[],[f1405,f1519,f1531,f1515,f1524]) ).
thf(f1540,plain,
( spl38_40
| spl38_36
| spl38_37
| spl38_38 ),
inference(avatar_split_clause,[],[f1404,f1519,f1515,f1511,f1531]) ).
thf(f1541,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f1406]) ).
thf(f1542,plain,
( ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1406]) ).
thf(f1543,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1407]) ).
thf(f1544,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ sK36 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1407]) ).
thf(f1545,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f1408]) ).
thf(f1546,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f1408]) ).
thf(f1547,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1409]) ).
thf(f1548,plain,
( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1409]) ).
thf(f1549,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1411]) ).
thf(f1550,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1411]) ).
thf(f1551,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1413]) ).
thf(f1552,plain,
( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( ( mrel @ mactual @ sK36 )
= $true )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1413]) ).
thf(f1553,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1415]) ).
thf(f1554,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1415]) ).
thf(f1555,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( ( mrel @ mactual @ sK16 )
= $true )
| ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f1417]) ).
thf(f1556,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ( ( mrel @ mactual @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1417]) ).
thf(f1557,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1418]) ).
thf(f1558,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1557]) ).
thf(f1559,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1419]) ).
thf(f1560,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1419]) ).
thf(f1561,plain,
! [X1: mworld] :
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1421]) ).
thf(f1562,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1423]) ).
thf(f1563,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1424]) ).
thf(f1564,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1563]) ).
thf(f1565,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1425]) ).
thf(f1566,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1565]) ).
thf(f1567,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1426]) ).
thf(f1568,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1426]) ).
thf(f1569,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1428]) ).
thf(f1570,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1428]) ).
thf(f1571,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1427]) ).
thf(f1572,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1571]) ).
thf(f1636,definition,
( spl38_45
<=> ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_45])],[avatar_definition]) ).
thf(f1637,plain,
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK16 ) )
| ~ spl38_45 ),
inference(avatar_component_clause,[],[f1636]) ).
thf(f1639,definition,
( spl38_46
<=> ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_46])],[avatar_definition]) ).
thf(f1640,plain,
( ( $true
= ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ~ spl38_46 ),
inference(avatar_component_clause,[],[f1639]) ).
thf(f1642,definition,
( spl38_47
<=> ( ( mrel @ mactual @ sK36 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl38_47])],[avatar_definition]) ).
thf(f1643,plain,
( ( ( mrel @ mactual @ sK36 )
= $true )
| ~ spl38_47 ),
inference(avatar_component_clause,[],[f1642]) ).
thf(f1645,definition,
( spl38_48
<=> ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_48])],[avatar_definition]) ).
thf(f1646,plain,
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ~ spl38_48 ),
inference(avatar_component_clause,[],[f1645]) ).
thf(f1647,plain,
( spl38_45
| spl38_46
| spl38_47
| spl38_48 ),
inference(avatar_split_clause,[],[f1542,f1645,f1642,f1639,f1636]) ).
thf(f1649,definition,
( spl38_49
<=> ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_49])],[avatar_definition]) ).
thf(f1650,plain,
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ~ spl38_49 ),
inference(avatar_component_clause,[],[f1649]) ).
thf(f1651,plain,
( spl38_47
| spl38_48
| spl38_45
| spl38_49 ),
inference(avatar_split_clause,[],[f1541,f1649,f1636,f1645,f1642]) ).
thf(f1653,definition,
( spl38_50
<=> ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl38_50])],[avatar_definition]) ).
thf(f1654,plain,
( ( ( mrel @ mactual @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) )
= $true )
| ~ spl38_50 ),
inference(avatar_component_clause,[],[f1653]) ).
thf(f1655,plain,
( spl38_50
| spl38_47
| spl38_46
| spl38_45 ),
inference(avatar_split_clause,[],[f1544,f1636,f1639,f1642,f1653]) ).
thf(f1656,plain,
( spl38_45
| spl38_50
| spl38_49
| spl38_47 ),
inference(avatar_split_clause,[],[f1543,f1642,f1649,f1653,f1636]) ).
thf(f1658,definition,
( spl38_51
<=> ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) ) ),
introduced(definition,[new_symbols(definition,[spl38_51])],[avatar_definition]) ).
thf(f1659,plain,
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK36 ) )
| ~ spl38_51 ),
inference(avatar_component_clause,[],[f1658]) ).
thf(f1660,plain,
( spl38_48
| spl38_49
| spl38_45
| spl38_51 ),
inference(avatar_split_clause,[],[f1545,f1658,f1636,f1649,f1645]) ).
thf(f1661,plain,
( spl38_45
| spl38_46
| spl38_48
| spl38_51 ),
inference(avatar_split_clause,[],[f1546,f1658,f1645,f1639,f1636]) ).
thf(f1662,plain,
( spl38_45
| spl38_50
| spl38_51
| spl38_46 ),
inference(avatar_split_clause,[],[f1548,f1639,f1658,f1653,f1636]) ).
thf(f1663,plain,
( spl38_51
| spl38_50
| spl38_45
| spl38_49 ),
inference(avatar_split_clause,[],[f1547,f1649,f1636,f1653,f1658]) ).
thf(f1665,definition,
( spl38_52
<=> ( ( mrel @ mactual @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl38_52])],[avatar_definition]) ).
thf(f1666,plain,
( ( ( mrel @ mactual @ sK16 )
= $true )
| ~ spl38_52 ),
inference(avatar_component_clause,[],[f1665]) ).
thf(f1667,plain,
( spl38_52
| spl38_50
| spl38_47
| spl38_49 ),
inference(avatar_split_clause,[],[f1550,f1649,f1642,f1653,f1665]) ).
thf(f1668,plain,
( spl38_49
| spl38_52
| spl38_48
| spl38_47 ),
inference(avatar_split_clause,[],[f1549,f1642,f1645,f1665,f1649]) ).
thf(f1669,plain,
( spl38_50
| spl38_52
| spl38_47
| spl38_46 ),
inference(avatar_split_clause,[],[f1552,f1639,f1642,f1665,f1653]) ).
thf(f1670,plain,
( spl38_46
| spl38_52
| spl38_48
| spl38_47 ),
inference(avatar_split_clause,[],[f1551,f1642,f1645,f1665,f1639]) ).
thf(f1671,plain,
( spl38_49
| spl38_52
| spl38_51
| spl38_50 ),
inference(avatar_split_clause,[],[f1554,f1653,f1658,f1665,f1649]) ).
thf(f1672,plain,
( spl38_52
| spl38_48
| spl38_51
| spl38_49 ),
inference(avatar_split_clause,[],[f1553,f1649,f1658,f1645,f1665]) ).
thf(f1673,plain,
( spl38_52
| spl38_46
| spl38_48
| spl38_51 ),
inference(avatar_split_clause,[],[f1555,f1658,f1645,f1639,f1665]) ).
thf(f1674,plain,
( spl38_52
| spl38_50
| spl38_51
| spl38_46 ),
inference(avatar_split_clause,[],[f1556,f1639,f1658,f1653,f1665]) ).
thf(f1675,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1558]) ).
thf(f1676,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1558]) ).
thf(f1677,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1560]) ).
thf(f1678,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1677]) ).
thf(f1679,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1559]) ).
thf(f1680,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1679]) ).
thf(f1681,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f1561]) ).
thf(f1682,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f1562]) ).
thf(f1683,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f1564]) ).
thf(f1684,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1566]) ).
thf(f1685,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1566]) ).
thf(f1686,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1568]) ).
thf(f1687,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1568]) ).
thf(f1688,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1567]) ).
thf(f1689,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1688]) ).
thf(f1690,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1569]) ).
thf(f1691,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1569]) ).
thf(f1692,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1570]) ).
thf(f1693,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1570]) ).
thf(f1694,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1572]) ).
thf(f1695,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1572]) ).
thf(f1755,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1675]) ).
thf(f1756,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1755]) ).
thf(f1757,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1676]) ).
thf(f1758,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1757]) ).
thf(f1759,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1678]) ).
thf(f1760,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1680]) ).
thf(f1761,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1680]) ).
thf(f1762,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1681]) ).
thf(f1763,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1681]) ).
thf(f1764,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1682]) ).
thf(f1765,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1682]) ).
thf(f1766,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1683]) ).
thf(f1767,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1685]) ).
thf(f1768,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1684]) ).
thf(f1769,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1768]) ).
thf(f1770,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1687]) ).
thf(f1771,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1770]) ).
thf(f1772,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1686]) ).
thf(f1773,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1772]) ).
thf(f1774,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1689]) ).
thf(f1775,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1689]) ).
thf(f1776,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1690]) ).
thf(f1777,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1776]) ).
thf(f1778,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1691]) ).
thf(f1779,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1691]) ).
thf(f1780,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1692]) ).
thf(f1781,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1692]) ).
thf(f1782,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1693]) ).
thf(f1783,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1693]) ).
thf(f1784,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1695]) ).
thf(f1785,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1695]) ).
thf(f1786,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1694]) ).
thf(f1787,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1694]) ).
thf(f1847,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1756]) ).
thf(f1848,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1758]) ).
thf(f1849,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1758]) ).
thf(f1850,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1759]) ).
thf(f1851,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1759]) ).
thf(f1852,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1761]) ).
thf(f1853,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1761]) ).
thf(f1854,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1760]) ).
thf(f1855,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1760]) ).
thf(f1856,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1762]) ).
thf(f1857,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1856]) ).
thf(f1858,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1763]) ).
thf(f1859,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1858]) ).
thf(f1860,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1765]) ).
thf(f1861,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1765]) ).
thf(f1862,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1764]) ).
thf(f1863,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1764]) ).
thf(f1864,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1766]) ).
thf(f1865,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1766]) ).
thf(f1866,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1767]) ).
thf(f1867,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1767]) ).
thf(f1868,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1769]) ).
thf(f1869,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1771]) ).
thf(f1870,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1771]) ).
thf(f1871,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1773]) ).
thf(f1872,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1871]) ).
thf(f1873,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1775]) ).
thf(f1874,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1775]) ).
thf(f1875,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1774]) ).
thf(f1876,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1777]) ).
thf(f1877,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1777]) ).
thf(f1878,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1779]) ).
thf(f1879,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1878]) ).
thf(f1880,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1778]) ).
thf(f1881,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1880]) ).
thf(f1882,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1781]) ).
thf(f1883,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1781]) ).
thf(f1884,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1780]) ).
thf(f1885,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1884]) ).
thf(f1886,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1783]) ).
thf(f1887,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1783]) ).
thf(f1888,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1782]) ).
thf(f1889,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1782]) ).
thf(f1890,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1784]) ).
thf(f1891,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1784]) ).
thf(f1892,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1785]) ).
thf(f1893,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1787]) ).
thf(f1894,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1787]) ).
thf(f1895,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1786]) ).
thf(f1896,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1895]) ).
thf(f1949,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1847]) ).
thf(f1950,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1847]) ).
thf(f1951,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1848]) ).
thf(f1952,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1849]) ).
thf(f1953,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1851]) ).
thf(f1954,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1851]) ).
thf(f1955,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1850]) ).
thf(f1956,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1850]) ).
thf(f1957,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1852]) ).
thf(f1958,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1957]) ).
thf(f1959,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1853]) ).
thf(f1960,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1959]) ).
thf(f1961,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1855]) ).
thf(f1962,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1961]) ).
thf(f1963,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1854]) ).
thf(f1964,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1857]) ).
thf(f1965,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1857]) ).
thf(f1966,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1859]) ).
thf(f1967,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1859]) ).
thf(f1968,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1860]) ).
thf(f1969,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1860]) ).
thf(f1970,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1861]) ).
thf(f1971,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1861]) ).
thf(f1972,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1863]) ).
thf(f1973,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1863]) ).
thf(f1974,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1862]) ).
thf(f1975,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1862]) ).
thf(f1976,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1865]) ).
thf(f1977,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1865]) ).
thf(f1978,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1864]) ).
thf(f1979,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1978]) ).
thf(f1980,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f1867]) ).
thf(f1981,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1980]) ).
thf(f1982,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1866]) ).
thf(f1983,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1866]) ).
thf(f1984,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1868]) ).
thf(f1985,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1869]) ).
thf(f1986,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1985]) ).
thf(f1987,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1870]) ).
thf(f1988,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1870]) ).
thf(f1989,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1872]) ).
thf(f1990,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1873]) ).
thf(f1991,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1990]) ).
thf(f1992,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1874]) ).
thf(f1993,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1874]) ).
thf(f1994,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1875]) ).
thf(f1995,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1994]) ).
thf(f1996,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1877]) ).
thf(f1997,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1876]) ).
thf(f1998,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1997]) ).
thf(f1999,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1879]) ).
thf(f2000,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1881]) ).
thf(f2001,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1882]) ).
thf(f2002,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1882]) ).
thf(f2003,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1883]) ).
thf(f2004,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1883]) ).
thf(f2005,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f2006,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f2007,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1886]) ).
thf(f2008,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1886]) ).
thf(f2009,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1887]) ).
thf(f2010,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1887]) ).
thf(f2011,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1889]) ).
thf(f2012,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1889]) ).
thf(f2013,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1888]) ).
thf(f2014,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2013]) ).
thf(f2015,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1890]) ).
thf(f2016,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2015]) ).
thf(f2017,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1891]) ).
thf(f2018,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2017]) ).
thf(f2019,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1892]) ).
thf(f2020,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1892]) ).
thf(f2021,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1893]) ).
thf(f2022,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2021]) ).
thf(f2023,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1894]) ).
thf(f2024,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1894]) ).
thf(f2025,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1896]) ).
thf(f2098,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1950]) ).
thf(f2099,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1950]) ).
thf(f2100,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1949]) ).
thf(f2101,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2100]) ).
thf(f2102,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1951]) ).
thf(f2103,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2102]) ).
thf(f2104,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1952]) ).
thf(f2105,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1952]) ).
thf(f2106,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1953]) ).
thf(f2107,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2106]) ).
thf(f2108,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1954]) ).
thf(f2109,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1954]) ).
thf(f2110,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1956]) ).
thf(f2111,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1956]) ).
thf(f2112,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1955]) ).
thf(f2113,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1955]) ).
thf(f2114,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1958]) ).
thf(f2115,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2114]) ).
thf(f2116,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1960]) ).
thf(f2117,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f1962]) ).
thf(f2118,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1962]) ).
thf(f2119,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1963]) ).
thf(f2120,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2119]) ).
thf(f2121,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1965]) ).
thf(f2122,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1964]) ).
thf(f2123,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2122]) ).
thf(f2124,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1966]) ).
thf(f2125,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1967]) ).
thf(f2126,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1967]) ).
thf(f2127,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1968]) ).
thf(f2128,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2127]) ).
thf(f2129,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1969]) ).
thf(f2130,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1969]) ).
thf(f2131,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1970]) ).
thf(f2132,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1970]) ).
thf(f2133,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1971]) ).
thf(f2134,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1971]) ).
thf(f2135,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1973]) ).
thf(f2136,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1973]) ).
thf(f2137,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1972]) ).
thf(f2138,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1972]) ).
thf(f2139,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1974]) ).
thf(f2140,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2139]) ).
thf(f2141,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1975]) ).
thf(f2142,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2141]) ).
thf(f2143,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1976]) ).
thf(f2144,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2143]) ).
thf(f2145,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1977]) ).
thf(f2146,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1977]) ).
thf(f2147,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1979]) ).
thf(f2148,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f1979]) ).
thf(f2149,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1981]) ).
thf(f2150,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1981]) ).
thf(f2151,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1983]) ).
thf(f2152,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2151]) ).
thf(f2153,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1982]) ).
thf(f2154,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2153]) ).
thf(f2155,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1984]) ).
thf(f2156,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2155]) ).
thf(f2157,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1986]) ).
thf(f2158,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2157]) ).
thf(f2159,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1988]) ).
thf(f2160,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f1988]) ).
thf(f2161,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1987]) ).
thf(f2162,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2161]) ).
thf(f2163,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1989]) ).
thf(f2164,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1991]) ).
thf(f2165,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1992]) ).
thf(f2166,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2165]) ).
thf(f2167,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1993]) ).
thf(f2168,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f1993]) ).
thf(f2169,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1995]) ).
thf(f2170,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1995]) ).
thf(f2171,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f1996]) ).
thf(f2172,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f1996]) ).
thf(f2173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f1998]) ).
thf(f2174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2173]) ).
thf(f2175,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f1999]) ).
thf(f2176,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1999]) ).
thf(f2177,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2000]) ).
thf(f2178,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2000]) ).
thf(f2179,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2001]) ).
thf(f2180,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2179]) ).
thf(f2181,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2002]) ).
thf(f2182,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2181]) ).
thf(f2183,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X2 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2003]) ).
thf(f2184,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2183]) ).
thf(f2185,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2004]) ).
thf(f2186,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2004]) ).
thf(f2187,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2006]) ).
thf(f2188,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2006]) ).
thf(f2189,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2005]) ).
thf(f2190,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2189]) ).
thf(f2191,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2007]) ).
thf(f2192,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2191]) ).
thf(f2193,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2008]) ).
thf(f2194,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2008]) ).
thf(f2195,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2009]) ).
thf(f2196,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2009]) ).
thf(f2197,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2010]) ).
thf(f2198,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2010]) ).
thf(f2199,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2011]) ).
thf(f2200,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2199]) ).
thf(f2201,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2012]) ).
thf(f2202,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2012]) ).
thf(f2203,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2014]) ).
thf(f2204,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2014]) ).
thf(f2205,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2016]) ).
thf(f2206,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2018]) ).
thf(f2207,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2018]) ).
thf(f2208,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2020]) ).
thf(f2209,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2020]) ).
thf(f2210,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2019]) ).
thf(f2211,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2210]) ).
thf(f2212,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f2022]) ).
thf(f2213,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2212]) ).
thf(f2214,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2024]) ).
thf(f2215,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2214]) ).
thf(f2216,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2023]) ).
thf(f2217,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2025]) ).
thf(f2270,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2098]) ).
thf(f2271,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2099]) ).
thf(f2272,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2101]) ).
thf(f2273,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2103]) ).
thf(f2274,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2103]) ).
thf(f2275,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2104]) ).
thf(f2276,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2104]) ).
thf(f2277,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2105]) ).
thf(f2278,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2105]) ).
thf(f2279,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2107]) ).
thf(f2280,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2107]) ).
thf(f2281,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2108]) ).
thf(f2282,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2108]) ).
thf(f2283,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2109]) ).
thf(f2284,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2109]) ).
thf(f2285,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2110]) ).
thf(f2286,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2285]) ).
thf(f2287,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2111]) ).
thf(f2288,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2111]) ).
thf(f2289,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2112]) ).
thf(f2290,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2289]) ).
thf(f2291,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2113]) ).
thf(f2292,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2291]) ).
thf(f2293,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2115]) ).
thf(f2294,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2115]) ).
thf(f2295,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2116]) ).
thf(f2296,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2116]) ).
thf(f2297,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2117]) ).
thf(f2298,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2118]) ).
thf(f2299,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2120]) ).
thf(f2300,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2299]) ).
thf(f2301,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2121]) ).
thf(f2302,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2301]) ).
thf(f2303,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2123]) ).
thf(f2304,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2303]) ).
thf(f2305,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2124]) ).
thf(f2306,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2124]) ).
thf(f2307,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2125]) ).
thf(f2308,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2307]) ).
thf(f2309,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2126]) ).
thf(f2310,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2128]) ).
thf(f2311,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2130]) ).
thf(f2312,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2311]) ).
thf(f2313,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2129]) ).
thf(f2314,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2313]) ).
thf(f2315,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2131]) ).
thf(f2316,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2131]) ).
thf(f2317,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2132]) ).
thf(f2318,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2317]) ).
thf(f2319,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2133]) ).
thf(f2320,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2133]) ).
thf(f2321,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2134]) ).
thf(f2322,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2134]) ).
thf(f2323,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2135]) ).
thf(f2324,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2323]) ).
thf(f2325,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2136]) ).
thf(f2326,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2325]) ).
thf(f2327,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2138]) ).
thf(f2328,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2327]) ).
thf(f2329,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2137]) ).
thf(f2330,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2329]) ).
thf(f2331,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2140]) ).
thf(f2332,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2142]) ).
thf(f2333,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2332]) ).
thf(f2334,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f2144]) ).
thf(f2335,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2144]) ).
thf(f2336,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2145]) ).
thf(f2337,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2336]) ).
thf(f2338,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2146]) ).
thf(f2339,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2146]) ).
thf(f2340,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2148]) ).
thf(f2341,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2148]) ).
thf(f2342,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2147]) ).
thf(f2343,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2150]) ).
thf(f2344,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2150]) ).
thf(f2345,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2149]) ).
thf(f2346,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2149]) ).
thf(f2347,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2152]) ).
thf(f2348,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2152]) ).
thf(f2349,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2154]) ).
thf(f2350,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2156]) ).
thf(f2351,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2158]) ).
thf(f2352,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2160]) ).
thf(f2353,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2160]) ).
thf(f2354,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2159]) ).
thf(f2355,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2159]) ).
thf(f2356,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2162]) ).
thf(f2357,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2162]) ).
thf(f2358,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2163]) ).
thf(f2359,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2163]) ).
thf(f2360,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2164]) ).
thf(f2361,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2360]) ).
thf(f2362,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2166]) ).
thf(f2363,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2168]) ).
thf(f2364,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2167]) ).
thf(f2365,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2167]) ).
thf(f2366,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2170]) ).
thf(f2367,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2366]) ).
thf(f2368,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2169]) ).
thf(f2369,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2368]) ).
thf(f2370,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2172]) ).
thf(f2371,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2172]) ).
thf(f2372,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2171]) ).
thf(f2373,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2372]) ).
thf(f2374,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2174]) ).
thf(f2375,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2176]) ).
thf(f2376,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2375]) ).
thf(f2377,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2175]) ).
thf(f2378,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2377]) ).
thf(f2379,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2178]) ).
thf(f2380,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2379]) ).
thf(f2381,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2177]) ).
thf(f2382,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2381]) ).
thf(f2383,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2180]) ).
thf(f2384,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2182]) ).
thf(f2385,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2384]) ).
thf(f2386,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2184]) ).
thf(f2387,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2386]) ).
thf(f2388,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2186]) ).
thf(f2389,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2388]) ).
thf(f2390,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2185]) ).
thf(f2391,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2390]) ).
thf(f2392,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2187]) ).
thf(f2393,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2392]) ).
thf(f2394,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2188]) ).
thf(f2395,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2394]) ).
thf(f2396,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2190]) ).
thf(f2397,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2396]) ).
thf(f2398,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2192]) ).
thf(f2399,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2193]) ).
thf(f2400,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2399]) ).
thf(f2401,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2194]) ).
thf(f2402,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2401]) ).
thf(f2403,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2195]) ).
thf(f2404,plain,
! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2195]) ).
thf(f2405,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2196]) ).
thf(f2406,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2405]) ).
thf(f2407,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2197]) ).
thf(f2408,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2197]) ).
thf(f2409,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2198]) ).
thf(f2410,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2198]) ).
thf(f2411,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2200]) ).
thf(f2412,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2411]) ).
thf(f2413,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2202]) ).
thf(f2414,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2202]) ).
thf(f2415,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2201]) ).
thf(f2416,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2415]) ).
thf(f2417,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2203]) ).
thf(f2418,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2204]) ).
thf(f2419,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2205]) ).
thf(f2420,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2419]) ).
thf(f2421,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2207]) ).
thf(f2422,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2206]) ).
thf(f2423,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2422]) ).
thf(f2424,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2208]) ).
thf(f2425,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2424]) ).
thf(f2426,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2209]) ).
thf(f2427,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2209]) ).
thf(f2428,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2211]) ).
thf(f2429,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2213]) ).
thf(f2430,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X4 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2215]) ).
thf(f2431,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2430]) ).
thf(f2432,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2216]) ).
thf(f2433,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2432]) ).
thf(f2434,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2217]) ).
thf(f2435,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2434]) ).
thf(f2497,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2270]) ).
thf(f2498,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2497]) ).
thf(f2499,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2271]) ).
thf(f2500,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2499]) ).
thf(f2501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2272]) ).
thf(f2502,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2501]) ).
thf(f2503,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2273]) ).
thf(f2504,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2503]) ).
thf(f2505,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2274]) ).
thf(f2506,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2275]) ).
thf(f2507,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2506]) ).
thf(f2508,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2276]) ).
thf(f2509,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2278]) ).
thf(f2510,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2509]) ).
thf(f2511,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2277]) ).
thf(f2512,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2511]) ).
thf(f2513,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2280]) ).
thf(f2514,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2280]) ).
thf(f2515,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2279]) ).
thf(f2516,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2282]) ).
thf(f2517,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2282]) ).
thf(f2518,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2281]) ).
thf(f2519,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2518]) ).
thf(f2520,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2283]) ).
thf(f2521,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2283]) ).
thf(f2522,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2284]) ).
thf(f2523,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2284]) ).
thf(f2524,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2286]) ).
thf(f2525,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2286]) ).
thf(f2526,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2287]) ).
thf(f2527,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2526]) ).
thf(f2528,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2288]) ).
thf(f2529,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2528]) ).
thf(f2530,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2290]) ).
thf(f2531,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2292]) ).
thf(f2532,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2292]) ).
thf(f2533,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2293]) ).
thf(f2534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2533]) ).
thf(f2535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2294]) ).
thf(f2536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2535]) ).
thf(f2537,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2295]) ).
thf(f2538,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2537]) ).
thf(f2539,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2296]) ).
thf(f2540,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2297]) ).
thf(f2541,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2540]) ).
thf(f2542,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2298]) ).
thf(f2543,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2542]) ).
thf(f2544,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2300]) ).
thf(f2545,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2302]) ).
thf(f2546,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2304]) ).
thf(f2547,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2306]) ).
thf(f2548,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2306]) ).
thf(f2549,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2305]) ).
thf(f2550,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2549]) ).
thf(f2551,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2308]) ).
thf(f2552,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2308]) ).
thf(f2553,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2309]) ).
thf(f2554,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2309]) ).
thf(f2555,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2310]) ).
thf(f2556,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2310]) ).
thf(f2557,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2312]) ).
thf(f2558,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2312]) ).
thf(f2559,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2314]) ).
thf(f2560,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2314]) ).
thf(f2561,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2316]) ).
thf(f2562,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2561]) ).
thf(f2563,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2315]) ).
thf(f2564,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2563]) ).
thf(f2565,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2318]) ).
thf(f2566,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2319]) ).
thf(f2567,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2319]) ).
thf(f2568,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2320]) ).
thf(f2569,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2568]) ).
thf(f2570,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2321]) ).
thf(f2571,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2570]) ).
thf(f2572,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2322]) ).
thf(f2573,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2322]) ).
thf(f2574,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2324]) ).
thf(f2575,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2326]) ).
thf(f2576,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2326]) ).
thf(f2577,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2328]) ).
thf(f2578,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2577]) ).
thf(f2579,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2330]) ).
thf(f2580,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2331]) ).
thf(f2581,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2580]) ).
thf(f2582,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2333]) ).
thf(f2583,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2334]) ).
thf(f2584,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2583]) ).
thf(f2585,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2335]) ).
thf(f2586,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2335]) ).
thf(f2587,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2337]) ).
thf(f2588,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2337]) ).
thf(f2589,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2339]) ).
thf(f2590,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2589]) ).
thf(f2591,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2338]) ).
thf(f2592,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2338]) ).
thf(f2593,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2341]) ).
thf(f2594,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2340]) ).
thf(f2595,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2342]) ).
thf(f2596,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2595]) ).
thf(f2597,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2343]) ).
thf(f2598,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2597]) ).
thf(f2599,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2344]) ).
thf(f2600,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2344]) ).
thf(f2601,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2345]) ).
thf(f2602,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2601]) ).
thf(f2603,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2346]) ).
thf(f2604,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2347]) ).
thf(f2605,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2604]) ).
thf(f2606,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2348]) ).
thf(f2607,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2606]) ).
thf(f2608,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2349]) ).
thf(f2609,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2608]) ).
thf(f2610,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2350]) ).
thf(f2611,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2350]) ).
thf(f2612,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2351]) ).
thf(f2613,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2353]) ).
thf(f2614,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2613]) ).
thf(f2615,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2352]) ).
thf(f2616,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2355]) ).
thf(f2617,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2354]) ).
thf(f2618,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2617]) ).
thf(f2619,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2357]) ).
thf(f2620,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2356]) ).
thf(f2621,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2620]) ).
thf(f2622,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2359]) ).
thf(f2623,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2359]) ).
thf(f2624,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2358]) ).
thf(f2625,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2624]) ).
thf(f2626,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2361]) ).
thf(f2627,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2362]) ).
thf(f2628,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2363]) ).
thf(f2629,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2363]) ).
thf(f2630,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2365]) ).
thf(f2631,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2630]) ).
thf(f2632,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2364]) ).
thf(f2633,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2367]) ).
thf(f2634,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2369]) ).
thf(f2635,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2634]) ).
thf(f2636,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2371]) ).
thf(f2637,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2636]) ).
thf(f2638,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2370]) ).
thf(f2639,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2638]) ).
thf(f2640,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2373]) ).
thf(f2641,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2640]) ).
thf(f2642,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2374]) ).
thf(f2643,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2376]) ).
thf(f2644,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2376]) ).
thf(f2645,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f2378]) ).
thf(f2646,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2378]) ).
thf(f2647,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2380]) ).
thf(f2648,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2647]) ).
thf(f2649,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2382]) ).
thf(f2650,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2383]) ).
thf(f2651,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2650]) ).
thf(f2652,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2385]) ).
thf(f2653,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2387]) ).
thf(f2654,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2389]) ).
thf(f2655,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2654]) ).
thf(f2656,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2391]) ).
thf(f2657,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2656]) ).
thf(f2658,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2393]) ).
thf(f2659,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2395]) ).
thf(f2660,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2397]) ).
thf(f2661,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2398]) ).
thf(f2662,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2398]) ).
thf(f2663,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2400]) ).
thf(f2664,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2663]) ).
thf(f2665,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2402]) ).
thf(f2666,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2665]) ).
thf(f2667,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2404]) ).
thf(f2668,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2667]) ).
thf(f2669,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2403]) ).
thf(f2670,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2669]) ).
thf(f2671,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2406]) ).
thf(f2672,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2671]) ).
thf(f2673,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2408]) ).
thf(f2674,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2673]) ).
thf(f2675,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2407]) ).
thf(f2676,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2675]) ).
thf(f2677,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2409]) ).
thf(f2678,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2409]) ).
thf(f2679,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2410]) ).
thf(f2680,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2410]) ).
thf(f2681,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2412]) ).
thf(f2682,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2413]) ).
thf(f2683,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2682]) ).
thf(f2684,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2414]) ).
thf(f2685,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2684]) ).
thf(f2686,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2416]) ).
thf(f2687,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2686]) ).
thf(f2688,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2417]) ).
thf(f2689,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2688]) ).
thf(f2690,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2418]) ).
thf(f2691,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2690]) ).
thf(f2692,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2420]) ).
thf(f2693,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2421]) ).
thf(f2694,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2423]) ).
thf(f2695,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2425]) ).
thf(f2696,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2426]) ).
thf(f2697,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2696]) ).
thf(f2698,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2427]) ).
thf(f2699,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2427]) ).
thf(f2700,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2428]) ).
thf(f2701,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2428]) ).
thf(f2702,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2429]) ).
thf(f2703,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2431]) ).
thf(f2704,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2433]) ).
thf(f2705,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2435]) ).
thf(f2739,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2498]) ).
thf(f2740,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2500]) ).
thf(f2741,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2500]) ).
thf(f2742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2502]) ).
thf(f2743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2504]) ).
thf(f2744,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2505]) ).
thf(f2745,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2505]) ).
thf(f2746,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2507]) ).
thf(f2747,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2508]) ).
thf(f2748,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2747]) ).
thf(f2749,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2510]) ).
thf(f2750,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2512]) ).
thf(f2751,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2512]) ).
thf(f2752,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2514]) ).
thf(f2753,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2514]) ).
thf(f2754,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2513]) ).
thf(f2755,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2515]) ).
thf(f2756,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2755]) ).
thf(f2757,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2516]) ).
thf(f2758,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2757]) ).
thf(f2759,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2517]) ).
thf(f2760,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2759]) ).
thf(f2761,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2519]) ).
thf(f2762,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2519]) ).
thf(f2763,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2521]) ).
thf(f2764,plain,
! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2521]) ).
thf(f2765,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2520]) ).
thf(f2766,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2765]) ).
thf(f2767,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2522]) ).
thf(f2768,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2767]) ).
thf(f2769,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2523]) ).
thf(f2770,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2769]) ).
thf(f2771,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2524]) ).
thf(f2772,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2525]) ).
thf(f2773,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2772]) ).
thf(f2774,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2527]) ).
thf(f2775,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2527]) ).
thf(f2776,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2529]) ).
thf(f2777,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2776]) ).
thf(f2778,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2530]) ).
thf(f2779,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f2778]) ).
thf(f2780,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2531]) ).
thf(f2781,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2532]) ).
thf(f2782,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2781]) ).
thf(f2783,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2534]) ).
thf(f2784,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2536]) ).
thf(f2785,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2538]) ).
thf(f2786,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2539]) ).
thf(f2787,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2786]) ).
thf(f2788,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2541]) ).
thf(f2789,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2543]) ).
thf(f2790,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2543]) ).
thf(f2791,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2544]) ).
thf(f2792,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2791]) ).
thf(f2793,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2545]) ).
thf(f2794,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2545]) ).
thf(f2795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2546]) ).
thf(f2796,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2547]) ).
thf(f2797,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2796]) ).
thf(f2798,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2548]) ).
thf(f2799,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2798]) ).
thf(f2800,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2550]) ).
thf(f2801,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2800]) ).
thf(f2802,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2552]) ).
thf(f2803,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2551]) ).
thf(f2804,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2553]) ).
thf(f2805,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2553]) ).
thf(f2806,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2554]) ).
thf(f2807,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2554]) ).
thf(f2808,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2555]) ).
thf(f2809,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2808]) ).
thf(f2810,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2556]) ).
thf(f2811,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2810]) ).
thf(f2812,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2557]) ).
thf(f2813,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2558]) ).
thf(f2814,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2558]) ).
thf(f2815,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2560]) ).
thf(f2816,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2560]) ).
thf(f2817,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2559]) ).
thf(f2818,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2817]) ).
thf(f2819,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2562]) ).
thf(f2820,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2819]) ).
thf(f2821,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2564]) ).
thf(f2822,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2821]) ).
thf(f2823,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2565]) ).
thf(f2824,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2565]) ).
thf(f2825,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2567]) ).
thf(f2826,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2567]) ).
thf(f2827,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2566]) ).
thf(f2828,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2827]) ).
thf(f2829,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2569]) ).
thf(f2830,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2829]) ).
thf(f2831,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2571]) ).
thf(f2832,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2571]) ).
thf(f2833,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2573]) ).
thf(f2834,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2833]) ).
thf(f2835,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2572]) ).
thf(f2836,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2835]) ).
thf(f2837,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2574]) ).
thf(f2838,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2837]) ).
thf(f2839,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2575]) ).
thf(f2840,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2575]) ).
thf(f2841,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2576]) ).
thf(f2842,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2578]) ).
thf(f2843,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2842]) ).
thf(f2844,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2579]) ).
thf(f2845,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2844]) ).
thf(f2846,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2581]) ).
thf(f2847,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2582]) ).
thf(f2848,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2584]) ).
thf(f2849,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2585]) ).
thf(f2850,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2849]) ).
thf(f2851,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2586]) ).
thf(f2852,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2851]) ).
thf(f2853,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2588]) ).
thf(f2854,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2587]) ).
thf(f2855,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2590]) ).
thf(f2856,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2592]) ).
thf(f2857,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2856]) ).
thf(f2858,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2591]) ).
thf(f2859,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2858]) ).
thf(f2860,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2593]) ).
thf(f2861,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2593]) ).
thf(f2862,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2594]) ).
thf(f2863,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2862]) ).
thf(f2864,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2596]) ).
thf(f2865,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2598]) ).
thf(f2866,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2600]) ).
thf(f2867,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2600]) ).
thf(f2868,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2599]) ).
thf(f2869,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2868]) ).
thf(f2870,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2602]) ).
thf(f2871,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2870]) ).
thf(f2872,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2603]) ).
thf(f2873,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2603]) ).
thf(f2874,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2605]) ).
thf(f2875,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2874]) ).
thf(f2876,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2607]) ).
thf(f2877,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2609]) ).
thf(f2878,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2610]) ).
thf(f2879,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2878]) ).
thf(f2880,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2611]) ).
thf(f2881,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2611]) ).
thf(f2882,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2612]) ).
thf(f2883,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2614]) ).
thf(f2884,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2614]) ).
thf(f2885,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2615]) ).
thf(f2886,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2615]) ).
thf(f2887,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2616]) ).
thf(f2888,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2887]) ).
thf(f2889,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2618]) ).
thf(f2890,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2889]) ).
thf(f2891,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2619]) ).
thf(f2892,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2621]) ).
thf(f2893,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2623]) ).
thf(f2894,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2893]) ).
thf(f2895,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2622]) ).
thf(f2896,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2895]) ).
thf(f2897,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2625]) ).
thf(f2898,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2897]) ).
thf(f2899,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2626]) ).
thf(f2900,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2626]) ).
thf(f2901,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2627]) ).
thf(f2902,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2627]) ).
thf(f2903,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2629]) ).
thf(f2904,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f2903]) ).
thf(f2905,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2628]) ).
thf(f2906,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2905]) ).
thf(f2907,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2631]) ).
thf(f2908,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2907]) ).
thf(f2909,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2632]) ).
thf(f2910,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2909]) ).
thf(f2911,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2633]) ).
thf(f2912,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2633]) ).
thf(f2913,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2635]) ).
thf(f2914,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2637]) ).
thf(f2915,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2639]) ).
thf(f2916,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2915]) ).
thf(f2917,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2641]) ).
thf(f2918,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2642]) ).
thf(f2919,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2644]) ).
thf(f2920,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2643]) ).
thf(f2921,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f2645]) ).
thf(f2922,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2921]) ).
thf(f2923,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2646]) ).
thf(f2924,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2646]) ).
thf(f2925,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2648]) ).
thf(f2926,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2649]) ).
thf(f2927,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2926]) ).
thf(f2928,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2651]) ).
thf(f2929,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2652]) ).
thf(f2930,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2652]) ).
thf(f2931,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2653]) ).
thf(f2932,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2655]) ).
thf(f2933,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2655]) ).
thf(f2934,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2657]) ).
thf(f2935,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f2657]) ).
thf(f2936,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2658]) ).
thf(f2937,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2936]) ).
thf(f2938,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2659]) ).
thf(f2939,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2660]) ).
thf(f2940,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2662]) ).
thf(f2941,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2940]) ).
thf(f2942,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2661]) ).
thf(f2943,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2942]) ).
thf(f2944,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2664]) ).
thf(f2945,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2666]) ).
thf(f2946,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2668]) ).
thf(f2947,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2946]) ).
thf(f2948,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2670]) ).
thf(f2949,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f2672]) ).
thf(f2950,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2672]) ).
thf(f2951,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2674]) ).
thf(f2952,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f2951]) ).
thf(f2953,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2676]) ).
thf(f2954,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2677]) ).
thf(f2955,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2954]) ).
thf(f2956,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2678]) ).
thf(f2957,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2956]) ).
thf(f2958,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2680]) ).
thf(f2959,plain,
! [X2: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2958]) ).
thf(f2960,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2679]) ).
thf(f2961,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2960]) ).
thf(f2962,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2681]) ).
thf(f2963,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2683]) ).
thf(f2964,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2963]) ).
thf(f2965,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2685]) ).
thf(f2966,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2687]) ).
thf(f2967,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2689]) ).
thf(f2968,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2967]) ).
thf(f2969,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2691]) ).
thf(f2970,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2691]) ).
thf(f2971,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2692]) ).
thf(f2972,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2693]) ).
thf(f2973,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2972]) ).
thf(f2974,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2694]) ).
thf(f2975,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f2695]) ).
thf(f2976,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2695]) ).
thf(f2977,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2697]) ).
thf(f2978,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2697]) ).
thf(f2979,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2699]) ).
thf(f2980,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f2979]) ).
thf(f2981,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2698]) ).
thf(f2982,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2981]) ).
thf(f2983,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2700]) ).
thf(f2984,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2983]) ).
thf(f2985,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2701]) ).
thf(f2986,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2701]) ).
thf(f2987,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2702]) ).
thf(f2988,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2703]) ).
thf(f2989,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2704]) ).
thf(f2990,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f2989]) ).
thf(f2992,definition,
( spl38_101
<=> ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_101])],[avatar_definition]) ).
thf(f2993,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_101 ),
inference(avatar_component_clause,[],[f2992]) ).
thf(f2995,definition,
( spl38_102
<=> ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_102])],[avatar_definition]) ).
thf(f2996,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) )
| ~ spl38_102 ),
inference(avatar_component_clause,[],[f2995]) ).
thf(f2998,definition,
( spl38_103
<=> ! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_103])],[avatar_definition]) ).
thf(f2999,plain,
( ! [X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) )
| ~ spl38_103 ),
inference(avatar_component_clause,[],[f2998]) ).
thf(f3001,definition,
( spl38_104
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_104])],[avatar_definition]) ).
thf(f3002,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) )
| ~ spl38_104 ),
inference(avatar_component_clause,[],[f3001]) ).
thf(f3003,plain,
( spl38_101
| spl38_102
| spl38_103
| spl38_104 ),
inference(avatar_split_clause,[],[f2705,f3001,f2998,f2995,f2992]) ).
thf(f3035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2739]) ).
thf(f3036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3035]) ).
thf(f3037,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2741]) ).
thf(f3038,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2740]) ).
thf(f3039,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3038]) ).
thf(f3040,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2742]) ).
thf(f3041,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2743]) ).
thf(f3042,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2745]) ).
thf(f3043,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f2745]) ).
thf(f3044,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2744]) ).
thf(f3045,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3044]) ).
thf(f3046,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2746]) ).
thf(f3047,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3046]) ).
thf(f3048,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2748]) ).
thf(f3049,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2749]) ).
thf(f3050,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2750]) ).
thf(f3051,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2751]) ).
thf(f3052,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2752]) ).
thf(f3053,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2753]) ).
thf(f3054,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2753]) ).
thf(f3055,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2754]) ).
thf(f3056,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3055]) ).
thf(f3057,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2756]) ).
thf(f3058,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2756]) ).
thf(f3059,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2758]) ).
thf(f3060,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2760]) ).
thf(f3061,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2761]) ).
thf(f3062,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2762]) ).
thf(f3063,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3062]) ).
thf(f3064,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2763]) ).
thf(f3065,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3064]) ).
thf(f3066,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2764]) ).
thf(f3067,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2764]) ).
thf(f3068,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2766]) ).
thf(f3069,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f2766]) ).
thf(f3070,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2768]) ).
thf(f3071,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2768]) ).
thf(f3072,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2770]) ).
thf(f3073,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2771]) ).
thf(f3074,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f3073]) ).
thf(f3075,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2773]) ).
thf(f3076,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f3075]) ).
thf(f3077,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2775]) ).
thf(f3078,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3077]) ).
thf(f3079,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2774]) ).
thf(f3080,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2777]) ).
thf(f3081,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2779]) ).
thf(f3082,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3081]) ).
thf(f3083,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2780]) ).
thf(f3084,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3083]) ).
thf(f3085,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2782]) ).
thf(f3086,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f3085]) ).
thf(f3087,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2783]) ).
thf(f3088,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2784]) ).
thf(f3089,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2785]) ).
thf(f3090,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2787]) ).
thf(f3091,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2787]) ).
thf(f3092,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2788]) ).
thf(f3093,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2789]) ).
thf(f3094,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2790]) ).
thf(f3095,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2792]) ).
thf(f3096,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2793]) ).
thf(f3097,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3096]) ).
thf(f3098,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2794]) ).
thf(f3099,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2794]) ).
thf(f3100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2795]) ).
thf(f3101,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2797]) ).
thf(f3102,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2799]) ).
thf(f3103,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3102]) ).
thf(f3104,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f2801]) ).
thf(f3105,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2802]) ).
thf(f3106,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2802]) ).
thf(f3107,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2803]) ).
thf(f3108,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2805]) ).
thf(f3109,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3108]) ).
thf(f3110,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2804]) ).
thf(f3111,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3110]) ).
thf(f3112,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2807]) ).
thf(f3113,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3112]) ).
thf(f3114,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2806]) ).
thf(f3115,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2806]) ).
thf(f3116,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2809]) ).
thf(f3117,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2811]) ).
thf(f3118,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2812]) ).
thf(f3119,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3118]) ).
thf(f3120,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2813]) ).
thf(f3121,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3120]) ).
thf(f3122,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2814]) ).
thf(f3123,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3122]) ).
thf(f3124,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2816]) ).
thf(f3125,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2816]) ).
thf(f3126,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2815]) ).
thf(f3127,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3126]) ).
thf(f3128,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2818]) ).
thf(f3129,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3128]) ).
thf(f3130,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2820]) ).
thf(f3131,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2822]) ).
thf(f3132,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2824]) ).
thf(f3133,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3132]) ).
thf(f3134,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2823]) ).
thf(f3135,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3134]) ).
thf(f3136,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2825]) ).
thf(f3137,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3136]) ).
thf(f3138,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2826]) ).
thf(f3139,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3138]) ).
thf(f3140,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2828]) ).
thf(f3141,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2830]) ).
thf(f3142,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2831]) ).
thf(f3143,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3142]) ).
thf(f3144,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2832]) ).
thf(f3145,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3144]) ).
thf(f3146,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2834]) ).
thf(f3147,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2836]) ).
thf(f3148,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3147]) ).
thf(f3149,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2838]) ).
thf(f3150,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2839]) ).
thf(f3151,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2840]) ).
thf(f3152,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2841]) ).
thf(f3153,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3152]) ).
thf(f3154,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2843]) ).
thf(f3155,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2845]) ).
thf(f3156,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2846]) ).
thf(f3157,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3156]) ).
thf(f3158,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2847]) ).
thf(f3159,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2847]) ).
thf(f3160,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2848]) ).
thf(f3161,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2850]) ).
thf(f3162,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2852]) ).
thf(f3163,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2853]) ).
thf(f3164,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f2853]) ).
thf(f3165,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2854]) ).
thf(f3166,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3165]) ).
thf(f3167,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2855]) ).
thf(f3168,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2855]) ).
thf(f3169,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2857]) ).
thf(f3170,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2857]) ).
thf(f3171,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2859]) ).
thf(f3172,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3171]) ).
thf(f3173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2861]) ).
thf(f3174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3173]) ).
thf(f3175,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2860]) ).
thf(f3176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3175]) ).
thf(f3177,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2863]) ).
thf(f3179,definition,
( spl38_109
<=> ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_109])],[avatar_definition]) ).
thf(f3180,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) )
| ~ spl38_109 ),
inference(avatar_component_clause,[],[f3179]) ).
thf(f3181,plain,
( spl38_101
| spl38_109
| spl38_102
| spl38_104 ),
inference(avatar_split_clause,[],[f2864,f3001,f2995,f3179,f2992]) ).
thf(f3182,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2865]) ).
thf(f3183,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3182]) ).
thf(f3184,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2867]) ).
thf(f3185,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3184]) ).
thf(f3186,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2866]) ).
thf(f3187,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3186]) ).
thf(f3188,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f2869]) ).
thf(f3189,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3188]) ).
thf(f3190,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2871]) ).
thf(f3191,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2872]) ).
thf(f3192,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3191]) ).
thf(f3193,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2873]) ).
thf(f3194,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3193]) ).
thf(f3195,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f2875]) ).
thf(f3196,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2876]) ).
thf(f3197,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f2876]) ).
thf(f3198,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2877]) ).
thf(f3199,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3198]) ).
thf(f3200,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2879]) ).
thf(f3201,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2881]) ).
thf(f3202,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2881]) ).
thf(f3203,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2880]) ).
thf(f3204,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3203]) ).
thf(f3205,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2882]) ).
thf(f3206,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2882]) ).
thf(f3207,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2883]) ).
thf(f3208,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2884]) ).
thf(f3209,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2886]) ).
thf(f3210,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3209]) ).
thf(f3211,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2885]) ).
thf(f3212,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3211]) ).
thf(f3213,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2888]) ).
thf(f3214,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3213]) ).
thf(f3215,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2890]) ).
thf(f3216,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2891]) ).
thf(f3217,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2891]) ).
thf(f3218,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f2892]) ).
thf(f3219,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3218]) ).
thf(f3220,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2894]) ).
thf(f3221,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2896]) ).
thf(f3222,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2898]) ).
thf(f3223,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2900]) ).
thf(f3224,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2900]) ).
thf(f3225,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2899]) ).
thf(f3226,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3225]) ).
thf(f3227,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2902]) ).
thf(f3228,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2902]) ).
thf(f3229,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2901]) ).
thf(f3230,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3229]) ).
thf(f3231,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2904]) ).
thf(f3232,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3231]) ).
thf(f3233,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2906]) ).
thf(f3234,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2908]) ).
thf(f3235,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2910]) ).
thf(f3236,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3235]) ).
thf(f3237,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2912]) ).
thf(f3238,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2911]) ).
thf(f3239,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2913]) ).
thf(f3240,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2914]) ).
thf(f3241,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3240]) ).
thf(f3242,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2916]) ).
thf(f3243,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2917]) ).
thf(f3245,definition,
( spl38_110
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_110])],[avatar_definition]) ).
thf(f3246,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_110 ),
inference(avatar_component_clause,[],[f3245]) ).
thf(f3247,plain,
( spl38_103
| spl38_110
| spl38_104
| spl38_101 ),
inference(avatar_split_clause,[],[f2918,f2992,f3001,f3245,f2998]) ).
thf(f3248,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2919]) ).
thf(f3249,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2919]) ).
thf(f3250,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2920]) ).
thf(f3251,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3250]) ).
thf(f3252,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2922]) ).
thf(f3253,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2924]) ).
thf(f3254,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2923]) ).
thf(f3255,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2925]) ).
thf(f3256,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2927]) ).
thf(f3257,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2928]) ).
thf(f3258,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3257]) ).
thf(f3259,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2930]) ).
thf(f3260,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2929]) ).
thf(f3261,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f2931]) ).
thf(f3262,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2931]) ).
thf(f3263,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2933]) ).
thf(f3264,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2932]) ).
thf(f3265,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3264]) ).
thf(f3266,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2935]) ).
thf(f3267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3266]) ).
thf(f3268,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f2934]) ).
thf(f3269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2937]) ).
thf(f3270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2938]) ).
thf(f3271,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3270]) ).
thf(f3272,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2939]) ).
thf(f3273,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2941]) ).
thf(f3274,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3273]) ).
thf(f3275,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2943]) ).
thf(f3276,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3275]) ).
thf(f3277,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f2944]) ).
thf(f3278,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3277]) ).
thf(f3279,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2945]) ).
thf(f3280,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2947]) ).
thf(f3281,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2948]) ).
thf(f3282,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3281]) ).
thf(f3283,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f2949]) ).
thf(f3284,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f2950]) ).
thf(f3285,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3284]) ).
thf(f3286,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2952]) ).
thf(f3287,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2952]) ).
thf(f3288,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2953]) ).
thf(f3289,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3288]) ).
thf(f3290,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2955]) ).
thf(f3291,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3290]) ).
thf(f3292,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2957]) ).
thf(f3293,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2959]) ).
thf(f3294,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f2961]) ).
thf(f3295,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3294]) ).
thf(f3296,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2962]) ).
thf(f3297,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3296]) ).
thf(f3298,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2964]) ).
thf(f3299,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2965]) ).
thf(f3300,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3299]) ).
thf(f3301,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2966]) ).
thf(f3302,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3301]) ).
thf(f3303,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2968]) ).
thf(f3304,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2970]) ).
thf(f3305,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2970]) ).
thf(f3306,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2969]) ).
thf(f3308,definition,
( spl38_111
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_111])],[avatar_definition]) ).
thf(f3309,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_111 ),
inference(avatar_component_clause,[],[f3308]) ).
thf(f3310,plain,
( spl38_111
| spl38_103
| spl38_104
| spl38_102 ),
inference(avatar_split_clause,[],[f2971,f2995,f3001,f2998,f3308]) ).
thf(f3311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2973]) ).
thf(f3312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2974]) ).
thf(f3313,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2976]) ).
thf(f3314,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3313]) ).
thf(f3315,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2975]) ).
thf(f3316,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3315]) ).
thf(f3317,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2978]) ).
thf(f3318,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2977]) ).
thf(f3319,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3318]) ).
thf(f3320,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2980]) ).
thf(f3321,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3320]) ).
thf(f3322,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2982]) ).
thf(f3323,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3322]) ).
thf(f3324,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2984]) ).
thf(f3325,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2985]) ).
thf(f3326,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3325]) ).
thf(f3327,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2986]) ).
thf(f3328,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3327]) ).
thf(f3330,definition,
( spl38_112
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_112])],[avatar_definition]) ).
thf(f3331,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_112 ),
inference(avatar_component_clause,[],[f3330]) ).
thf(f3332,plain,
( spl38_102
| spl38_103
| spl38_112
| spl38_101 ),
inference(avatar_split_clause,[],[f2987,f2992,f3330,f2998,f2995]) ).
thf(f3333,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2988]) ).
thf(f3334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2990]) ).
thf(f3365,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3036]) ).
thf(f3366,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3037]) ).
thf(f3367,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3366]) ).
thf(f3368,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3039]) ).
thf(f3370,definition,
( spl38_117
<=> ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_117])],[avatar_definition]) ).
thf(f3371,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) )
| ~ spl38_117 ),
inference(avatar_component_clause,[],[f3370]) ).
thf(f3372,plain,
( spl38_117
| spl38_101
| spl38_102
| spl38_104 ),
inference(avatar_split_clause,[],[f3040,f3001,f2995,f2992,f3370]) ).
thf(f3373,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3041]) ).
thf(f3374,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3042]) ).
thf(f3375,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3374]) ).
thf(f3376,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3043]) ).
thf(f3377,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3045]) ).
thf(f3378,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3047]) ).
thf(f3379,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3048]) ).
thf(f3380,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3379]) ).
thf(f3381,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3049]) ).
thf(f3382,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3049]) ).
thf(f3383,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3050]) ).
thf(f3384,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3383]) ).
thf(f3385,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3051]) ).
thf(f3386,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3051]) ).
thf(f3387,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3052]) ).
thf(f3388,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3387]) ).
thf(f3389,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3053]) ).
thf(f3390,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3389]) ).
thf(f3391,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3054]) ).
thf(f3392,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3056]) ).
thf(f3393,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3056]) ).
thf(f3394,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3058]) ).
thf(f3395,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3057]) ).
thf(f3396,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3395]) ).
thf(f3397,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3059]) ).
thf(f3398,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3059]) ).
thf(f3399,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3060]) ).
thf(f3400,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3060]) ).
thf(f3401,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3061]) ).
thf(f3402,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3401]) ).
thf(f3403,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3063]) ).
thf(f3404,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3065]) ).
thf(f3405,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3066]) ).
thf(f3406,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3405]) ).
thf(f3407,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3067]) ).
thf(f3408,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3407]) ).
thf(f3409,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3068]) ).
thf(f3410,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3409]) ).
thf(f3411,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3069]) ).
thf(f3412,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3069]) ).
thf(f3413,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3070]) ).
thf(f3414,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3413]) ).
thf(f3415,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3071]) ).
thf(f3416,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3071]) ).
thf(f3417,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3072]) ).
thf(f3418,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3072]) ).
thf(f3419,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3074]) ).
thf(f3420,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3419]) ).
thf(f3421,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3076]) ).
thf(f3422,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3078]) ).
thf(f3423,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3422]) ).
thf(f3424,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3079]) ).
thf(f3425,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3424]) ).
thf(f3426,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f3080]) ).
thf(f3427,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3080]) ).
thf(f3428,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3082]) ).
thf(f3429,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3084]) ).
thf(f3430,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3429]) ).
thf(f3431,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3086]) ).
thf(f3432,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3087]) ).
thf(f3433,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3088]) ).
thf(f3434,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3089]) ).
thf(f3435,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3089]) ).
thf(f3436,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3091]) ).
thf(f3437,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3090]) ).
thf(f3438,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3437]) ).
thf(f3439,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3092]) ).
thf(f3440,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3439]) ).
thf(f3441,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3093]) ).
thf(f3442,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3094]) ).
thf(f3443,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3095]) ).
thf(f3444,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3097]) ).
thf(f3445,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3099]) ).
thf(f3446,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3445]) ).
thf(f3447,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3098]) ).
thf(f3448,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3447]) ).
thf(f3450,definition,
( spl38_118
<=> ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_118])],[avatar_definition]) ).
thf(f3451,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) )
| ~ spl38_118 ),
inference(avatar_component_clause,[],[f3450]) ).
thf(f3452,plain,
( spl38_101
| spl38_104
| spl38_118
| spl38_102 ),
inference(avatar_split_clause,[],[f3100,f2995,f3450,f3001,f2992]) ).
thf(f3453,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3101]) ).
thf(f3454,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3453]) ).
thf(f3455,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3103]) ).
thf(f3456,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3104]) ).
thf(f3457,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3106]) ).
thf(f3458,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3105]) ).
thf(f3459,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3107]) ).
thf(f3460,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3459]) ).
thf(f3461,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3109]) ).
thf(f3462,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3111]) ).
thf(f3463,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3113]) ).
thf(f3464,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3115]) ).
thf(f3465,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3464]) ).
thf(f3466,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3114]) ).
thf(f3467,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3466]) ).
thf(f3468,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3116]) ).
thf(f3469,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3468]) ).
thf(f3470,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3117]) ).
thf(f3471,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3117]) ).
thf(f3472,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3119]) ).
thf(f3473,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3472]) ).
thf(f3474,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3121]) ).
thf(f3475,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3474]) ).
thf(f3476,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3123]) ).
thf(f3477,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3123]) ).
thf(f3478,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f3124]) ).
thf(f3479,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3478]) ).
thf(f3480,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f3125]) ).
thf(f3481,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3480]) ).
thf(f3482,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3127]) ).
thf(f3483,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3482]) ).
thf(f3484,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3129]) ).
thf(f3485,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3130]) ).
thf(f3486,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3131]) ).
thf(f3487,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3133]) ).
thf(f3488,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3135]) ).
thf(f3489,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3135]) ).
thf(f3490,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3137]) ).
thf(f3491,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3490]) ).
thf(f3492,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3139]) ).
thf(f3493,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3492]) ).
thf(f3494,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3140]) ).
thf(f3495,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3494]) ).
thf(f3496,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3141]) ).
thf(f3497,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f3141]) ).
thf(f3498,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3143]) ).
thf(f3499,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3145]) ).
thf(f3500,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3499]) ).
thf(f3501,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3146]) ).
thf(f3502,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3146]) ).
thf(f3503,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3148]) ).
thf(f3504,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f3148]) ).
thf(f3505,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3149]) ).
thf(f3506,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3149]) ).
thf(f3507,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3150]) ).
thf(f3508,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3507]) ).
thf(f3509,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3151]) ).
thf(f3510,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3509]) ).
thf(f3511,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3153]) ).
thf(f3512,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3154]) ).
thf(f3513,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3155]) ).
thf(f3514,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3513]) ).
thf(f3515,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3157]) ).
thf(f3516,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3158]) ).
thf(f3517,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3516]) ).
thf(f3518,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3159]) ).
thf(f3519,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3159]) ).
thf(f3520,plain,
( spl38_104
| spl38_109
| spl38_101
| spl38_110 ),
inference(avatar_split_clause,[],[f3160,f3245,f2992,f3179,f3001]) ).
thf(f3521,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3161]) ).
thf(f3522,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3162]) ).
thf(f3523,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3163]) ).
thf(f3524,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3523]) ).
thf(f3525,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3164]) ).
thf(f3526,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3525]) ).
thf(f3527,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3166]) ).
thf(f3528,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3167]) ).
thf(f3529,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3528]) ).
thf(f3530,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3168]) ).
thf(f3531,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3168]) ).
thf(f3532,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3169]) ).
thf(f3533,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3170]) ).
thf(f3534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3172]) ).
thf(f3535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3174]) ).
thf(f3536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3176]) ).
thf(f3537,plain,
( spl38_101
| spl38_112
| spl38_102
| spl38_109 ),
inference(avatar_split_clause,[],[f3177,f3179,f2995,f3330,f2992]) ).
thf(f3538,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3183]) ).
thf(f3539,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3185]) ).
thf(f3540,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3187]) ).
thf(f3541,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3189]) ).
thf(f3542,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3190]) ).
thf(f3543,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3192]) ).
thf(f3544,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3194]) ).
thf(f3545,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3194]) ).
thf(f3546,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3195]) ).
thf(f3547,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3196]) ).
thf(f3548,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3197]) ).
thf(f3549,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3199]) ).
thf(f3550,plain,
( spl38_111
| spl38_104
| spl38_102
| spl38_109 ),
inference(avatar_split_clause,[],[f3200,f3179,f2995,f3001,f3308]) ).
thf(f3551,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3202]) ).
thf(f3552,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3551]) ).
thf(f3553,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3201]) ).
thf(f3554,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3553]) ).
thf(f3555,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3204]) ).
thf(f3556,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3206]) ).
thf(f3557,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3206]) ).
thf(f3558,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3205]) ).
thf(f3559,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3558]) ).
thf(f3560,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3207]) ).
thf(f3561,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f3208]) ).
thf(f3562,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3561]) ).
thf(f3563,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3210]) ).
thf(f3564,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3563]) ).
thf(f3565,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3212]) ).
thf(f3566,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3565]) ).
thf(f3567,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3214]) ).
thf(f3568,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3215]) ).
thf(f3569,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3216]) ).
thf(f3570,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3569]) ).
thf(f3571,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3217]) ).
thf(f3572,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3571]) ).
thf(f3573,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3219]) ).
thf(f3574,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3220]) ).
thf(f3575,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3220]) ).
thf(f3576,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3221]) ).
thf(f3577,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3576]) ).
thf(f3578,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3222]) ).
thf(f3579,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3223]) ).
thf(f3580,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3224]) ).
thf(f3581,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3580]) ).
thf(f3582,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3226]) ).
thf(f3583,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3227]) ).
thf(f3584,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3583]) ).
thf(f3585,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3228]) ).
thf(f3586,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3585]) ).
thf(f3587,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3230]) ).
thf(f3588,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3232]) ).
thf(f3589,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3233]) ).
thf(f3590,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3233]) ).
thf(f3591,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3234]) ).
thf(f3592,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f3236]) ).
thf(f3593,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3592]) ).
thf(f3594,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f3237]) ).
thf(f3595,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3237]) ).
thf(f3596,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3238]) ).
thf(f3597,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3596]) ).
thf(f3598,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3239]) ).
thf(f3599,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3241]) ).
thf(f3600,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3242]) ).
thf(f3601,plain,
( spl38_101
| spl38_112
| spl38_103
| spl38_110 ),
inference(avatar_split_clause,[],[f3243,f3245,f2998,f3330,f2992]) ).
thf(f3602,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3249]) ).
thf(f3603,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3602]) ).
thf(f3604,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3248]) ).
thf(f3605,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3604]) ).
thf(f3606,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3251]) ).
thf(f3607,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3252]) ).
thf(f3608,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3253]) ).
thf(f3609,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3608]) ).
thf(f3610,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3254]) ).
thf(f3611,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3610]) ).
thf(f3613,definition,
( spl38_119
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_119])],[avatar_definition]) ).
thf(f3614,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) )
| ~ spl38_119 ),
inference(avatar_component_clause,[],[f3613]) ).
thf(f3615,plain,
( spl38_103
| spl38_101
| spl38_119
| spl38_104 ),
inference(avatar_split_clause,[],[f3255,f3001,f3613,f2992,f2998]) ).
thf(f3617,definition,
( spl38_120
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl38_120])],[avatar_definition]) ).
thf(f3618,plain,
( ! [X3: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) )
| ~ spl38_120 ),
inference(avatar_component_clause,[],[f3617]) ).
thf(f3619,plain,
( spl38_120
| spl38_104
| spl38_101
| spl38_103 ),
inference(avatar_split_clause,[],[f3256,f2998,f2992,f3001,f3617]) ).
thf(f3620,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3258]) ).
thf(f3621,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3259]) ).
thf(f3622,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3621]) ).
thf(f3623,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3260]) ).
thf(f3624,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3623]) ).
thf(f3625,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3262]) ).
thf(f3626,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f3625]) ).
thf(f3627,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3261]) ).
thf(f3628,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3627]) ).
thf(f3629,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3263]) ).
thf(f3630,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f3265]) ).
thf(f3631,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3267]) ).
thf(f3632,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3268]) ).
thf(f3633,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3632]) ).
thf(f3634,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3269]) ).
thf(f3635,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3271]) ).
thf(f3636,plain,
( spl38_110
| spl38_104
| spl38_111
| spl38_103 ),
inference(avatar_split_clause,[],[f3272,f2998,f3308,f3001,f3245]) ).
thf(f3637,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3274]) ).
thf(f3638,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3276]) ).
thf(f3639,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3278]) ).
thf(f3640,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3279]) ).
thf(f3641,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3640]) ).
thf(f3642,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3280]) ).
thf(f3643,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3282]) ).
thf(f3644,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f3283]) ).
thf(f3645,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3644]) ).
thf(f3646,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3285]) ).
thf(f3647,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3286]) ).
thf(f3648,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3647]) ).
thf(f3649,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3287]) ).
thf(f3650,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3289]) ).
thf(f3651,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3289]) ).
thf(f3652,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3291]) ).
thf(f3653,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3292]) ).
thf(f3654,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f3653]) ).
thf(f3655,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3293]) ).
thf(f3656,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3655]) ).
thf(f3657,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3295]) ).
thf(f3658,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3297]) ).
thf(f3659,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3298]) ).
thf(f3660,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3300]) ).
thf(f3661,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3660]) ).
thf(f3662,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3302]) ).
thf(f3663,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3303]) ).
thf(f3664,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3305]) ).
thf(f3665,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3664]) ).
thf(f3666,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3304]) ).
thf(f3667,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3306]) ).
thf(f3668,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3667]) ).
thf(f3670,definition,
( spl38_121
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_121])],[avatar_definition]) ).
thf(f3671,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_121 ),
inference(avatar_component_clause,[],[f3670]) ).
thf(f3672,plain,
( spl38_102
| spl38_121
| spl38_104
| spl38_103 ),
inference(avatar_split_clause,[],[f3311,f2998,f3001,f3670,f2995]) ).
thf(f3674,definition,
( spl38_122
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl38_122])],[avatar_definition]) ).
thf(f3675,plain,
( ! [X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_122 ),
inference(avatar_component_clause,[],[f3674]) ).
thf(f3676,plain,
( spl38_122
| spl38_104
| spl38_103
| spl38_102 ),
inference(avatar_split_clause,[],[f3312,f2995,f2998,f3001,f3674]) ).
thf(f3677,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3314]) ).
thf(f3678,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3316]) ).
thf(f3679,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3317]) ).
thf(f3680,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3679]) ).
thf(f3681,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3319]) ).
thf(f3682,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3321]) ).
thf(f3683,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3323]) ).
thf(f3684,plain,
( spl38_102
| spl38_112
| spl38_103
| spl38_111 ),
inference(avatar_split_clause,[],[f3324,f3308,f2998,f3330,f2995]) ).
thf(f3685,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3326]) ).
thf(f3686,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3328]) ).
thf(f3688,definition,
( spl38_123
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_123])],[avatar_definition]) ).
thf(f3689,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) )
| ~ spl38_123 ),
inference(avatar_component_clause,[],[f3688]) ).
thf(f3690,plain,
( spl38_123
| spl38_103
| spl38_102
| spl38_101 ),
inference(avatar_split_clause,[],[f3333,f2992,f2995,f2998,f3688]) ).
thf(f3692,definition,
( spl38_124
<=> ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl38_124])],[avatar_definition]) ).
thf(f3693,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) )
| ~ spl38_124 ),
inference(avatar_component_clause,[],[f3692]) ).
thf(f3694,plain,
( spl38_101
| spl38_103
| spl38_102
| spl38_124 ),
inference(avatar_split_clause,[],[f3334,f3692,f2995,f2998,f2992]) ).
thf(f3736,plain,
( spl38_110
| spl38_101
| spl38_104
| spl38_117 ),
inference(avatar_split_clause,[],[f3365,f3370,f3001,f2992,f3245]) ).
thf(f3737,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3367]) ).
thf(f3738,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3368]) ).
thf(f3739,plain,
( spl38_117
| spl38_102
| spl38_112
| spl38_101 ),
inference(avatar_split_clause,[],[f3373,f2992,f3330,f2995,f3370]) ).
thf(f3740,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3375]) ).
thf(f3741,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3376]) ).
thf(f3742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3741]) ).
thf(f3743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3377]) ).
thf(f3744,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3378]) ).
thf(f3745,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3380]) ).
thf(f3746,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3382]) ).
thf(f3747,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3382]) ).
thf(f3748,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3381]) ).
thf(f3749,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3748]) ).
thf(f3750,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3384]) ).
thf(f3751,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3386]) ).
thf(f3752,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3385]) ).
thf(f3753,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3752]) ).
thf(f3754,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3388]) ).
thf(f3755,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f3388]) ).
thf(f3756,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3390]) ).
thf(f3757,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3756]) ).
thf(f3758,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3391]) ).
thf(f3759,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3758]) ).
thf(f3760,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3393]) ).
thf(f3761,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3392]) ).
thf(f3762,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3394]) ).
thf(f3763,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3394]) ).
thf(f3764,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3396]) ).
thf(f3765,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3397]) ).
thf(f3766,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3765]) ).
thf(f3767,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3398]) ).
thf(f3768,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f3767]) ).
thf(f3769,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3400]) ).
thf(f3770,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f3769]) ).
thf(f3771,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3399]) ).
thf(f3772,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f3771]) ).
thf(f3773,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3402]) ).
thf(f3774,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3403]) ).
thf(f3775,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3404]) ).
thf(f3776,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3775]) ).
thf(f3777,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3406]) ).
thf(f3778,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3408]) ).
thf(f3779,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3778]) ).
thf(f3780,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3410]) ).
thf(f3781,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3412]) ).
thf(f3782,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3781]) ).
thf(f3783,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3411]) ).
thf(f3784,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3783]) ).
thf(f3785,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3414]) ).
thf(f3786,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3415]) ).
thf(f3787,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3786]) ).
thf(f3788,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3416]) ).
thf(f3789,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3788]) ).
thf(f3790,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3418]) ).
thf(f3791,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3418]) ).
thf(f3792,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3417]) ).
thf(f3793,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3792]) ).
thf(f3794,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3420]) ).
thf(f3795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3421]) ).
thf(f3796,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3423]) ).
thf(f3797,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3425]) ).
thf(f3798,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3797]) ).
thf(f3799,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3427]) ).
thf(f3800,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3426]) ).
thf(f3801,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3800]) ).
thf(f3802,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3428]) ).
thf(f3803,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3430]) ).
thf(f3804,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3431]) ).
thf(f3805,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3432]) ).
thf(f3806,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3433]) ).
thf(f3807,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3435]) ).
thf(f3808,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3435]) ).
thf(f3809,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3434]) ).
thf(f3810,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3809]) ).
thf(f3811,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3436]) ).
thf(f3812,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3436]) ).
thf(f3813,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f3438]) ).
thf(f3814,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3440]) ).
thf(f3815,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3441]) ).
thf(f3816,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3815]) ).
thf(f3817,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3442]) ).
thf(f3818,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3817]) ).
thf(f3819,plain,
( spl38_102
| spl38_117
| spl38_104
| spl38_111 ),
inference(avatar_split_clause,[],[f3443,f3308,f3001,f3370,f2995]) ).
thf(f3820,plain,
( spl38_112
| spl38_101
| spl38_102
| spl38_118 ),
inference(avatar_split_clause,[],[f3444,f3450,f2995,f2992,f3330]) ).
thf(f3821,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3446]) ).
thf(f3822,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3448]) ).
thf(f3823,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3454]) ).
thf(f3824,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3455]) ).
thf(f3825,plain,
( spl38_110
| spl38_118
| spl38_101
| spl38_104 ),
inference(avatar_split_clause,[],[f3456,f3001,f2992,f3450,f3245]) ).
thf(f3826,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3457]) ).
thf(f3827,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3826]) ).
thf(f3828,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3458]) ).
thf(f3829,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3828]) ).
thf(f3830,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3460]) ).
thf(f3831,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3461]) ).
thf(f3832,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f3831]) ).
thf(f3833,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3462]) ).
thf(f3834,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3833]) ).
thf(f3835,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3463]) ).
thf(f3836,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3463]) ).
thf(f3837,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3465]) ).
thf(f3838,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3467]) ).
thf(f3839,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3469]) ).
thf(f3840,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3471]) ).
thf(f3841,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3471]) ).
thf(f3842,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3470]) ).
thf(f3843,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3842]) ).
thf(f3844,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3473]) ).
thf(f3845,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3475]) ).
thf(f3846,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3476]) ).
thf(f3847,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3846]) ).
thf(f3848,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3477]) ).
thf(f3849,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3848]) ).
thf(f3850,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f3479]) ).
thf(f3851,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3481]) ).
thf(f3852,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f3483]) ).
thf(f3853,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3484]) ).
thf(f3854,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3485]) ).
thf(f3855,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3854]) ).
thf(f3856,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3486]) ).
thf(f3857,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3856]) ).
thf(f3858,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3487]) ).
thf(f3859,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f3487]) ).
thf(f3860,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3489]) ).
thf(f3861,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3489]) ).
thf(f3862,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3488]) ).
thf(f3863,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3491]) ).
thf(f3864,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3493]) ).
thf(f3865,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3493]) ).
thf(f3866,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3495]) ).
thf(f3867,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3497]) ).
thf(f3868,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3496]) ).
thf(f3869,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3498]) ).
thf(f3870,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3500]) ).
thf(f3871,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3501]) ).
thf(f3872,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3871]) ).
thf(f3873,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3502]) ).
thf(f3874,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3873]) ).
thf(f3875,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3503]) ).
thf(f3876,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3504]) ).
thf(f3877,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3505]) ).
thf(f3878,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3877]) ).
thf(f3879,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3506]) ).
thf(f3880,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3879]) ).
thf(f3881,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3508]) ).
thf(f3882,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3510]) ).
thf(f3883,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3882]) ).
thf(f3884,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f3511]) ).
thf(f3885,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3511]) ).
thf(f3886,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3512]) ).
thf(f3887,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3514]) ).
thf(f3888,plain,
( spl38_104
| spl38_111
| spl38_102
| spl38_118 ),
inference(avatar_split_clause,[],[f3515,f3450,f2995,f3308,f3001]) ).
thf(f3889,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3517]) ).
thf(f3890,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3518]) ).
thf(f3891,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3890]) ).
thf(f3892,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3519]) ).
thf(f3893,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3892]) ).
thf(f3894,plain,
( spl38_101
| spl38_120
| spl38_109
| spl38_104 ),
inference(avatar_split_clause,[],[f3521,f3001,f3179,f3617,f2992]) ).
thf(f3895,plain,
( spl38_104
| spl38_109
| spl38_101
| spl38_119 ),
inference(avatar_split_clause,[],[f3522,f3613,f2992,f3179,f3001]) ).
thf(f3896,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3524]) ).
thf(f3897,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3526]) ).
thf(f3898,plain,
( spl38_101
| spl38_110
| spl38_112
| spl38_109 ),
inference(avatar_split_clause,[],[f3527,f3179,f3330,f3245,f2992]) ).
thf(f3899,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3529]) ).
thf(f3900,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3530]) ).
thf(f3901,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3900]) ).
thf(f3902,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3531]) ).
thf(f3903,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3902]) ).
thf(f3904,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3532]) ).
thf(f3905,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3904]) ).
thf(f3906,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3533]) ).
thf(f3907,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3906]) ).
thf(f3908,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3534]) ).
thf(f3909,plain,
( spl38_101
| spl38_123
| spl38_102
| spl38_109 ),
inference(avatar_split_clause,[],[f3535,f3179,f2995,f3688,f2992]) ).
thf(f3910,plain,
( spl38_102
| spl38_124
| spl38_101
| spl38_109 ),
inference(avatar_split_clause,[],[f3536,f3179,f2992,f3692,f2995]) ).
thf(f3911,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3538]) ).
thf(f3912,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3539]) ).
thf(f3913,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3912]) ).
thf(f3914,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3540]) ).
thf(f3915,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3914]) ).
thf(f3916,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3541]) ).
thf(f3917,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3542]) ).
thf(f3918,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3543]) ).
thf(f3919,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3918]) ).
thf(f3920,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3544]) ).
thf(f3921,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3545]) ).
thf(f3922,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3921]) ).
thf(f3923,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3546]) ).
thf(f3924,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3547]) ).
thf(f3925,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3924]) ).
thf(f3926,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3548]) ).
thf(f3927,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3926]) ).
thf(f3928,plain,
( spl38_112
| spl38_111
| spl38_102
| spl38_109 ),
inference(avatar_split_clause,[],[f3549,f3179,f2995,f3308,f3330]) ).
thf(f3929,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3552]) ).
thf(f3930,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3554]) ).
thf(f3931,plain,
( spl38_110
| spl38_104
| spl38_109
| spl38_111 ),
inference(avatar_split_clause,[],[f3555,f3308,f3179,f3001,f3245]) ).
thf(f3932,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3556]) ).
thf(f3933,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3932]) ).
thf(f3934,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3557]) ).
thf(f3935,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3934]) ).
thf(f3936,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3559]) ).
thf(f3937,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3560]) ).
thf(f3938,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3937]) ).
thf(f3939,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f3562]) ).
thf(f3940,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f3564]) ).
thf(f3941,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3940]) ).
thf(f3942,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3566]) ).
thf(f3943,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3942]) ).
thf(f3944,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3567]) ).
thf(f3945,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3944]) ).
thf(f3946,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3568]) ).
thf(f3947,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3570]) ).
thf(f3948,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3572]) ).
thf(f3949,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3948]) ).
thf(f3950,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3573]) ).
thf(f3951,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3574]) ).
thf(f3952,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3951]) ).
thf(f3953,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3575]) ).
thf(f3954,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3953]) ).
thf(f3955,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3577]) ).
thf(f3956,plain,
( spl38_104
| spl38_121
| spl38_109
| spl38_102 ),
inference(avatar_split_clause,[],[f3578,f2995,f3179,f3670,f3001]) ).
thf(f3957,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3579]) ).
thf(f3958,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f3957]) ).
thf(f3959,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3581]) ).
thf(f3960,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3582]) ).
thf(f3961,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3584]) ).
thf(f3962,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3586]) ).
thf(f3963,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3962]) ).
thf(f3964,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3587]) ).
thf(f3965,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3964]) ).
thf(f3966,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3588]) ).
thf(f3967,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f3588]) ).
thf(f3968,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f3590]) ).
thf(f3969,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f3968]) ).
thf(f3970,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3589]) ).
thf(f3971,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3970]) ).
thf(f3972,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3591]) ).
thf(f3973,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3593]) ).
thf(f3974,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3594]) ).
thf(f3975,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3974]) ).
thf(f3976,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3595]) ).
thf(f3977,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3976]) ).
thf(f3978,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3597]) ).
thf(f3979,plain,
( spl38_122
| spl38_102
| spl38_104
| spl38_109 ),
inference(avatar_split_clause,[],[f3598,f3179,f3001,f2995,f3674]) ).
thf(f3980,plain,
( spl38_103
| spl38_110
| spl38_101
| spl38_123 ),
inference(avatar_split_clause,[],[f3599,f3688,f2992,f3245,f2998]) ).
thf(f3981,plain,
( spl38_101
| spl38_124
| spl38_110
| spl38_103 ),
inference(avatar_split_clause,[],[f3600,f2998,f3245,f3692,f2992]) ).
thf(f3982,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3603]) ).
thf(f3983,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3605]) ).
thf(f3984,plain,
( spl38_101
| spl38_103
| spl38_119
| spl38_112 ),
inference(avatar_split_clause,[],[f3606,f3330,f3613,f2998,f2992]) ).
thf(f3985,plain,
( spl38_101
| spl38_103
| spl38_120
| spl38_112 ),
inference(avatar_split_clause,[],[f3607,f3330,f3617,f2998,f2992]) ).
thf(f3986,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3609]) ).
thf(f3987,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3611]) ).
thf(f3988,plain,
( spl38_111
| spl38_112
| spl38_110
| spl38_103 ),
inference(avatar_split_clause,[],[f3620,f2998,f3245,f3330,f3308]) ).
thf(f3989,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3622]) ).
thf(f3990,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3624]) ).
thf(f3991,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3626]) ).
thf(f3992,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3628]) ).
thf(f3993,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3629]) ).
thf(f3994,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3993]) ).
thf(f3995,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3630]) ).
thf(f3996,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3631]) ).
thf(f3997,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3633]) ).
thf(f3998,plain,
( spl38_103
| spl38_104
| spl38_122
| spl38_110 ),
inference(avatar_split_clause,[],[f3634,f3245,f3674,f3001,f2998]) ).
thf(f3999,plain,
( spl38_104
| spl38_103
| spl38_121
| spl38_110 ),
inference(avatar_split_clause,[],[f3635,f3245,f3670,f2998,f3001]) ).
thf(f4000,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3637]) ).
thf(f4001,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3638]) ).
thf(f4002,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3639]) ).
thf(f4003,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3641]) ).
thf(f4004,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3642]) ).
thf(f4005,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f4004]) ).
thf(f4006,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3643]) ).
thf(f4007,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4006]) ).
thf(f4008,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3645]) ).
thf(f4009,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3646]) ).
thf(f4010,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3648]) ).
thf(f4011,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3649]) ).
thf(f4012,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f4011]) ).
thf(f4013,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3651]) ).
thf(f4014,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3650]) ).
thf(f4015,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3652]) ).
thf(f4016,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4015]) ).
thf(f4017,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3654]) ).
thf(f4018,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4017]) ).
thf(f4019,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3656]) ).
thf(f4020,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4019]) ).
thf(f4021,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3657]) ).
thf(f4022,plain,
( spl38_119
| spl38_111
| spl38_103
| spl38_104 ),
inference(avatar_split_clause,[],[f3658,f3001,f2998,f3308,f3613]) ).
thf(f4023,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3659]) ).
thf(f4024,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4023]) ).
thf(f4025,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3661]) ).
thf(f4026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3662]) ).
thf(f4027,plain,
( spl38_111
| spl38_104
| spl38_120
| spl38_103 ),
inference(avatar_split_clause,[],[f3663,f2998,f3617,f3001,f3308]) ).
thf(f4028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3665]) ).
thf(f4029,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3666]) ).
thf(f4030,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4029]) ).
thf(f4031,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3668]) ).
thf(f4032,plain,
( spl38_103
| spl38_112
| spl38_121
| spl38_102 ),
inference(avatar_split_clause,[],[f3677,f2995,f3670,f3330,f2998]) ).
thf(f4033,plain,
( spl38_103
| spl38_122
| spl38_102
| spl38_112 ),
inference(avatar_split_clause,[],[f3678,f3330,f2995,f3674,f2998]) ).
thf(f4034,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3680]) ).
thf(f4035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3681]) ).
thf(f4036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3682]) ).
thf(f4037,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3683]) ).
thf(f4038,plain,
( spl38_124
| spl38_102
| spl38_111
| spl38_103 ),
inference(avatar_split_clause,[],[f3685,f2998,f3308,f2995,f3692]) ).
thf(f4039,plain,
( spl38_102
| spl38_123
| spl38_103
| spl38_111 ),
inference(avatar_split_clause,[],[f3686,f3308,f2998,f3688,f2995]) ).
thf(f4055,plain,
( spl38_104
| spl38_119
| spl38_117
| spl38_101 ),
inference(avatar_split_clause,[],[f3737,f2992,f3370,f3613,f3001]) ).
thf(f4056,plain,
( spl38_104
| spl38_101
| spl38_117
| spl38_120 ),
inference(avatar_split_clause,[],[f3738,f3617,f3370,f2992,f3001]) ).
thf(f4057,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3740]) ).
thf(f4058,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3742]) ).
thf(f4059,plain,
( spl38_110
| spl38_112
| spl38_117
| spl38_101 ),
inference(avatar_split_clause,[],[f3743,f2992,f3370,f3330,f3245]) ).
thf(f4060,plain,
( spl38_117
| spl38_102
| spl38_124
| spl38_101 ),
inference(avatar_split_clause,[],[f3744,f2992,f3692,f2995,f3370]) ).
thf(f4061,plain,
( spl38_102
| spl38_123
| spl38_101
| spl38_117 ),
inference(avatar_split_clause,[],[f3745,f3370,f2992,f3688,f2995]) ).
thf(f4062,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3746]) ).
thf(f4063,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4062]) ).
thf(f4064,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3747]) ).
thf(f4065,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4064]) ).
thf(f4066,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3749]) ).
thf(f4067,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3750]) ).
thf(f4068,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3751]) ).
thf(f4069,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4068]) ).
thf(f4070,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3753]) ).
thf(f4071,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3755]) ).
thf(f4072,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3754]) ).
thf(f4073,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4072]) ).
thf(f4074,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3757]) ).
thf(f4075,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3759]) ).
thf(f4076,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4075]) ).
thf(f4077,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3760]) ).
thf(f4078,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4077]) ).
thf(f4079,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3761]) ).
thf(f4080,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f4079]) ).
thf(f4081,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3763]) ).
thf(f4082,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4081]) ).
thf(f4083,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3762]) ).
thf(f4084,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4083]) ).
thf(f4085,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3764]) ).
thf(f4086,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3766]) ).
thf(f4087,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4086]) ).
thf(f4088,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3768]) ).
thf(f4089,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3770]) ).
thf(f4090,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3772]) ).
thf(f4091,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4090]) ).
thf(f4092,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3773]) ).
thf(f4093,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4092]) ).
thf(f4094,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3774]) ).
thf(f4095,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4094]) ).
thf(f4096,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3776]) ).
thf(f4097,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3777]) ).
thf(f4098,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4097]) ).
thf(f4099,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3779]) ).
thf(f4100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3780]) ).
thf(f4101,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4100]) ).
thf(f4102,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f3782]) ).
thf(f4103,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3784]) ).
thf(f4104,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4103]) ).
thf(f4105,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3785]) ).
thf(f4106,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4105]) ).
thf(f4107,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3787]) ).
thf(f4108,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3789]) ).
thf(f4109,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4108]) ).
thf(f4110,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3790]) ).
thf(f4111,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4110]) ).
thf(f4112,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3791]) ).
thf(f4113,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4112]) ).
thf(f4114,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3793]) ).
thf(f4115,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3794]) ).
thf(f4116,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3795]) ).
thf(f4117,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3796]) ).
thf(f4118,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3798]) ).
thf(f4119,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3799]) ).
thf(f4120,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4119]) ).
thf(f4121,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3801]) ).
thf(f4122,plain,
( spl38_117
| spl38_111
| spl38_104
| spl38_110 ),
inference(avatar_split_clause,[],[f3802,f3245,f3001,f3308,f3370]) ).
thf(f4123,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3803]) ).
thf(f4124,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3804]) ).
thf(f4125,plain,
( spl38_122
| spl38_104
| spl38_102
| spl38_117 ),
inference(avatar_split_clause,[],[f3805,f3370,f2995,f3001,f3674]) ).
thf(f4126,plain,
( spl38_117
| spl38_102
| spl38_121
| spl38_104 ),
inference(avatar_split_clause,[],[f3806,f3001,f3670,f2995,f3370]) ).
thf(f4127,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3808]) ).
thf(f4128,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4127]) ).
thf(f4129,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3807]) ).
thf(f4130,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4129]) ).
thf(f4131,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3810]) ).
thf(f4132,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3811]) ).
thf(f4133,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4132]) ).
thf(f4134,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3812]) ).
thf(f4135,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4134]) ).
thf(f4136,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3813]) ).
thf(f4137,plain,
( spl38_111
| spl38_102
| spl38_112
| spl38_117 ),
inference(avatar_split_clause,[],[f3814,f3370,f3330,f2995,f3308]) ).
thf(f4138,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3816]) ).
thf(f4139,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3818]) ).
thf(f4140,plain,
( spl38_118
| spl38_101
| spl38_102
| spl38_123 ),
inference(avatar_split_clause,[],[f3821,f3688,f2995,f2992,f3450]) ).
thf(f4141,plain,
( spl38_124
| spl38_101
| spl38_102
| spl38_118 ),
inference(avatar_split_clause,[],[f3822,f3450,f2995,f2992,f3692]) ).
thf(f4142,plain,
( spl38_101
| spl38_118
| spl38_104
| spl38_120 ),
inference(avatar_split_clause,[],[f3823,f3617,f3001,f3450,f2992]) ).
thf(f4143,plain,
( spl38_101
| spl38_104
| spl38_119
| spl38_118 ),
inference(avatar_split_clause,[],[f3824,f3450,f3613,f3001,f2992]) ).
thf(f4144,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3827]) ).
thf(f4145,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3829]) ).
thf(f4146,plain,
( spl38_118
| spl38_101
| spl38_110
| spl38_112 ),
inference(avatar_split_clause,[],[f3830,f3330,f3245,f2992,f3450]) ).
thf(f4147,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3832]) ).
thf(f4148,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3834]) ).
thf(f4149,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3835]) ).
thf(f4150,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4149]) ).
thf(f4151,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3836]) ).
thf(f4152,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4151]) ).
thf(f4153,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3837]) ).
thf(f4154,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4153]) ).
thf(f4155,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3838]) ).
thf(f4156,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4155]) ).
thf(f4157,plain,
( spl38_118
| spl38_111
| spl38_102
| spl38_112 ),
inference(avatar_split_clause,[],[f3839,f3330,f2995,f3308,f3450]) ).
thf(f4158,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3840]) ).
thf(f4159,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4158]) ).
thf(f4160,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3841]) ).
thf(f4161,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4160]) ).
thf(f4162,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3843]) ).
thf(f4163,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3844]) ).
thf(f4164,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3845]) ).
thf(f4165,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3847]) ).
thf(f4166,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3849]) ).
thf(f4167,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3850]) ).
thf(f4168,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4167]) ).
thf(f4169,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3851]) ).
thf(f4170,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4169]) ).
thf(f4171,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3852]) ).
thf(f4172,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3853]) ).
thf(f4173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3855]) ).
thf(f4174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3857]) ).
thf(f4175,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3858]) ).
thf(f4176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4175]) ).
thf(f4177,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3859]) ).
thf(f4178,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f3859]) ).
thf(f4179,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3860]) ).
thf(f4180,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3861]) ).
thf(f4181,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3862]) ).
thf(f4182,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f4181]) ).
thf(f4183,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3863]) ).
thf(f4184,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f3865]) ).
thf(f4185,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4184]) ).
thf(f4186,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3864]) ).
thf(f4187,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3866]) ).
thf(f4188,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4187]) ).
thf(f4189,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f3867]) ).
thf(f4190,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f3867]) ).
thf(f4191,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3868]) ).
thf(f4192,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4191]) ).
thf(f4193,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3869]) ).
thf(f4194,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4193]) ).
thf(f4195,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3870]) ).
thf(f4196,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3872]) ).
thf(f4197,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f4196]) ).
thf(f4198,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3874]) ).
thf(f4199,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3875]) ).
thf(f4200,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3876]) ).
thf(f4201,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3878]) ).
thf(f4202,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3880]) ).
thf(f4203,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3881]) ).
thf(f4204,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4203]) ).
thf(f4205,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3883]) ).
thf(f4206,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3884]) ).
thf(f4207,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4206]) ).
thf(f4208,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3885]) ).
thf(f4209,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4208]) ).
thf(f4210,plain,
( spl38_118
| spl38_121
| spl38_102
| spl38_104 ),
inference(avatar_split_clause,[],[f3886,f3001,f2995,f3670,f3450]) ).
thf(f4211,plain,
( spl38_122
| spl38_118
| spl38_104
| spl38_102 ),
inference(avatar_split_clause,[],[f3887,f2995,f3001,f3450,f3674]) ).
thf(f4212,plain,
( spl38_104
| spl38_118
| spl38_110
| spl38_111 ),
inference(avatar_split_clause,[],[f3889,f3308,f3245,f3450,f3001]) ).
thf(f4213,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3891]) ).
thf(f4214,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3893]) ).
thf(f4215,plain,
( spl38_109
| spl38_112
| spl38_120
| spl38_101 ),
inference(avatar_split_clause,[],[f3896,f2992,f3617,f3330,f3179]) ).
thf(f4216,plain,
( spl38_112
| spl38_101
| spl38_119
| spl38_109 ),
inference(avatar_split_clause,[],[f3897,f3179,f3613,f2992,f3330]) ).
thf(f4217,plain,
( spl38_110
| spl38_123
| spl38_109
| spl38_101 ),
inference(avatar_split_clause,[],[f3899,f2992,f3179,f3688,f3245]) ).
thf(f4218,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3901]) ).
thf(f4219,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3903]) ).
thf(f4220,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3905]) ).
thf(f4221,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3907]) ).
thf(f4222,plain,
( spl38_101
| spl38_110
| spl38_109
| spl38_124 ),
inference(avatar_split_clause,[],[f3908,f3692,f3179,f3245,f2992]) ).
thf(f4223,plain,
( spl38_123
| spl38_102
| spl38_111
| spl38_109 ),
inference(avatar_split_clause,[],[f3911,f3179,f3308,f2995,f3688]) ).
thf(f4224,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3913]) ).
thf(f4225,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3915]) ).
thf(f4226,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3916]) ).
thf(f4227,plain,
( spl38_124
| spl38_111
| spl38_102
| spl38_109 ),
inference(avatar_split_clause,[],[f3917,f3179,f2995,f3308,f3692]) ).
thf(f4228,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3919]) ).
thf(f4229,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3920]) ).
thf(f4230,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4229]) ).
thf(f4231,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3922]) ).
thf(f4232,plain,
( spl38_112
| spl38_110
| spl38_109
| spl38_111 ),
inference(avatar_split_clause,[],[f3923,f3308,f3179,f3245,f3330]) ).
thf(f4233,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3925]) ).
thf(f4234,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3927]) ).
thf(f4235,plain,
( spl38_104
| spl38_109
| spl38_119
| spl38_111 ),
inference(avatar_split_clause,[],[f3929,f3308,f3613,f3179,f3001]) ).
thf(f4236,plain,
( spl38_104
| spl38_120
| spl38_111
| spl38_109 ),
inference(avatar_split_clause,[],[f3930,f3179,f3308,f3617,f3001]) ).
thf(f4237,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3933]) ).
thf(f4238,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3935]) ).
thf(f4239,plain,
( spl38_102
| spl38_109
| spl38_112
| spl38_121 ),
inference(avatar_split_clause,[],[f3936,f3670,f3330,f3179,f2995]) ).
thf(f4240,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3938]) ).
thf(f4241,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4240]) ).
thf(f4242,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3939]) ).
thf(f4243,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4242]) ).
thf(f4244,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3941]) ).
thf(f4245,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3943]) ).
thf(f4246,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3945]) ).
thf(f4247,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3946]) ).
thf(f4248,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4247]) ).
thf(f4249,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3947]) ).
thf(f4250,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4249]) ).
thf(f4251,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3949]) ).
thf(f4252,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3950]) ).
thf(f4253,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3952]) ).
thf(f4254,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3954]) ).
thf(f4255,plain,
( spl38_121
| spl38_109
| spl38_104
| spl38_110 ),
inference(avatar_split_clause,[],[f3955,f3245,f3001,f3179,f3670]) ).
thf(f4256,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3958]) ).
thf(f4257,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3959]) ).
thf(f4258,plain,
( spl38_109
| spl38_102
| spl38_122
| spl38_112 ),
inference(avatar_split_clause,[],[f3960,f3330,f3674,f2995,f3179]) ).
thf(f4259,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3961]) ).
thf(f4260,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4259]) ).
thf(f4261,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3963]) ).
thf(f4262,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3965]) ).
thf(f4263,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3967]) ).
thf(f4264,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f4263]) ).
thf(f4265,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3966]) ).
thf(f4266,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4265]) ).
thf(f4267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3969]) ).
thf(f4268,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4267]) ).
thf(f4269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f3971]) ).
thf(f4270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4269]) ).
thf(f4271,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3972]) ).
thf(f4272,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4271]) ).
thf(f4273,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3973]) ).
thf(f4274,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3975]) ).
thf(f4275,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3977]) ).
thf(f4276,plain,
( spl38_122
| spl38_109
| spl38_110
| spl38_104 ),
inference(avatar_split_clause,[],[f3978,f3001,f3245,f3179,f3674]) ).
thf(f4277,plain,
( spl38_123
| spl38_119
| spl38_103
| spl38_101 ),
inference(avatar_split_clause,[],[f3982,f2992,f2998,f3613,f3688]) ).
thf(f4278,plain,
( spl38_124
| spl38_103
| spl38_101
| spl38_119 ),
inference(avatar_split_clause,[],[f3983,f3613,f2992,f2998,f3692]) ).
thf(f4279,plain,
( spl38_103
| spl38_120
| spl38_101
| spl38_123 ),
inference(avatar_split_clause,[],[f3986,f3688,f2992,f3617,f2998]) ).
thf(f4280,plain,
( spl38_103
| spl38_124
| spl38_120
| spl38_101 ),
inference(avatar_split_clause,[],[f3987,f2992,f3617,f3692,f2998]) ).
thf(f4281,plain,
( spl38_112
| spl38_121
| spl38_103
| spl38_110 ),
inference(avatar_split_clause,[],[f3989,f3245,f2998,f3670,f3330]) ).
thf(f4282,plain,
( spl38_112
| spl38_103
| spl38_110
| spl38_122 ),
inference(avatar_split_clause,[],[f3990,f3674,f3245,f2998,f3330]) ).
thf(f4283,plain,
( spl38_123
| spl38_103
| spl38_111
| spl38_110 ),
inference(avatar_split_clause,[],[f3991,f3245,f3308,f2998,f3688]) ).
thf(f4284,plain,
( spl38_124
| spl38_111
| spl38_103
| spl38_110 ),
inference(avatar_split_clause,[],[f3992,f3245,f2998,f3308,f3692]) ).
thf(f4285,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3994]) ).
thf(f4286,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3995]) ).
thf(f4287,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3996]) ).
thf(f4288,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f3997]) ).
thf(f4289,plain,
( spl38_120
| spl38_103
| spl38_104
| spl38_121 ),
inference(avatar_split_clause,[],[f4000,f3670,f3001,f2998,f3617]) ).
thf(f4290,plain,
( spl38_104
| spl38_122
| spl38_120
| spl38_103 ),
inference(avatar_split_clause,[],[f4001,f2998,f3617,f3674,f3001]) ).
thf(f4291,plain,
( spl38_104
| spl38_103
| spl38_122
| spl38_119 ),
inference(avatar_split_clause,[],[f4002,f3613,f3674,f2998,f3001]) ).
thf(f4292,plain,
( spl38_119
| spl38_104
| spl38_121
| spl38_103 ),
inference(avatar_split_clause,[],[f4003,f2998,f3670,f3001,f3613]) ).
thf(f4293,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4005]) ).
thf(f4294,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4007]) ).
thf(f4295,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4008]) ).
thf(f4296,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4009]) ).
thf(f4297,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4010]) ).
thf(f4298,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4012]) ).
thf(f4299,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4013]) ).
thf(f4300,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4299]) ).
thf(f4301,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4014]) ).
thf(f4302,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4301]) ).
thf(f4303,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4016]) ).
thf(f4304,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f4018]) ).
thf(f4305,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f4020]) ).
thf(f4306,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4021]) ).
thf(f4307,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4306]) ).
thf(f4308,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4024]) ).
thf(f4309,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4025]) ).
thf(f4310,plain,
( spl38_119
| spl38_111
| spl38_112
| spl38_103 ),
inference(avatar_split_clause,[],[f4026,f2998,f3330,f3308,f3613]) ).
thf(f4311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4028]) ).
thf(f4312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4030]) ).
thf(f4313,plain,
( spl38_103
| spl38_120
| spl38_112
| spl38_111 ),
inference(avatar_split_clause,[],[f4031,f3308,f3330,f3617,f2998]) ).
thf(f4314,plain,
( spl38_123
| spl38_102
| spl38_103
| spl38_122 ),
inference(avatar_split_clause,[],[f4034,f3674,f2998,f2995,f3688]) ).
thf(f4315,plain,
( spl38_122
| spl38_124
| spl38_103
| spl38_102 ),
inference(avatar_split_clause,[],[f4035,f2995,f2998,f3692,f3674]) ).
thf(f4316,plain,
( spl38_102
| spl38_103
| spl38_123
| spl38_121 ),
inference(avatar_split_clause,[],[f4036,f3670,f3688,f2998,f2995]) ).
thf(f4317,plain,
( spl38_124
| spl38_121
| spl38_103
| spl38_102 ),
inference(avatar_split_clause,[],[f4037,f2995,f2998,f3670,f3692]) ).
thf(f4333,plain,
( spl38_117
| spl38_101
| spl38_120
| spl38_112 ),
inference(avatar_split_clause,[],[f4057,f3330,f3617,f2992,f3370]) ).
thf(f4334,plain,
( spl38_101
| spl38_117
| spl38_119
| spl38_112 ),
inference(avatar_split_clause,[],[f4058,f3330,f3613,f3370,f2992]) ).
thf(f4335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4063]) ).
thf(f4336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4065]) ).
thf(f4337,plain,
( spl38_123
| spl38_117
| spl38_101
| spl38_110 ),
inference(avatar_split_clause,[],[f4066,f3245,f2992,f3370,f3688]) ).
thf(f4338,plain,
( spl38_101
| spl38_124
| spl38_117
| spl38_110 ),
inference(avatar_split_clause,[],[f4067,f3245,f3370,f3692,f2992]) ).
thf(f4339,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4069]) ).
thf(f4340,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4070]) ).
thf(f4341,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4071]) ).
thf(f4342,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4341]) ).
thf(f4343,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4073]) ).
thf(f4344,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4074]) ).
thf(f4345,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4076]) ).
thf(f4346,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4078]) ).
thf(f4347,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4080]) ).
thf(f4348,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4082]) ).
thf(f4349,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4084]) ).
thf(f4350,plain,
( spl38_112
| spl38_111
| spl38_117
| spl38_110 ),
inference(avatar_split_clause,[],[f4085,f3245,f3370,f3308,f3330]) ).
thf(f4351,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4087]) ).
thf(f4352,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4088]) ).
thf(f4353,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4352]) ).
thf(f4354,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4089]) ).
thf(f4355,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4354]) ).
thf(f4356,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4091]) ).
thf(f4357,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4093]) ).
thf(f4358,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4095]) ).
thf(f4359,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4096]) ).
thf(f4360,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4359]) ).
thf(f4361,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4098]) ).
thf(f4362,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4099]) ).
thf(f4363,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4101]) ).
thf(f4364,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4102]) ).
thf(f4365,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f4364]) ).
thf(f4366,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f4104]) ).
thf(f4367,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f4106]) ).
thf(f4368,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4107]) ).
thf(f4369,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4109]) ).
thf(f4370,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4111]) ).
thf(f4371,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4370]) ).
thf(f4372,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4113]) ).
thf(f4373,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4114]) ).
thf(f4374,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4373]) ).
thf(f4375,plain,
( spl38_117
| spl38_104
| spl38_111
| spl38_120 ),
inference(avatar_split_clause,[],[f4115,f3617,f3308,f3001,f3370]) ).
thf(f4376,plain,
( spl38_104
| spl38_111
| spl38_119
| spl38_117 ),
inference(avatar_split_clause,[],[f4116,f3370,f3613,f3308,f3001]) ).
thf(f4377,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4117]) ).
thf(f4378,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4118]) ).
thf(f4379,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4120]) ).
thf(f4380,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4121]) ).
thf(f4381,plain,
( spl38_110
| spl38_122
| spl38_104
| spl38_117 ),
inference(avatar_split_clause,[],[f4123,f3370,f3001,f3674,f3245]) ).
thf(f4382,plain,
( spl38_121
| spl38_110
| spl38_117
| spl38_104 ),
inference(avatar_split_clause,[],[f4124,f3001,f3370,f3245,f3670]) ).
thf(f4383,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4128]) ).
thf(f4384,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4130]) ).
thf(f4385,plain,
( spl38_102
| spl38_117
| spl38_122
| spl38_112 ),
inference(avatar_split_clause,[],[f4131,f3330,f3674,f3370,f2995]) ).
thf(f4386,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4133]) ).
thf(f4387,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4135]) ).
thf(f4388,plain,
( spl38_102
| spl38_117
| spl38_112
| spl38_121 ),
inference(avatar_split_clause,[],[f4136,f3670,f3330,f3370,f2995]) ).
thf(f4389,plain,
( spl38_111
| spl38_124
| spl38_117
| spl38_102 ),
inference(avatar_split_clause,[],[f4138,f2995,f3370,f3692,f3308]) ).
thf(f4390,plain,
( spl38_117
| spl38_123
| spl38_102
| spl38_111 ),
inference(avatar_split_clause,[],[f4139,f3308,f2995,f3688,f3370]) ).
thf(f4391,plain,
( spl38_123
| spl38_110
| spl38_118
| spl38_101 ),
inference(avatar_split_clause,[],[f4144,f2992,f3450,f3245,f3688]) ).
thf(f4392,plain,
( spl38_101
| spl38_118
| spl38_124
| spl38_110 ),
inference(avatar_split_clause,[],[f4145,f3245,f3692,f3450,f2992]) ).
thf(f4393,plain,
( spl38_119
| spl38_118
| spl38_112
| spl38_101 ),
inference(avatar_split_clause,[],[f4147,f2992,f3330,f3450,f3613]) ).
thf(f4394,plain,
( spl38_112
| spl38_118
| spl38_120
| spl38_101 ),
inference(avatar_split_clause,[],[f4148,f2992,f3617,f3450,f3330]) ).
thf(f4395,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4150]) ).
thf(f4396,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4152]) ).
thf(f4397,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4154]) ).
thf(f4398,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4156]) ).
thf(f4399,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4159]) ).
thf(f4400,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4161]) ).
thf(f4401,plain,
( spl38_110
| spl38_118
| spl38_112
| spl38_111 ),
inference(avatar_split_clause,[],[f4162,f3308,f3330,f3450,f3245]) ).
thf(f4402,plain,
( spl38_118
| spl38_102
| spl38_111
| spl38_123 ),
inference(avatar_split_clause,[],[f4163,f3688,f3308,f2995,f3450]) ).
thf(f4403,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4164]) ).
thf(f4404,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4165]) ).
thf(f4405,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4166]) ).
thf(f4406,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4168]) ).
thf(f4407,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4170]) ).
thf(f4408,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4171]) ).
thf(f4409,plain,
( spl38_102
| spl38_111
| spl38_124
| spl38_118 ),
inference(avatar_split_clause,[],[f4172,f3450,f3692,f3308,f2995]) ).
thf(f4410,plain,
( spl38_102
| spl38_121
| spl38_118
| spl38_112 ),
inference(avatar_split_clause,[],[f4173,f3330,f3450,f3670,f2995]) ).
thf(f4411,plain,
( spl38_102
| spl38_122
| spl38_118
| spl38_112 ),
inference(avatar_split_clause,[],[f4174,f3330,f3450,f3674,f2995]) ).
thf(f4412,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4176]) ).
thf(f4413,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4178]) ).
thf(f4414,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4413]) ).
thf(f4415,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4177]) ).
thf(f4416,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4415]) ).
thf(f4417,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4179]) ).
thf(f4418,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4417]) ).
thf(f4419,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4180]) ).
thf(f4420,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4419]) ).
thf(f4421,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4182]) ).
thf(f4422,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4183]) ).
thf(f4423,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4422]) ).
thf(f4424,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4185]) ).
thf(f4425,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4186]) ).
thf(f4426,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4425]) ).
thf(f4427,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4188]) ).
thf(f4428,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f4190]) ).
thf(f4429,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f4190]) ).
thf(f4430,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4189]) ).
thf(f4431,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4430]) ).
thf(f4432,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4192]) ).
thf(f4433,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4194]) ).
thf(f4434,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4195]) ).
thf(f4435,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4197]) ).
thf(f4436,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f4198]) ).
thf(f4437,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f4198]) ).
thf(f4438,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4199]) ).
thf(f4439,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4438]) ).
thf(f4440,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f4200]) ).
thf(f4441,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f4200]) ).
thf(f4442,plain,
( spl38_122
| spl38_110
| spl38_104
| spl38_118 ),
inference(avatar_split_clause,[],[f4201,f3450,f3001,f3245,f3674]) ).
thf(f4443,plain,
( spl38_104
| spl38_121
| spl38_118
| spl38_110 ),
inference(avatar_split_clause,[],[f4202,f3245,f3450,f3670,f3001]) ).
thf(f4444,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4204]) ).
thf(f4445,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4205]) ).
thf(f4446,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4207]) ).
thf(f4447,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4209]) ).
thf(f4448,plain,
( spl38_104
| spl38_118
| spl38_111
| spl38_120 ),
inference(avatar_split_clause,[],[f4213,f3617,f3308,f3450,f3001]) ).
thf(f4449,plain,
( spl38_111
| spl38_118
| spl38_104
| spl38_119 ),
inference(avatar_split_clause,[],[f4214,f3613,f3001,f3450,f3308]) ).
thf(f4450,plain,
( spl38_123
| spl38_120
| spl38_101
| spl38_109 ),
inference(avatar_split_clause,[],[f4218,f3179,f2992,f3617,f3688]) ).
thf(f4451,plain,
( spl38_109
| spl38_123
| spl38_119
| spl38_101 ),
inference(avatar_split_clause,[],[f4219,f2992,f3613,f3688,f3179]) ).
thf(f4452,plain,
( spl38_101
| spl38_124
| spl38_109
| spl38_120 ),
inference(avatar_split_clause,[],[f4220,f3617,f3179,f3692,f2992]) ).
thf(f4453,plain,
( spl38_109
| spl38_119
| spl38_124
| spl38_101 ),
inference(avatar_split_clause,[],[f4221,f2992,f3692,f3613,f3179]) ).
thf(f4454,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4224]) ).
thf(f4455,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4225]) ).
thf(f4456,plain,
( spl38_109
| spl38_111
| spl38_110
| spl38_123 ),
inference(avatar_split_clause,[],[f4226,f3688,f3245,f3308,f3179]) ).
thf(f4457,plain,
( spl38_109
| spl38_111
| spl38_124
| spl38_110 ),
inference(avatar_split_clause,[],[f4228,f3245,f3692,f3308,f3179]) ).
thf(f4458,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4230]) ).
thf(f4459,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4231]) ).
thf(f4460,plain,
( spl38_109
| spl38_120
| spl38_112
| spl38_111 ),
inference(avatar_split_clause,[],[f4233,f3308,f3330,f3617,f3179]) ).
thf(f4461,plain,
( spl38_109
| spl38_111
| spl38_119
| spl38_112 ),
inference(avatar_split_clause,[],[f4234,f3330,f3613,f3308,f3179]) ).
thf(f4462,plain,
( spl38_124
| spl38_102
| spl38_121
| spl38_109 ),
inference(avatar_split_clause,[],[f4237,f3179,f3670,f2995,f3692]) ).
thf(f4463,plain,
( spl38_109
| spl38_102
| spl38_121
| spl38_123 ),
inference(avatar_split_clause,[],[f4238,f3688,f3670,f2995,f3179]) ).
thf(f4464,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4241]) ).
thf(f4465,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4243]) ).
thf(f4466,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4244]) ).
thf(f4467,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4245]) ).
thf(f4468,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4246]) ).
thf(f4469,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4248]) ).
thf(f4470,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4250]) ).
thf(f4471,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4251]) ).
thf(f4472,plain,
( spl38_109
| spl38_110
| spl38_112
| spl38_121 ),
inference(avatar_split_clause,[],[f4252,f3670,f3330,f3245,f3179]) ).
thf(f4473,plain,
( spl38_120
| spl38_109
| spl38_104
| spl38_121 ),
inference(avatar_split_clause,[],[f4253,f3670,f3001,f3179,f3617]) ).
thf(f4474,plain,
( spl38_104
| spl38_109
| spl38_119
| spl38_121 ),
inference(avatar_split_clause,[],[f4254,f3670,f3613,f3179,f3001]) ).
thf(f4475,plain,
( spl38_102
| spl38_124
| spl38_122
| spl38_109 ),
inference(avatar_split_clause,[],[f4256,f3179,f3674,f3692,f2995]) ).
thf(f4476,plain,
( spl38_102
| spl38_123
| spl38_122
| spl38_109 ),
inference(avatar_split_clause,[],[f4257,f3179,f3674,f3688,f2995]) ).
thf(f4477,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4260]) ).
thf(f4478,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4261]) ).
thf(f4479,plain,
( spl38_122
| spl38_110
| spl38_112
| spl38_109 ),
inference(avatar_split_clause,[],[f4262,f3179,f3330,f3245,f3674]) ).
thf(f4480,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4264]) ).
thf(f4481,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4266]) ).
thf(f4482,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f4268]) ).
thf(f4483,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f4270]) ).
thf(f4484,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4272]) ).
thf(f4485,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4273]) ).
thf(f4486,plain,
( spl38_109
| spl38_120
| spl38_104
| spl38_122 ),
inference(avatar_split_clause,[],[f4274,f3674,f3001,f3617,f3179]) ).
thf(f4487,plain,
( spl38_104
| spl38_119
| spl38_122
| spl38_109 ),
inference(avatar_split_clause,[],[f4275,f3179,f3674,f3613,f3001]) ).
thf(f4488,plain,
( spl38_121
| spl38_123
| spl38_103
| spl38_110 ),
inference(avatar_split_clause,[],[f4285,f3245,f2998,f3688,f3670]) ).
thf(f4489,plain,
( spl38_124
| spl38_121
| spl38_103
| spl38_110 ),
inference(avatar_split_clause,[],[f4286,f3245,f2998,f3670,f3692]) ).
thf(f4490,plain,
( spl38_122
| spl38_110
| spl38_123
| spl38_103 ),
inference(avatar_split_clause,[],[f4287,f2998,f3688,f3245,f3674]) ).
thf(f4491,plain,
( spl38_110
| spl38_103
| spl38_124
| spl38_122 ),
inference(avatar_split_clause,[],[f4288,f3674,f3692,f2998,f3245]) ).
thf(f4492,plain,
( spl38_112
| spl38_120
| spl38_103
| spl38_121 ),
inference(avatar_split_clause,[],[f4293,f3670,f2998,f3617,f3330]) ).
thf(f4493,plain,
( spl38_103
| spl38_112
| spl38_120
| spl38_122 ),
inference(avatar_split_clause,[],[f4294,f3674,f3617,f3330,f2998]) ).
thf(f4494,plain,
( spl38_119
| spl38_103
| spl38_122
| spl38_112 ),
inference(avatar_split_clause,[],[f4295,f3330,f3674,f2998,f3613]) ).
thf(f4495,plain,
( spl38_112
| spl38_103
| spl38_121
| spl38_119 ),
inference(avatar_split_clause,[],[f4296,f3613,f3670,f2998,f3330]) ).
thf(f4496,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4297]) ).
thf(f4497,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4298]) ).
thf(f4498,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4300]) ).
thf(f4499,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4302]) ).
thf(f4500,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4303]) ).
thf(f4501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4304]) ).
thf(f4502,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4305]) ).
thf(f4503,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4307]) ).
thf(f4504,plain,
( spl38_124
| spl38_111
| spl38_103
| spl38_119 ),
inference(avatar_split_clause,[],[f4308,f3613,f2998,f3308,f3692]) ).
thf(f4505,plain,
( spl38_103
| spl38_111
| spl38_123
| spl38_119 ),
inference(avatar_split_clause,[],[f4309,f3613,f3688,f3308,f2998]) ).
thf(f4506,plain,
( spl38_120
| spl38_103
| spl38_111
| spl38_123 ),
inference(avatar_split_clause,[],[f4311,f3688,f3308,f2998,f3617]) ).
thf(f4507,plain,
( spl38_111
| spl38_103
| spl38_124
| spl38_120 ),
inference(avatar_split_clause,[],[f4312,f3617,f3692,f2998,f3308]) ).
thf(f4523,plain,
( spl38_123
| spl38_117
| spl38_101
| spl38_120 ),
inference(avatar_split_clause,[],[f4335,f3617,f2992,f3370,f3688]) ).
thf(f4524,plain,
( spl38_101
| spl38_117
| spl38_123
| spl38_119 ),
inference(avatar_split_clause,[],[f4336,f3613,f3688,f3370,f2992]) ).
thf(f4525,plain,
( spl38_101
| spl38_117
| spl38_124
| spl38_119 ),
inference(avatar_split_clause,[],[f4339,f3613,f3692,f3370,f2992]) ).
thf(f4526,plain,
( spl38_101
| spl38_124
| spl38_120
| spl38_117 ),
inference(avatar_split_clause,[],[f4340,f3370,f3617,f3692,f2992]) ).
thf(f4527,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4342]) ).
thf(f4528,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4343]) ).
thf(f4529,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4344]) ).
thf(f4530,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4345]) ).
thf(f4531,plain,
( spl38_110
| spl38_112
| spl38_117
| spl38_121 ),
inference(avatar_split_clause,[],[f4346,f3670,f3370,f3330,f3245]) ).
thf(f4532,plain,
( spl38_122
| spl38_110
| spl38_112
| spl38_117 ),
inference(avatar_split_clause,[],[f4347,f3370,f3330,f3245,f3674]) ).
thf(f4533,plain,
( spl38_117
| spl38_111
| spl38_119
| spl38_112 ),
inference(avatar_split_clause,[],[f4348,f3330,f3613,f3308,f3370]) ).
thf(f4534,plain,
( spl38_117
| spl38_111
| spl38_112
| spl38_120 ),
inference(avatar_split_clause,[],[f4349,f3617,f3330,f3308,f3370]) ).
thf(f4535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4351]) ).
thf(f4536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4353]) ).
thf(f4537,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4355]) ).
thf(f4538,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4356]) ).
thf(f4539,plain,
( spl38_110
| spl38_117
| spl38_124
| spl38_111 ),
inference(avatar_split_clause,[],[f4357,f3308,f3692,f3370,f3245]) ).
thf(f4540,plain,
( spl38_123
| spl38_111
| spl38_110
| spl38_117 ),
inference(avatar_split_clause,[],[f4358,f3370,f3245,f3308,f3688]) ).
thf(f4541,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4360]) ).
thf(f4542,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4361]) ).
thf(f4543,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4542]) ).
thf(f4544,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4362]) ).
thf(f4545,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4544]) ).
thf(f4546,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4363]) ).
thf(f4547,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4365]) ).
thf(f4548,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4366]) ).
thf(f4549,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4367]) ).
thf(f4550,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4368]) ).
thf(f4551,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4550]) ).
thf(f4552,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4369]) ).
thf(f4553,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4371]) ).
thf(f4554,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4372]) ).
thf(f4555,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4554]) ).
thf(f4556,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4374]) ).
thf(f4557,plain,
( spl38_117
| spl38_120
| spl38_104
| spl38_121 ),
inference(avatar_split_clause,[],[f4377,f3670,f3001,f3617,f3370]) ).
thf(f4558,plain,
( spl38_117
| spl38_120
| spl38_122
| spl38_104 ),
inference(avatar_split_clause,[],[f4378,f3001,f3674,f3617,f3370]) ).
thf(f4559,plain,
( spl38_121
| spl38_119
| spl38_104
| spl38_117 ),
inference(avatar_split_clause,[],[f4379,f3370,f3001,f3613,f3670]) ).
thf(f4560,plain,
( spl38_122
| spl38_104
| spl38_117
| spl38_119 ),
inference(avatar_split_clause,[],[f4380,f3613,f3370,f3001,f3674]) ).
thf(f4561,plain,
( spl38_122
| spl38_117
| spl38_102
| spl38_123 ),
inference(avatar_split_clause,[],[f4383,f3688,f2995,f3370,f3674]) ).
thf(f4562,plain,
( spl38_117
| spl38_122
| spl38_102
| spl38_124 ),
inference(avatar_split_clause,[],[f4384,f3692,f2995,f3674,f3370]) ).
thf(f4563,plain,
( spl38_121
| spl38_124
| spl38_102
| spl38_117 ),
inference(avatar_split_clause,[],[f4386,f3370,f2995,f3692,f3670]) ).
thf(f4564,plain,
( spl38_102
| spl38_123
| spl38_117
| spl38_121 ),
inference(avatar_split_clause,[],[f4387,f3670,f3370,f3688,f2995]) ).
thf(f4565,plain,
( spl38_118
| spl38_119
| spl38_124
| spl38_101 ),
inference(avatar_split_clause,[],[f4395,f2992,f3692,f3613,f3450]) ).
thf(f4566,plain,
( spl38_123
| spl38_119
| spl38_118
| spl38_101 ),
inference(avatar_split_clause,[],[f4396,f2992,f3450,f3613,f3688]) ).
thf(f4567,plain,
( spl38_118
| spl38_123
| spl38_101
| spl38_120 ),
inference(avatar_split_clause,[],[f4397,f3617,f2992,f3688,f3450]) ).
thf(f4568,plain,
( spl38_118
| spl38_120
| spl38_101
| spl38_124 ),
inference(avatar_split_clause,[],[f4398,f3692,f2992,f3617,f3450]) ).
thf(f4569,plain,
( spl38_111
| spl38_120
| spl38_118
| spl38_112 ),
inference(avatar_split_clause,[],[f4399,f3330,f3450,f3617,f3308]) ).
thf(f4570,plain,
( spl38_119
| spl38_118
| spl38_111
| spl38_112 ),
inference(avatar_split_clause,[],[f4400,f3330,f3308,f3450,f3613]) ).
thf(f4571,plain,
( spl38_123
| spl38_110
| spl38_111
| spl38_118 ),
inference(avatar_split_clause,[],[f4403,f3450,f3308,f3245,f3688]) ).
thf(f4572,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4404]) ).
thf(f4573,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4405]) ).
thf(f4574,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4406]) ).
thf(f4575,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4407]) ).
thf(f4576,plain,
( spl38_124
| spl38_118
| spl38_111
| spl38_110 ),
inference(avatar_split_clause,[],[f4408,f3245,f3308,f3450,f3692]) ).
thf(f4577,plain,
( spl38_121
| spl38_118
| spl38_110
| spl38_112 ),
inference(avatar_split_clause,[],[f4412,f3330,f3245,f3450,f3670]) ).
thf(f4578,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4414]) ).
thf(f4579,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4416]) ).
thf(f4580,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4418]) ).
thf(f4581,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4420]) ).
thf(f4582,plain,
( spl38_122
| spl38_118
| spl38_112
| spl38_110 ),
inference(avatar_split_clause,[],[f4421,f3245,f3330,f3450,f3674]) ).
thf(f4583,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4423]) ).
thf(f4584,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4424]) ).
thf(f4585,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4426]) ).
thf(f4586,plain,
( spl38_124
| spl38_122
| spl38_102
| spl38_118 ),
inference(avatar_split_clause,[],[f4427,f3450,f2995,f3674,f3692]) ).
thf(f4587,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4429]) ).
thf(f4588,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f4587]) ).
thf(f4589,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4428]) ).
thf(f4590,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4589]) ).
thf(f4591,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4431]) ).
thf(f4592,plain,
( spl38_118
| spl38_122
| spl38_102
| spl38_123 ),
inference(avatar_split_clause,[],[f4432,f3688,f2995,f3674,f3450]) ).
thf(f4593,plain,
( spl38_124
| spl38_102
| spl38_121
| spl38_118 ),
inference(avatar_split_clause,[],[f4433,f3450,f3670,f2995,f3692]) ).
thf(f4594,plain,
( spl38_102
| spl38_123
| spl38_118
| spl38_121 ),
inference(avatar_split_clause,[],[f4434,f3670,f3450,f3688,f2995]) ).
thf(f4595,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4435]) ).
thf(f4596,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4436]) ).
thf(f4597,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4596]) ).
thf(f4598,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4437]) ).
thf(f4599,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f4598]) ).
thf(f4600,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4439]) ).
thf(f4601,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4441]) ).
thf(f4602,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4601]) ).
thf(f4603,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f4440]) ).
thf(f4604,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( ( ( mrel @ sK9 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4603]) ).
thf(f4605,plain,
( spl38_104
| spl38_118
| spl38_120
| spl38_122 ),
inference(avatar_split_clause,[],[f4444,f3674,f3617,f3450,f3001]) ).
thf(f4606,plain,
( spl38_122
| spl38_119
| spl38_104
| spl38_118 ),
inference(avatar_split_clause,[],[f4445,f3450,f3001,f3613,f3674]) ).
thf(f4607,plain,
( spl38_118
| spl38_121
| spl38_120
| spl38_104 ),
inference(avatar_split_clause,[],[f4446,f3001,f3617,f3670,f3450]) ).
thf(f4608,plain,
( spl38_118
| spl38_104
| spl38_121
| spl38_119 ),
inference(avatar_split_clause,[],[f4447,f3613,f3670,f3001,f3450]) ).
thf(f4609,plain,
( spl38_123
| spl38_119
| spl38_111
| spl38_109 ),
inference(avatar_split_clause,[],[f4454,f3179,f3308,f3613,f3688]) ).
thf(f4610,plain,
( spl38_123
| spl38_120
| spl38_111
| spl38_109 ),
inference(avatar_split_clause,[],[f4455,f3179,f3308,f3617,f3688]) ).
thf(f4611,plain,
( spl38_124
| spl38_120
| spl38_109
| spl38_111 ),
inference(avatar_split_clause,[],[f4458,f3308,f3179,f3617,f3692]) ).
thf(f4612,plain,
( spl38_124
| spl38_119
| spl38_111
| spl38_109 ),
inference(avatar_split_clause,[],[f4459,f3179,f3308,f3613,f3692]) ).
thf(f4613,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4464]) ).
thf(f4614,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4465]) ).
thf(f4615,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4466]) ).
thf(f4616,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4467]) ).
thf(f4617,plain,
( spl38_121
| spl38_119
| spl38_109
| spl38_112 ),
inference(avatar_split_clause,[],[f4468,f3330,f3179,f3613,f3670]) ).
thf(f4618,plain,
( spl38_112
| spl38_121
| spl38_120
| spl38_109 ),
inference(avatar_split_clause,[],[f4469,f3179,f3617,f3670,f3330]) ).
thf(f4619,plain,
( spl38_109
| spl38_121
| spl38_124
| spl38_110 ),
inference(avatar_split_clause,[],[f4470,f3245,f3692,f3670,f3179]) ).
thf(f4620,plain,
( spl38_109
| spl38_123
| spl38_121
| spl38_110 ),
inference(avatar_split_clause,[],[f4471,f3245,f3670,f3688,f3179]) ).
thf(f4621,plain,
( spl38_110
| spl38_122
| spl38_124
| spl38_109 ),
inference(avatar_split_clause,[],[f4477,f3179,f3692,f3674,f3245]) ).
thf(f4622,plain,
( spl38_109
| spl38_110
| spl38_122
| spl38_123 ),
inference(avatar_split_clause,[],[f4478,f3688,f3674,f3245,f3179]) ).
thf(f4623,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4480]) ).
thf(f4624,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 )
= $true )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4481]) ).
thf(f4625,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4482]) ).
thf(f4626,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4483]) ).
thf(f4627,plain,
( spl38_109
| spl38_112
| spl38_119
| spl38_122 ),
inference(avatar_split_clause,[],[f4484,f3674,f3613,f3330,f3179]) ).
thf(f4628,plain,
( spl38_120
| spl38_122
| spl38_109
| spl38_112 ),
inference(avatar_split_clause,[],[f4485,f3330,f3179,f3674,f3617]) ).
thf(f4629,plain,
( spl38_120
| spl38_124
| spl38_103
| spl38_121 ),
inference(avatar_split_clause,[],[f4496,f3670,f2998,f3692,f3617]) ).
thf(f4630,plain,
( spl38_103
| spl38_123
| spl38_120
| spl38_121 ),
inference(avatar_split_clause,[],[f4497,f3670,f3617,f3688,f2998]) ).
thf(f4631,plain,
( spl38_120
| spl38_123
| spl38_122
| spl38_103 ),
inference(avatar_split_clause,[],[f4498,f2998,f3674,f3688,f3617]) ).
thf(f4632,plain,
( spl38_120
| spl38_122
| spl38_103
| spl38_124 ),
inference(avatar_split_clause,[],[f4499,f3692,f2998,f3674,f3617]) ).
thf(f4633,plain,
( spl38_122
| spl38_103
| spl38_124
| spl38_119 ),
inference(avatar_split_clause,[],[f4500,f3613,f3692,f2998,f3674]) ).
thf(f4634,plain,
( spl38_103
| spl38_119
| spl38_123
| spl38_122 ),
inference(avatar_split_clause,[],[f4501,f3674,f3688,f3613,f2998]) ).
thf(f4635,plain,
( spl38_123
| spl38_119
| spl38_103
| spl38_121 ),
inference(avatar_split_clause,[],[f4502,f3670,f2998,f3613,f3688]) ).
thf(f4636,plain,
( spl38_103
| spl38_124
| spl38_121
| spl38_119 ),
inference(avatar_split_clause,[],[f4503,f3613,f3670,f3692,f2998]) ).
thf(f4652,plain,
( spl38_121
| spl38_112
| spl38_120
| spl38_117 ),
inference(avatar_split_clause,[],[f4527,f3370,f3617,f3330,f3670]) ).
thf(f4653,plain,
( spl38_112
| spl38_122
| spl38_117
| spl38_120 ),
inference(avatar_split_clause,[],[f4528,f3617,f3370,f3674,f3330]) ).
thf(f4654,plain,
( spl38_112
| spl38_122
| spl38_119
| spl38_117 ),
inference(avatar_split_clause,[],[f4529,f3370,f3613,f3674,f3330]) ).
thf(f4655,plain,
( spl38_121
| spl38_119
| spl38_112
| spl38_117 ),
inference(avatar_split_clause,[],[f4530,f3370,f3330,f3613,f3670]) ).
thf(f4656,plain,
( spl38_120
| spl38_117
| spl38_124
| spl38_111 ),
inference(avatar_split_clause,[],[f4535,f3308,f3692,f3370,f3617]) ).
thf(f4657,plain,
( spl38_111
| spl38_117
| spl38_120
| spl38_123 ),
inference(avatar_split_clause,[],[f4536,f3688,f3617,f3370,f3308]) ).
thf(f4658,plain,
( spl38_111
| spl38_123
| spl38_119
| spl38_117 ),
inference(avatar_split_clause,[],[f4537,f3370,f3613,f3688,f3308]) ).
thf(f4659,plain,
( spl38_111
| spl38_124
| spl38_117
| spl38_119 ),
inference(avatar_split_clause,[],[f4538,f3613,f3370,f3692,f3308]) ).
thf(f4660,plain,
( spl38_122
| spl38_110
| spl38_123
| spl38_117 ),
inference(avatar_split_clause,[],[f4541,f3370,f3688,f3245,f3674]) ).
thf(f4661,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4543]) ).
thf(f4662,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4545]) ).
thf(f4663,plain,
( spl38_110
| spl38_117
| spl38_122
| spl38_124 ),
inference(avatar_split_clause,[],[f4546,f3692,f3674,f3370,f3245]) ).
thf(f4664,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4547]) ).
thf(f4665,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 )
= $true )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4548]) ).
thf(f4666,plain,
( spl38_124
| spl38_121
| spl38_117
| spl38_110 ),
inference(avatar_split_clause,[],[f4549,f3245,f3370,f3670,f3692]) ).
thf(f4667,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4551]) ).
thf(f4668,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4552]) ).
thf(f4669,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4553]) ).
thf(f4670,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4555]) ).
thf(f4671,plain,
( spl38_123
| spl38_121
| spl38_110
| spl38_117 ),
inference(avatar_split_clause,[],[f4556,f3370,f3245,f3670,f3688]) ).
thf(f4672,plain,
( spl38_111
| spl38_120
| spl38_123
| spl38_118 ),
inference(avatar_split_clause,[],[f4572,f3450,f3688,f3617,f3308]) ).
thf(f4673,plain,
( spl38_111
| spl38_123
| spl38_118
| spl38_119 ),
inference(avatar_split_clause,[],[f4573,f3613,f3450,f3688,f3308]) ).
thf(f4674,plain,
( spl38_118
| spl38_120
| spl38_111
| spl38_124 ),
inference(avatar_split_clause,[],[f4574,f3692,f3308,f3617,f3450]) ).
thf(f4675,plain,
( spl38_118
| spl38_124
| spl38_111
| spl38_119 ),
inference(avatar_split_clause,[],[f4575,f3613,f3308,f3692,f3450]) ).
thf(f4676,plain,
( spl38_121
| spl38_119
| spl38_118
| spl38_112 ),
inference(avatar_split_clause,[],[f4578,f3330,f3450,f3613,f3670]) ).
thf(f4677,plain,
( spl38_121
| spl38_118
| spl38_112
| spl38_120 ),
inference(avatar_split_clause,[],[f4579,f3617,f3330,f3450,f3670]) ).
thf(f4678,plain,
( spl38_120
| spl38_122
| spl38_112
| spl38_118 ),
inference(avatar_split_clause,[],[f4580,f3450,f3330,f3674,f3617]) ).
thf(f4679,plain,
( spl38_112
| spl38_122
| spl38_119
| spl38_118 ),
inference(avatar_split_clause,[],[f4581,f3450,f3613,f3674,f3330]) ).
thf(f4680,plain,
( spl38_124
| spl38_122
| spl38_110
| spl38_118 ),
inference(avatar_split_clause,[],[f4583,f3450,f3245,f3674,f3692]) ).
thf(f4681,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4584]) ).
thf(f4682,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4585]) ).
thf(f4683,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4588]) ).
thf(f4684,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 )
= $true )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4590]) ).
thf(f4685,plain,
( spl38_110
| spl38_118
| spl38_122
| spl38_123 ),
inference(avatar_split_clause,[],[f4591,f3688,f3674,f3450,f3245]) ).
thf(f4686,plain,
( spl38_118
| spl38_121
| spl38_110
| spl38_123 ),
inference(avatar_split_clause,[],[f4595,f3688,f3245,f3670,f3450]) ).
thf(f4687,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4597]) ).
thf(f4688,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f4599]) ).
thf(f4689,plain,
( spl38_110
| spl38_121
| spl38_118
| spl38_124 ),
inference(avatar_split_clause,[],[f4600,f3692,f3450,f3670,f3245]) ).
thf(f4690,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4602]) ).
thf(f4691,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X3 ) )
| ( $false
= ( mrel @ sK9 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK9 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
| ( $false
= ( mrel @ sK9 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4604]) ).
thf(f4692,plain,
( spl38_120
| spl38_109
| spl38_121
| spl38_123 ),
inference(avatar_split_clause,[],[f4613,f3688,f3670,f3179,f3617]) ).
thf(f4693,plain,
( spl38_123
| spl38_109
| spl38_119
| spl38_121 ),
inference(avatar_split_clause,[],[f4614,f3670,f3613,f3179,f3688]) ).
thf(f4694,plain,
( spl38_121
| spl38_109
| spl38_119
| spl38_124 ),
inference(avatar_split_clause,[],[f4615,f3692,f3613,f3179,f3670]) ).
thf(f4695,plain,
( spl38_109
| spl38_124
| spl38_121
| spl38_120 ),
inference(avatar_split_clause,[],[f4616,f3617,f3670,f3692,f3179]) ).
thf(f4696,plain,
( spl38_122
| spl38_123
| spl38_109
| spl38_119 ),
inference(avatar_split_clause,[],[f4623,f3613,f3179,f3688,f3674]) ).
thf(f4697,plain,
( spl38_119
| spl38_124
| spl38_109
| spl38_122 ),
inference(avatar_split_clause,[],[f4624,f3674,f3179,f3692,f3613]) ).
thf(f4698,plain,
( spl38_122
| spl38_123
| spl38_120
| spl38_109 ),
inference(avatar_split_clause,[],[f4625,f3179,f3617,f3688,f3674]) ).
thf(f4699,plain,
( spl38_120
| spl38_122
| spl38_109
| spl38_124 ),
inference(avatar_split_clause,[],[f4626,f3692,f3179,f3674,f3617]) ).
thf(f4715,plain,
( spl38_123
| spl38_122
| spl38_117
| spl38_120 ),
inference(avatar_split_clause,[],[f4661,f3617,f3370,f3674,f3688]) ).
thf(f4716,plain,
( spl38_123
| spl38_119
| spl38_117
| spl38_122 ),
inference(avatar_split_clause,[],[f4662,f3674,f3370,f3613,f3688]) ).
thf(f4717,plain,
( spl38_124
| spl38_119
| spl38_122
| spl38_117 ),
inference(avatar_split_clause,[],[f4664,f3370,f3674,f3613,f3692]) ).
thf(f4718,plain,
( spl38_117
| spl38_120
| spl38_124
| spl38_122 ),
inference(avatar_split_clause,[],[f4665,f3674,f3692,f3617,f3370]) ).
thf(f4719,plain,
( spl38_117
| spl38_124
| spl38_121
| spl38_120 ),
inference(avatar_split_clause,[],[f4667,f3617,f3670,f3692,f3370]) ).
thf(f4720,plain,
( spl38_117
| spl38_121
| spl38_119
| spl38_124 ),
inference(avatar_split_clause,[],[f4668,f3692,f3613,f3670,f3370]) ).
thf(f4721,plain,
( spl38_117
| spl38_121
| spl38_123
| spl38_120 ),
inference(avatar_split_clause,[],[f4669,f3617,f3688,f3670,f3370]) ).
thf(f4722,plain,
( spl38_121
| spl38_117
| spl38_119
| spl38_123 ),
inference(avatar_split_clause,[],[f4670,f3688,f3613,f3370,f3670]) ).
thf(f4723,plain,
( spl38_118
| spl38_124
| spl38_119
| spl38_122 ),
inference(avatar_split_clause,[],[f4681,f3674,f3613,f3692,f3450]) ).
thf(f4724,plain,
( spl38_120
| spl38_124
| spl38_118
| spl38_122 ),
inference(avatar_split_clause,[],[f4682,f3674,f3450,f3692,f3617]) ).
thf(f4725,plain,
( spl38_119
| spl38_123
| spl38_122
| spl38_118 ),
inference(avatar_split_clause,[],[f4683,f3450,f3674,f3688,f3613]) ).
thf(f4726,plain,
( spl38_118
| spl38_123
| spl38_120
| spl38_122 ),
inference(avatar_split_clause,[],[f4684,f3674,f3617,f3688,f3450]) ).
thf(f4727,plain,
( spl38_120
| spl38_121
| spl38_123
| spl38_118 ),
inference(avatar_split_clause,[],[f4687,f3450,f3688,f3670,f3617]) ).
thf(f4728,plain,
( spl38_119
| spl38_118
| spl38_121
| spl38_123 ),
inference(avatar_split_clause,[],[f4688,f3688,f3670,f3450,f3613]) ).
thf(f4729,plain,
( spl38_118
| spl38_119
| spl38_124
| spl38_121 ),
inference(avatar_split_clause,[],[f4690,f3670,f3692,f3613,f3450]) ).
thf(f4730,plain,
( spl38_124
| spl38_120
| spl38_121
| spl38_118 ),
inference(avatar_split_clause,[],[f4691,f3450,f3670,f3617,f3692]) ).
thf(f5086,plain,
( ( $false
= ( mrel @ sK9 @ sK27 ) )
| ( $false = $true )
| ~ spl38_11
| ~ spl38_118 ),
inference(constrained_superposition,[],[f1203,f3451]) ).
thf(f5087,plain,
( ( $false
= ( mrel @ sK9 @ sK27 ) )
| ~ spl38_11
| ~ spl38_118 ),
inference(trivial_inequality_removal,[],[f5086]) ).
thf(f5112,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ sK27 ) ) )
| ~ spl38_11
| ~ spl38_118 ),
inference(constrained_superposition,[],[f5087,f412]) ).
thf(f5117,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK27 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_11
| ~ spl38_118 ),
inference(trivial_inequality_removal,[],[f5112]) ).
thf(f5121,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(constrained_superposition,[],[f5117,f1210]) ).
thf(f5130,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(trivial_inequality_removal,[],[f5121]) ).
thf(f5138,plain,
( ( $false = $true )
| ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(constrained_superposition,[],[f5130,f598]) ).
thf(f5143,plain,
( $false
| ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(trivial_inequality_removal,[],[f5138]) ).
thf(f5144,plain,
( ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(avatar_contradiction_clause,[],[f5143]) ).
thf(f5156,plain,
( ( $false
= ( mrel @ sK9 @ sK14 ) )
| ( $false = $true )
| ~ spl38_15
| ~ spl38_109 ),
inference(constrained_superposition,[],[f1219,f3180]) ).
thf(f5159,plain,
( ( $false
= ( mrel @ sK9 @ sK14 ) )
| ~ spl38_15
| ~ spl38_109 ),
inference(trivial_inequality_removal,[],[f5156]) ).
thf(f5174,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ sK14 ) ) )
| ~ spl38_15
| ~ spl38_109 ),
inference(constrained_superposition,[],[f412,f5159]) ).
thf(f5175,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK14 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_15
| ~ spl38_109 ),
inference(trivial_inequality_removal,[],[f5174]) ).
thf(f5186,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(constrained_superposition,[],[f1197,f5175]) ).
thf(f5189,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(trivial_inequality_removal,[],[f5186]) ).
thf(f5198,plain,
( ( $false = $true )
| ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(constrained_superposition,[],[f5189,f598]) ).
thf(f5205,plain,
( $false
| ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(trivial_inequality_removal,[],[f5198]) ).
thf(f5206,plain,
( ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(avatar_contradiction_clause,[],[f5205]) ).
thf(f5217,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false = $true )
| ~ spl38_38
| ~ spl38_110 ),
inference(constrained_superposition,[],[f3246,f1520]) ).
thf(f5219,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ~ spl38_38
| ~ spl38_110 ),
inference(trivial_inequality_removal,[],[f5217]) ).
thf(f5222,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_38
| ~ spl38_110 ),
inference(constrained_superposition,[],[f412,f5219]) ).
thf(f5223,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ ( sK37 @ e2 @ mactual @ ( op @ e1 @ e1 ) ) )
= $false )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_38
| ~ spl38_110 ),
inference(trivial_inequality_removal,[],[f5222]) ).
thf(f5241,plain,
( ( ( mrel @ sK9 @ sK21 )
= $false )
| ( $false = $true )
| ~ spl38_37
| ~ spl38_120 ),
inference(constrained_superposition,[],[f3618,f1516]) ).
thf(f5243,plain,
( ( ( mrel @ sK9 @ sK21 )
= $false )
| ~ spl38_37
| ~ spl38_120 ),
inference(trivial_inequality_removal,[],[f5241]) ).
thf(f5245,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ sK21 ) )
| ( $false = $true ) )
| ~ spl38_37
| ~ spl38_120 ),
inference(constrained_superposition,[],[f5243,f412]) ).
thf(f5247,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK21 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_37
| ~ spl38_120 ),
inference(trivial_inequality_removal,[],[f5245]) ).
thf(f5266,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(constrained_superposition,[],[f1506,f5223]) ).
thf(f5267,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(trivial_inequality_removal,[],[f5266]) ).
thf(f5274,plain,
( ( $false = $true )
| ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(constrained_superposition,[],[f5267,f598]) ).
thf(f5281,plain,
( $false
| ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(trivial_inequality_removal,[],[f5274]) ).
thf(f5282,plain,
( ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(avatar_contradiction_clause,[],[f5281]) ).
thf(f5294,plain,
( ( $false
= ( mrel @ sK9 @ sK35 ) )
| ( $false = $true )
| ~ spl38_26
| ~ spl38_122 ),
inference(constrained_superposition,[],[f1369,f3675]) ).
thf(f5295,plain,
( ( $false
= ( mrel @ sK9 @ sK35 ) )
| ~ spl38_26
| ~ spl38_122 ),
inference(trivial_inequality_removal,[],[f5294]) ).
thf(f5298,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK35 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_26
| ~ spl38_122 ),
inference(constrained_superposition,[],[f412,f5295]) ).
thf(f5299,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK35 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_26
| ~ spl38_122 ),
inference(trivial_inequality_removal,[],[f5298]) ).
thf(f5306,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(constrained_superposition,[],[f1361,f5299]) ).
thf(f5308,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(trivial_inequality_removal,[],[f5306]) ).
thf(f5316,plain,
( ( $false = $true )
| ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(constrained_superposition,[],[f598,f5308]) ).
thf(f5321,plain,
( $false
| ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(trivial_inequality_removal,[],[f5316]) ).
thf(f5322,plain,
( ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(avatar_contradiction_clause,[],[f5321]) ).
thf(f5327,plain,
( ( $false
= ( mrel @ sK9 @ sK15 ) )
| ( $false = $true )
| ~ spl38_27
| ~ spl38_111 ),
inference(constrained_superposition,[],[f1374,f3309]) ).
thf(f5333,plain,
( ( $false
= ( mrel @ sK9 @ sK15 ) )
| ~ spl38_27
| ~ spl38_111 ),
inference(trivial_inequality_removal,[],[f5327]) ).
thf(f5345,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK15 ) ) )
| ~ spl38_27
| ~ spl38_111 ),
inference(constrained_superposition,[],[f5333,f412]) ).
thf(f5347,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK15 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_27
| ~ spl38_111 ),
inference(trivial_inequality_removal,[],[f5345]) ).
thf(f5351,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(constrained_superposition,[],[f5347,f1352]) ).
thf(f5358,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(trivial_inequality_removal,[],[f5351]) ).
thf(f5368,plain,
( ( $false = $true )
| ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(constrained_superposition,[],[f598,f5358]) ).
thf(f5372,plain,
( $false
| ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(trivial_inequality_removal,[],[f5368]) ).
thf(f5373,plain,
( ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(avatar_contradiction_clause,[],[f5372]) ).
thf(f5391,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false = $true )
| ~ spl38_49
| ~ spl38_123 ),
inference(constrained_superposition,[],[f3689,f1650]) ).
thf(f5393,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ~ spl38_49
| ~ spl38_123 ),
inference(trivial_inequality_removal,[],[f5391]) ).
thf(f5438,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false = $true ) )
| ~ spl38_49
| ~ spl38_123 ),
inference(constrained_superposition,[],[f5393,f412]) ).
thf(f5440,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK37 @ e3 @ mactual @ ( op @ e3 @ e3 ) ) ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_49
| ~ spl38_123 ),
inference(trivial_inequality_removal,[],[f5438]) ).
thf(f5447,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(constrained_superposition,[],[f1640,f5440]) ).
thf(f5449,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(trivial_inequality_removal,[],[f5447]) ).
thf(f5457,plain,
( ( $false = $true )
| ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(constrained_superposition,[],[f598,f5449]) ).
thf(f5462,plain,
( $false
| ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(trivial_inequality_removal,[],[f5457]) ).
thf(f5463,plain,
( ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(avatar_contradiction_clause,[],[f5462]) ).
thf(f5464,plain,
( ( $false
= ( mrel @ sK9 @ sK36 ) )
| ( $false = $true )
| ~ spl38_51
| ~ spl38_124 ),
inference(constrained_superposition,[],[f1659,f3693]) ).
thf(f5466,plain,
( ( $false
= ( mrel @ sK9 @ sK36 ) )
| ~ spl38_51
| ~ spl38_124 ),
inference(trivial_inequality_removal,[],[f5464]) ).
thf(f5469,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK36 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_51
| ~ spl38_124 ),
inference(constrained_superposition,[],[f412,f5466]) ).
thf(f5470,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK36 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_51
| ~ spl38_124 ),
inference(trivial_inequality_removal,[],[f5469]) ).
thf(f5474,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(constrained_superposition,[],[f5470,f1643]) ).
thf(f5478,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(trivial_inequality_removal,[],[f5474]) ).
thf(f5485,plain,
( ( $false = $true )
| ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(constrained_superposition,[],[f5478,f598]) ).
thf(f5492,plain,
( $false
| ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(trivial_inequality_removal,[],[f5485]) ).
thf(f5493,plain,
( ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(avatar_contradiction_clause,[],[f5492]) ).
thf(f5502,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false = $true )
| ~ spl38_48
| ~ spl38_112 ),
inference(constrained_superposition,[],[f1646,f3331]) ).
thf(f5506,plain,
( ( $false
= ( mrel @ sK9 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ~ spl38_48
| ~ spl38_112 ),
inference(trivial_inequality_removal,[],[f5502]) ).
thf(f5552,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(constrained_superposition,[],[f1503,f5247]) ).
thf(f5555,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(trivial_inequality_removal,[],[f5552]) ).
thf(f5560,plain,
( ( $false = $true )
| ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(constrained_superposition,[],[f5555,f598]) ).
thf(f5567,plain,
( $false
| ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(trivial_inequality_removal,[],[f5560]) ).
thf(f5568,plain,
( ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(avatar_contradiction_clause,[],[f5567]) ).
thf(f5635,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false = $true ) )
| ~ spl38_48
| ~ spl38_112 ),
inference(constrained_superposition,[],[f5506,f412]) ).
thf(f5637,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK37 @ e3 @ mactual @ ( op @ e1 @ e1 ) ) ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_48
| ~ spl38_112 ),
inference(trivial_inequality_removal,[],[f5635]) ).
thf(f5753,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(constrained_superposition,[],[f5637,f1654]) ).
thf(f5759,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(trivial_inequality_removal,[],[f5753]) ).
thf(f5764,plain,
( ( $false = $true )
| ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(constrained_superposition,[],[f5759,f598]) ).
thf(f5769,plain,
( $false
| ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(trivial_inequality_removal,[],[f5764]) ).
thf(f5770,plain,
( ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(avatar_contradiction_clause,[],[f5769]) ).
thf(f5788,plain,
( ( $false = $true )
| ( ( mrel @ sK9 @ sK30 )
= $false )
| ~ spl38_10
| ~ spl38_117 ),
inference(constrained_superposition,[],[f3371,f1200]) ).
thf(f5789,plain,
( ( ( mrel @ sK9 @ sK30 )
= $false )
| ~ spl38_10
| ~ spl38_117 ),
inference(trivial_inequality_removal,[],[f5788]) ).
thf(f5800,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK30 ) ) )
| ~ spl38_10
| ~ spl38_117 ),
inference(constrained_superposition,[],[f412,f5789]) ).
thf(f5801,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK30 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_10
| ~ spl38_117 ),
inference(trivial_inequality_removal,[],[f5800]) ).
thf(f5844,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(constrained_superposition,[],[f1214,f5801]) ).
thf(f5846,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(trivial_inequality_removal,[],[f5844]) ).
thf(f5852,plain,
( ( $false = $true )
| ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(constrained_superposition,[],[f5846,f598]) ).
thf(f5858,plain,
( $false
| ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(trivial_inequality_removal,[],[f5852]) ).
thf(f5859,plain,
( ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(avatar_contradiction_clause,[],[f5858]) ).
thf(f5871,plain,
( ( $false
= ( mrel @ sK9 @ sK0 ) )
| ( $false = $true )
| ~ spl38_16
| ~ spl38_103 ),
inference(constrained_superposition,[],[f1226,f2999]) ).
thf(f5873,plain,
( ( $false
= ( mrel @ sK9 @ sK0 ) )
| ~ spl38_16
| ~ spl38_103 ),
inference(trivial_inequality_removal,[],[f5871]) ).
thf(f5876,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK0 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_16
| ~ spl38_103 ),
inference(constrained_superposition,[],[f412,f5873]) ).
thf(f5877,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ sK0 ) ) )
| ~ spl38_16
| ~ spl38_103 ),
inference(trivial_inequality_removal,[],[f5876]) ).
thf(f5888,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl38_16
| ~ spl38_103 ),
inference(constrained_superposition,[],[f598,f5877]) ).
thf(f5893,plain,
( ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl38_16
| ~ spl38_103 ),
inference(trivial_inequality_removal,[],[f5888]) ).
thf(f5898,plain,
( ( $false = $true )
| ~ spl38_12
| ~ spl38_16
| ~ spl38_103 ),
inference(constrained_superposition,[],[f1206,f5893]) ).
thf(f5903,plain,
( $false
| ~ spl38_12
| ~ spl38_16
| ~ spl38_103 ),
inference(trivial_inequality_removal,[],[f5898]) ).
thf(f5904,plain,
( ~ spl38_12
| ~ spl38_16
| ~ spl38_103 ),
inference(avatar_contradiction_clause,[],[f5903]) ).
thf(f5924,plain,
( ( $false = $true )
| ( $false
= ( mrel @ sK9 @ sK4 ) )
| ~ spl38_28
| ~ spl38_101 ),
inference(constrained_superposition,[],[f2993,f1381]) ).
thf(f5925,plain,
( ( $false
= ( mrel @ sK9 @ sK4 ) )
| ~ spl38_28
| ~ spl38_101 ),
inference(trivial_inequality_removal,[],[f5924]) ).
thf(f5927,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK4 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false = $true ) )
| ~ spl38_28
| ~ spl38_101 ),
inference(constrained_superposition,[],[f5925,f412]) ).
thf(f5929,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false
= ( mrel @ X0 @ sK4 ) ) )
| ~ spl38_28
| ~ spl38_101 ),
inference(trivial_inequality_removal,[],[f5927]) ).
thf(f5937,plain,
( ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false = $true )
| ~ spl38_28
| ~ spl38_101 ),
inference(constrained_superposition,[],[f5929,f598]) ).
thf(f5942,plain,
( ( $false
= ( mrel @ mactual @ sK4 ) )
| ~ spl38_28
| ~ spl38_101 ),
inference(trivial_inequality_removal,[],[f5937]) ).
thf(f5950,plain,
( ( $false = $true )
| ~ spl38_23
| ~ spl38_28
| ~ spl38_101 ),
inference(constrained_superposition,[],[f1358,f5942]) ).
thf(f5955,plain,
( $false
| ~ spl38_23
| ~ spl38_28
| ~ spl38_101 ),
inference(trivial_inequality_removal,[],[f5950]) ).
thf(f5956,plain,
( ~ spl38_23
| ~ spl38_28
| ~ spl38_101 ),
inference(avatar_contradiction_clause,[],[f5955]) ).
thf(f5957,plain,
( ( $false = $true )
| ( $false
= ( mrel @ sK9 @ sK31 ) )
| ~ spl38_22
| ~ spl38_121 ),
inference(constrained_superposition,[],[f1355,f3671]) ).
thf(f5959,plain,
( ( $false
= ( mrel @ sK9 @ sK31 ) )
| ~ spl38_22
| ~ spl38_121 ),
inference(trivial_inequality_removal,[],[f5957]) ).
thf(f5961,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK31 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_22
| ~ spl38_121 ),
inference(constrained_superposition,[],[f5959,f412]) ).
thf(f5963,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK31 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_22
| ~ spl38_121 ),
inference(trivial_inequality_removal,[],[f5961]) ).
thf(f6019,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(constrained_superposition,[],[f5963,f1365]) ).
thf(f6024,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(trivial_inequality_removal,[],[f6019]) ).
thf(f6030,plain,
( ( $false = $true )
| ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(constrained_superposition,[],[f6024,f598]) ).
thf(f6037,plain,
( $false
| ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(trivial_inequality_removal,[],[f6030]) ).
thf(f6038,plain,
( ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(avatar_contradiction_clause,[],[f6037]) ).
thf(f6049,plain,
( ( ( mrel @ sK9 @ sK28 )
= $false )
| ( $false = $true )
| ~ spl38_35
| ~ spl38_102 ),
inference(constrained_superposition,[],[f1509,f2996]) ).
thf(f6054,plain,
( ( ( mrel @ sK9 @ sK28 )
= $false )
| ~ spl38_35
| ~ spl38_102 ),
inference(trivial_inequality_removal,[],[f6049]) ).
thf(f6068,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK28 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) )
| ( $false = $true ) )
| ~ spl38_35
| ~ spl38_102 ),
inference(constrained_superposition,[],[f412,f6054]) ).
thf(f6069,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK28 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_35
| ~ spl38_102 ),
inference(trivial_inequality_removal,[],[f6068]) ).
thf(f6080,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ( $false = $true )
| ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(constrained_superposition,[],[f1532,f6069]) ).
thf(f6081,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(trivial_inequality_removal,[],[f6080]) ).
thf(f6090,plain,
( ( $false = $true )
| ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(constrained_superposition,[],[f598,f6081]) ).
thf(f6094,plain,
( $false
| ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(trivial_inequality_removal,[],[f6090]) ).
thf(f6095,plain,
( ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(avatar_contradiction_clause,[],[f6094]) ).
thf(f6101,plain,
( ( $false = $true )
| ( $false
= ( mrel @ sK9 @ sK32 ) )
| ~ spl38_36
| ~ spl38_119 ),
inference(constrained_superposition,[],[f1512,f3614]) ).
thf(f6103,plain,
( ( $false
= ( mrel @ sK9 @ sK32 ) )
| ~ spl38_36
| ~ spl38_119 ),
inference(trivial_inequality_removal,[],[f6101]) ).
thf(f6110,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK32 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_36
| ~ spl38_119 ),
inference(constrained_superposition,[],[f412,f6103]) ).
thf(f6111,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK32 ) )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_36
| ~ spl38_119 ),
inference(trivial_inequality_removal,[],[f6110]) ).
thf(f6125,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(constrained_superposition,[],[f6111,f1525]) ).
thf(f6133,plain,
( ( $false
= ( mrel @ mactual @ sK9 ) )
| ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(trivial_inequality_removal,[],[f6125]) ).
thf(f6152,plain,
( ( $false = $true )
| ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(constrained_superposition,[],[f6133,f598]) ).
thf(f6158,plain,
( $false
| ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(trivial_inequality_removal,[],[f6152]) ).
thf(f6159,plain,
( ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(avatar_contradiction_clause,[],[f6158]) ).
thf(f6168,plain,
( ( $false
= ( mrel @ sK9 @ sK16 ) )
| ( $false = $true )
| ~ spl38_45
| ~ spl38_104 ),
inference(constrained_superposition,[],[f3002,f1637]) ).
thf(f6169,plain,
( ( $false
= ( mrel @ sK9 @ sK16 ) )
| ~ spl38_45
| ~ spl38_104 ),
inference(trivial_inequality_removal,[],[f6168]) ).
thf(f6171,plain,
( ! [X0: mworld] :
( ( $false = $true )
| ( ( mrel @ X0 @ sK16 )
= $false )
| ( $false
= ( mrel @ X0 @ sK9 ) ) )
| ~ spl38_45
| ~ spl38_104 ),
inference(constrained_superposition,[],[f6169,f412]) ).
thf(f6173,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK9 ) )
| ( ( mrel @ X0 @ sK16 )
= $false ) )
| ~ spl38_45
| ~ spl38_104 ),
inference(trivial_inequality_removal,[],[f6171]) ).
thf(f6177,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK16 ) )
| ~ spl38_45
| ~ spl38_104 ),
inference(constrained_superposition,[],[f6173,f598]) ).
thf(f6182,plain,
( ( $false
= ( mrel @ mactual @ sK16 ) )
| ~ spl38_45
| ~ spl38_104 ),
inference(trivial_inequality_removal,[],[f6177]) ).
thf(f6188,plain,
( ( $false = $true )
| ~ spl38_45
| ~ spl38_52
| ~ spl38_104 ),
inference(constrained_superposition,[],[f6182,f1666]) ).
thf(f6193,plain,
( $false
| ~ spl38_45
| ~ spl38_52
| ~ spl38_104 ),
inference(trivial_inequality_removal,[],[f6188]) ).
thf(f6194,plain,
( ~ spl38_45
| ~ spl38_52
| ~ spl38_104 ),
inference(avatar_contradiction_clause,[],[f6193]) ).
cnf(s3,plain,
( spl38_9
| spl38_10
| spl38_11
| spl38_12 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s4,plain,
( spl38_9
| spl38_10
| spl38_12
| spl38_13 ),
inference(sat_conversion,[],[f1211]) ).
cnf(s5,plain,
( spl38_9
| spl38_12
| spl38_13
| spl38_14 ),
inference(sat_conversion,[],[f1215]) ).
cnf(s6,plain,
( spl38_9
| spl38_11
| spl38_12
| spl38_14 ),
inference(sat_conversion,[],[f1216]) ).
cnf(s7,plain,
( spl38_11
| spl38_12
| spl38_14
| spl38_15 ),
inference(sat_conversion,[],[f1220]) ).
cnf(s8,plain,
( spl38_12
| spl38_13
| spl38_14
| spl38_15 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s9,plain,
( spl38_10
| spl38_11
| spl38_12
| spl38_15 ),
inference(sat_conversion,[],[f1222]) ).
cnf(s10,plain,
( spl38_10
| spl38_12
| spl38_13
| spl38_15 ),
inference(sat_conversion,[],[f1223]) ).
cnf(s11,plain,
( spl38_9
| spl38_11
| spl38_14
| spl38_16 ),
inference(sat_conversion,[],[f1227]) ).
cnf(s12,plain,
( spl38_9
| spl38_10
| spl38_11
| spl38_16 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s13,plain,
( spl38_9
| spl38_13
| spl38_14
| spl38_16 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s14,plain,
( spl38_9
| spl38_10
| spl38_13
| spl38_16 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s15,plain,
( spl38_13
| spl38_14
| spl38_15
| spl38_16 ),
inference(sat_conversion,[],[f1231]) ).
cnf(s16,plain,
( spl38_11
| spl38_14
| spl38_15
| spl38_16 ),
inference(sat_conversion,[],[f1232]) ).
cnf(s17,plain,
( spl38_10
| spl38_11
| spl38_15
| spl38_16 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s18,plain,
( spl38_10
| spl38_13
| spl38_15
| spl38_16 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s20,plain,
( spl38_21
| spl38_22
| spl38_23
| spl38_24 ),
inference(sat_conversion,[],[f1362]) ).
cnf(s21,plain,
( spl38_21
| spl38_23
| spl38_24
| spl38_25 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s22,plain,
( spl38_21
| spl38_23
| spl38_25
| spl38_26 ),
inference(sat_conversion,[],[f1370]) ).
cnf(s23,plain,
( spl38_21
| spl38_22
| spl38_23
| spl38_26 ),
inference(sat_conversion,[],[f1371]) ).
cnf(s24,plain,
( spl38_22
| spl38_23
| spl38_24
| spl38_27 ),
inference(sat_conversion,[],[f1375]) ).
cnf(s25,plain,
( spl38_22
| spl38_23
| spl38_26
| spl38_27 ),
inference(sat_conversion,[],[f1376]) ).
cnf(s26,plain,
( spl38_23
| spl38_24
| spl38_25
| spl38_27 ),
inference(sat_conversion,[],[f1377]) ).
cnf(s27,plain,
( spl38_23
| spl38_25
| spl38_26
| spl38_27 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s28,plain,
( spl38_22
| spl38_24
| spl38_27
| spl38_28 ),
inference(sat_conversion,[],[f1382]) ).
cnf(s29,plain,
( spl38_21
| spl38_22
| spl38_24
| spl38_28 ),
inference(sat_conversion,[],[f1383]) ).
cnf(s30,plain,
( spl38_21
| spl38_24
| spl38_25
| spl38_28 ),
inference(sat_conversion,[],[f1384]) ).
cnf(s31,plain,
( spl38_24
| spl38_25
| spl38_27
| spl38_28 ),
inference(sat_conversion,[],[f1385]) ).
cnf(s32,plain,
( spl38_22
| spl38_26
| spl38_27
| spl38_28 ),
inference(sat_conversion,[],[f1386]) ).
cnf(s33,plain,
( spl38_25
| spl38_26
| spl38_27
| spl38_28 ),
inference(sat_conversion,[],[f1387]) ).
cnf(s34,plain,
( spl38_21
| spl38_25
| spl38_26
| spl38_28 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s35,plain,
( spl38_21
| spl38_22
| spl38_26
| spl38_28 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s37,plain,
( spl38_33
| spl38_34
| spl38_35
| spl38_36 ),
inference(sat_conversion,[],[f1513]) ).
cnf(s38,plain,
( spl38_34
| spl38_35
| spl38_36
| spl38_37 ),
inference(sat_conversion,[],[f1517]) ).
cnf(s39,plain,
( spl38_35
| spl38_36
| spl38_37
| spl38_38 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s40,plain,
( spl38_33
| spl38_35
| spl38_36
| spl38_38 ),
inference(sat_conversion,[],[f1522]) ).
cnf(s41,plain,
( spl38_33
| spl38_34
| spl38_35
| spl38_39 ),
inference(sat_conversion,[],[f1526]) ).
cnf(s42,plain,
( spl38_34
| spl38_35
| spl38_37
| spl38_39 ),
inference(sat_conversion,[],[f1527]) ).
cnf(s43,plain,
( spl38_35
| spl38_37
| spl38_38
| spl38_39 ),
inference(sat_conversion,[],[f1528]) ).
cnf(s44,plain,
( spl38_33
| spl38_35
| spl38_38
| spl38_39 ),
inference(sat_conversion,[],[f1529]) ).
cnf(s45,plain,
( spl38_33
| spl38_36
| spl38_38
| spl38_40 ),
inference(sat_conversion,[],[f1533]) ).
cnf(s46,plain,
( spl38_33
| spl38_34
| spl38_36
| spl38_40 ),
inference(sat_conversion,[],[f1534]) ).
cnf(s47,plain,
( spl38_33
| spl38_38
| spl38_39
| spl38_40 ),
inference(sat_conversion,[],[f1535]) ).
cnf(s48,plain,
( spl38_33
| spl38_34
| spl38_39
| spl38_40 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s49,plain,
( spl38_34
| spl38_37
| spl38_39
| spl38_40 ),
inference(sat_conversion,[],[f1537]) ).
cnf(s50,plain,
( spl38_34
| spl38_36
| spl38_37
| spl38_40 ),
inference(sat_conversion,[],[f1538]) ).
cnf(s51,plain,
( spl38_37
| spl38_38
| spl38_39
| spl38_40 ),
inference(sat_conversion,[],[f1539]) ).
cnf(s52,plain,
( spl38_36
| spl38_37
| spl38_38
| spl38_40 ),
inference(sat_conversion,[],[f1540]) ).
cnf(s54,plain,
( spl38_45
| spl38_46
| spl38_47
| spl38_48 ),
inference(sat_conversion,[],[f1647]) ).
cnf(s55,plain,
( spl38_45
| spl38_47
| spl38_48
| spl38_49 ),
inference(sat_conversion,[],[f1651]) ).
cnf(s56,plain,
( spl38_45
| spl38_46
| spl38_47
| spl38_50 ),
inference(sat_conversion,[],[f1655]) ).
cnf(s57,plain,
( spl38_45
| spl38_47
| spl38_49
| spl38_50 ),
inference(sat_conversion,[],[f1656]) ).
cnf(s58,plain,
( spl38_45
| spl38_48
| spl38_49
| spl38_51 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s59,plain,
( spl38_45
| spl38_46
| spl38_48
| spl38_51 ),
inference(sat_conversion,[],[f1661]) ).
cnf(s60,plain,
( spl38_45
| spl38_46
| spl38_50
| spl38_51 ),
inference(sat_conversion,[],[f1662]) ).
cnf(s61,plain,
( spl38_45
| spl38_49
| spl38_50
| spl38_51 ),
inference(sat_conversion,[],[f1663]) ).
cnf(s62,plain,
( spl38_47
| spl38_49
| spl38_50
| spl38_52 ),
inference(sat_conversion,[],[f1667]) ).
cnf(s63,plain,
( spl38_47
| spl38_48
| spl38_49
| spl38_52 ),
inference(sat_conversion,[],[f1668]) ).
cnf(s64,plain,
( spl38_46
| spl38_47
| spl38_50
| spl38_52 ),
inference(sat_conversion,[],[f1669]) ).
cnf(s65,plain,
( spl38_46
| spl38_47
| spl38_48
| spl38_52 ),
inference(sat_conversion,[],[f1670]) ).
cnf(s66,plain,
( spl38_49
| spl38_50
| spl38_51
| spl38_52 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s67,plain,
( spl38_48
| spl38_49
| spl38_51
| spl38_52 ),
inference(sat_conversion,[],[f1672]) ).
cnf(s68,plain,
( spl38_46
| spl38_48
| spl38_51
| spl38_52 ),
inference(sat_conversion,[],[f1673]) ).
cnf(s69,plain,
( spl38_46
| spl38_50
| spl38_51
| spl38_52 ),
inference(sat_conversion,[],[f1674]) ).
cnf(s82,plain,
( spl38_101
| spl38_102
| spl38_103
| spl38_104 ),
inference(sat_conversion,[],[f3003]) ).
cnf(s84,plain,
( spl38_101
| spl38_102
| spl38_104
| spl38_109 ),
inference(sat_conversion,[],[f3181]) ).
cnf(s85,plain,
( spl38_101
| spl38_103
| spl38_104
| spl38_110 ),
inference(sat_conversion,[],[f3247]) ).
cnf(s86,plain,
( spl38_102
| spl38_103
| spl38_104
| spl38_111 ),
inference(sat_conversion,[],[f3310]) ).
cnf(s87,plain,
( spl38_101
| spl38_102
| spl38_103
| spl38_112 ),
inference(sat_conversion,[],[f3332]) ).
cnf(s89,plain,
( spl38_101
| spl38_102
| spl38_104
| spl38_117 ),
inference(sat_conversion,[],[f3372]) ).
cnf(s90,plain,
( spl38_101
| spl38_102
| spl38_104
| spl38_118 ),
inference(sat_conversion,[],[f3452]) ).
cnf(s91,plain,
( spl38_101
| spl38_104
| spl38_109
| spl38_110 ),
inference(sat_conversion,[],[f3520]) ).
cnf(s92,plain,
( spl38_101
| spl38_102
| spl38_109
| spl38_112 ),
inference(sat_conversion,[],[f3537]) ).
cnf(s93,plain,
( spl38_102
| spl38_104
| spl38_109
| spl38_111 ),
inference(sat_conversion,[],[f3550]) ).
cnf(s94,plain,
( spl38_101
| spl38_103
| spl38_110
| spl38_112 ),
inference(sat_conversion,[],[f3601]) ).
cnf(s95,plain,
( spl38_101
| spl38_103
| spl38_104
| spl38_119 ),
inference(sat_conversion,[],[f3615]) ).
cnf(s96,plain,
( spl38_101
| spl38_103
| spl38_104
| spl38_120 ),
inference(sat_conversion,[],[f3619]) ).
cnf(s97,plain,
( spl38_103
| spl38_104
| spl38_110
| spl38_111 ),
inference(sat_conversion,[],[f3636]) ).
cnf(s98,plain,
( spl38_102
| spl38_103
| spl38_104
| spl38_121 ),
inference(sat_conversion,[],[f3672]) ).
cnf(s99,plain,
( spl38_102
| spl38_103
| spl38_104
| spl38_122 ),
inference(sat_conversion,[],[f3676]) ).
cnf(s100,plain,
( spl38_102
| spl38_103
| spl38_111
| spl38_112 ),
inference(sat_conversion,[],[f3684]) ).
cnf(s101,plain,
( spl38_101
| spl38_102
| spl38_103
| spl38_123 ),
inference(sat_conversion,[],[f3690]) ).
cnf(s102,plain,
( spl38_101
| spl38_102
| spl38_103
| spl38_124 ),
inference(sat_conversion,[],[f3694]) ).
cnf(s105,plain,
( spl38_101
| spl38_104
| spl38_110
| spl38_117 ),
inference(sat_conversion,[],[f3736]) ).
cnf(s106,plain,
( spl38_101
| spl38_102
| spl38_112
| spl38_117 ),
inference(sat_conversion,[],[f3739]) ).
cnf(s107,plain,
( spl38_102
| spl38_104
| spl38_111
| spl38_117 ),
inference(sat_conversion,[],[f3819]) ).
cnf(s108,plain,
( spl38_101
| spl38_102
| spl38_112
| spl38_118 ),
inference(sat_conversion,[],[f3820]) ).
cnf(s109,plain,
( spl38_101
| spl38_104
| spl38_110
| spl38_118 ),
inference(sat_conversion,[],[f3825]) ).
cnf(s110,plain,
( spl38_102
| spl38_104
| spl38_111
| spl38_118 ),
inference(sat_conversion,[],[f3888]) ).
cnf(s111,plain,
( spl38_101
| spl38_104
| spl38_109
| spl38_120 ),
inference(sat_conversion,[],[f3894]) ).
cnf(s112,plain,
( spl38_101
| spl38_104
| spl38_109
| spl38_119 ),
inference(sat_conversion,[],[f3895]) ).
cnf(s113,plain,
( spl38_101
| spl38_109
| spl38_110
| spl38_112 ),
inference(sat_conversion,[],[f3898]) ).
cnf(s114,plain,
( spl38_101
| spl38_102
| spl38_109
| spl38_123 ),
inference(sat_conversion,[],[f3909]) ).
cnf(s115,plain,
( spl38_101
| spl38_102
| spl38_109
| spl38_124 ),
inference(sat_conversion,[],[f3910]) ).
cnf(s116,plain,
( spl38_102
| spl38_109
| spl38_111
| spl38_112 ),
inference(sat_conversion,[],[f3928]) ).
cnf(s117,plain,
( spl38_104
| spl38_109
| spl38_110
| spl38_111 ),
inference(sat_conversion,[],[f3931]) ).
cnf(s118,plain,
( spl38_102
| spl38_104
| spl38_109
| spl38_121 ),
inference(sat_conversion,[],[f3956]) ).
cnf(s119,plain,
( spl38_102
| spl38_104
| spl38_109
| spl38_122 ),
inference(sat_conversion,[],[f3979]) ).
cnf(s120,plain,
( spl38_101
| spl38_103
| spl38_110
| spl38_123 ),
inference(sat_conversion,[],[f3980]) ).
cnf(s121,plain,
( spl38_101
| spl38_103
| spl38_110
| spl38_124 ),
inference(sat_conversion,[],[f3981]) ).
cnf(s122,plain,
( spl38_101
| spl38_103
| spl38_112
| spl38_119 ),
inference(sat_conversion,[],[f3984]) ).
cnf(s123,plain,
( spl38_101
| spl38_103
| spl38_112
| spl38_120 ),
inference(sat_conversion,[],[f3985]) ).
cnf(s124,plain,
( spl38_103
| spl38_110
| spl38_111
| spl38_112 ),
inference(sat_conversion,[],[f3988]) ).
cnf(s125,plain,
( spl38_103
| spl38_104
| spl38_110
| spl38_122 ),
inference(sat_conversion,[],[f3998]) ).
cnf(s126,plain,
( spl38_103
| spl38_104
| spl38_110
| spl38_121 ),
inference(sat_conversion,[],[f3999]) ).
cnf(s127,plain,
( spl38_103
| spl38_104
| spl38_111
| spl38_119 ),
inference(sat_conversion,[],[f4022]) ).
cnf(s128,plain,
( spl38_103
| spl38_104
| spl38_111
| spl38_120 ),
inference(sat_conversion,[],[f4027]) ).
cnf(s129,plain,
( spl38_102
| spl38_103
| spl38_112
| spl38_121 ),
inference(sat_conversion,[],[f4032]) ).
cnf(s130,plain,
( spl38_102
| spl38_103
| spl38_112
| spl38_122 ),
inference(sat_conversion,[],[f4033]) ).
cnf(s131,plain,
( spl38_102
| spl38_103
| spl38_111
| spl38_124 ),
inference(sat_conversion,[],[f4038]) ).
cnf(s132,plain,
( spl38_102
| spl38_103
| spl38_111
| spl38_123 ),
inference(sat_conversion,[],[f4039]) ).
cnf(s133,plain,
( spl38_101
| spl38_104
| spl38_117
| spl38_119 ),
inference(sat_conversion,[],[f4055]) ).
cnf(s134,plain,
( spl38_101
| spl38_104
| spl38_117
| spl38_120 ),
inference(sat_conversion,[],[f4056]) ).
cnf(s135,plain,
( spl38_101
| spl38_110
| spl38_112
| spl38_117 ),
inference(sat_conversion,[],[f4059]) ).
cnf(s136,plain,
( spl38_101
| spl38_102
| spl38_117
| spl38_124 ),
inference(sat_conversion,[],[f4060]) ).
cnf(s137,plain,
( spl38_101
| spl38_102
| spl38_117
| spl38_123 ),
inference(sat_conversion,[],[f4061]) ).
cnf(s138,plain,
( spl38_104
| spl38_110
| spl38_111
| spl38_117 ),
inference(sat_conversion,[],[f4122]) ).
cnf(s139,plain,
( spl38_102
| spl38_104
| spl38_117
| spl38_122 ),
inference(sat_conversion,[],[f4125]) ).
cnf(s140,plain,
( spl38_102
| spl38_104
| spl38_117
| spl38_121 ),
inference(sat_conversion,[],[f4126]) ).
cnf(s141,plain,
( spl38_102
| spl38_111
| spl38_112
| spl38_117 ),
inference(sat_conversion,[],[f4137]) ).
cnf(s142,plain,
( spl38_101
| spl38_102
| spl38_118
| spl38_123 ),
inference(sat_conversion,[],[f4140]) ).
cnf(s143,plain,
( spl38_101
| spl38_102
| spl38_118
| spl38_124 ),
inference(sat_conversion,[],[f4141]) ).
cnf(s144,plain,
( spl38_101
| spl38_104
| spl38_118
| spl38_120 ),
inference(sat_conversion,[],[f4142]) ).
cnf(s145,plain,
( spl38_101
| spl38_104
| spl38_118
| spl38_119 ),
inference(sat_conversion,[],[f4143]) ).
cnf(s146,plain,
( spl38_101
| spl38_110
| spl38_112
| spl38_118 ),
inference(sat_conversion,[],[f4146]) ).
cnf(s147,plain,
( spl38_102
| spl38_111
| spl38_112
| spl38_118 ),
inference(sat_conversion,[],[f4157]) ).
cnf(s148,plain,
( spl38_102
| spl38_104
| spl38_118
| spl38_121 ),
inference(sat_conversion,[],[f4210]) ).
cnf(s149,plain,
( spl38_102
| spl38_104
| spl38_118
| spl38_122 ),
inference(sat_conversion,[],[f4211]) ).
cnf(s150,plain,
( spl38_104
| spl38_110
| spl38_111
| spl38_118 ),
inference(sat_conversion,[],[f4212]) ).
cnf(s151,plain,
( spl38_101
| spl38_109
| spl38_112
| spl38_120 ),
inference(sat_conversion,[],[f4215]) ).
cnf(s152,plain,
( spl38_101
| spl38_109
| spl38_112
| spl38_119 ),
inference(sat_conversion,[],[f4216]) ).
cnf(s153,plain,
( spl38_101
| spl38_109
| spl38_110
| spl38_123 ),
inference(sat_conversion,[],[f4217]) ).
cnf(s154,plain,
( spl38_101
| spl38_109
| spl38_110
| spl38_124 ),
inference(sat_conversion,[],[f4222]) ).
cnf(s155,plain,
( spl38_102
| spl38_109
| spl38_111
| spl38_123 ),
inference(sat_conversion,[],[f4223]) ).
cnf(s156,plain,
( spl38_102
| spl38_109
| spl38_111
| spl38_124 ),
inference(sat_conversion,[],[f4227]) ).
cnf(s157,plain,
( spl38_109
| spl38_110
| spl38_111
| spl38_112 ),
inference(sat_conversion,[],[f4232]) ).
cnf(s158,plain,
( spl38_104
| spl38_109
| spl38_111
| spl38_119 ),
inference(sat_conversion,[],[f4235]) ).
cnf(s159,plain,
( spl38_104
| spl38_109
| spl38_111
| spl38_120 ),
inference(sat_conversion,[],[f4236]) ).
cnf(s160,plain,
( spl38_102
| spl38_109
| spl38_112
| spl38_121 ),
inference(sat_conversion,[],[f4239]) ).
cnf(s161,plain,
( spl38_104
| spl38_109
| spl38_110
| spl38_121 ),
inference(sat_conversion,[],[f4255]) ).
cnf(s162,plain,
( spl38_102
| spl38_109
| spl38_112
| spl38_122 ),
inference(sat_conversion,[],[f4258]) ).
cnf(s163,plain,
( spl38_104
| spl38_109
| spl38_110
| spl38_122 ),
inference(sat_conversion,[],[f4276]) ).
cnf(s164,plain,
( spl38_101
| spl38_103
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4277]) ).
cnf(s165,plain,
( spl38_101
| spl38_103
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4278]) ).
cnf(s166,plain,
( spl38_101
| spl38_103
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4279]) ).
cnf(s167,plain,
( spl38_101
| spl38_103
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4280]) ).
cnf(s168,plain,
( spl38_103
| spl38_110
| spl38_112
| spl38_121 ),
inference(sat_conversion,[],[f4281]) ).
cnf(s169,plain,
( spl38_103
| spl38_110
| spl38_112
| spl38_122 ),
inference(sat_conversion,[],[f4282]) ).
cnf(s170,plain,
( spl38_103
| spl38_110
| spl38_111
| spl38_123 ),
inference(sat_conversion,[],[f4283]) ).
cnf(s171,plain,
( spl38_103
| spl38_110
| spl38_111
| spl38_124 ),
inference(sat_conversion,[],[f4284]) ).
cnf(s172,plain,
( spl38_103
| spl38_104
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4289]) ).
cnf(s173,plain,
( spl38_103
| spl38_104
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4290]) ).
cnf(s174,plain,
( spl38_103
| spl38_104
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4291]) ).
cnf(s175,plain,
( spl38_103
| spl38_104
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4292]) ).
cnf(s176,plain,
( spl38_103
| spl38_111
| spl38_112
| spl38_119 ),
inference(sat_conversion,[],[f4310]) ).
cnf(s177,plain,
( spl38_103
| spl38_111
| spl38_112
| spl38_120 ),
inference(sat_conversion,[],[f4313]) ).
cnf(s178,plain,
( spl38_102
| spl38_103
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4314]) ).
cnf(s179,plain,
( spl38_102
| spl38_103
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4315]) ).
cnf(s180,plain,
( spl38_102
| spl38_103
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4316]) ).
cnf(s181,plain,
( spl38_102
| spl38_103
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4317]) ).
cnf(s182,plain,
( spl38_101
| spl38_112
| spl38_117
| spl38_120 ),
inference(sat_conversion,[],[f4333]) ).
cnf(s183,plain,
( spl38_101
| spl38_112
| spl38_117
| spl38_119 ),
inference(sat_conversion,[],[f4334]) ).
cnf(s184,plain,
( spl38_101
| spl38_110
| spl38_117
| spl38_123 ),
inference(sat_conversion,[],[f4337]) ).
cnf(s185,plain,
( spl38_101
| spl38_110
| spl38_117
| spl38_124 ),
inference(sat_conversion,[],[f4338]) ).
cnf(s186,plain,
( spl38_110
| spl38_111
| spl38_112
| spl38_117 ),
inference(sat_conversion,[],[f4350]) ).
cnf(s187,plain,
( spl38_104
| spl38_111
| spl38_117
| spl38_120 ),
inference(sat_conversion,[],[f4375]) ).
cnf(s188,plain,
( spl38_104
| spl38_111
| spl38_117
| spl38_119 ),
inference(sat_conversion,[],[f4376]) ).
cnf(s189,plain,
( spl38_104
| spl38_110
| spl38_117
| spl38_122 ),
inference(sat_conversion,[],[f4381]) ).
cnf(s190,plain,
( spl38_104
| spl38_110
| spl38_117
| spl38_121 ),
inference(sat_conversion,[],[f4382]) ).
cnf(s191,plain,
( spl38_102
| spl38_112
| spl38_117
| spl38_122 ),
inference(sat_conversion,[],[f4385]) ).
cnf(s192,plain,
( spl38_102
| spl38_112
| spl38_117
| spl38_121 ),
inference(sat_conversion,[],[f4388]) ).
cnf(s193,plain,
( spl38_102
| spl38_111
| spl38_117
| spl38_124 ),
inference(sat_conversion,[],[f4389]) ).
cnf(s194,plain,
( spl38_102
| spl38_111
| spl38_117
| spl38_123 ),
inference(sat_conversion,[],[f4390]) ).
cnf(s195,plain,
( spl38_101
| spl38_110
| spl38_118
| spl38_123 ),
inference(sat_conversion,[],[f4391]) ).
cnf(s196,plain,
( spl38_101
| spl38_110
| spl38_118
| spl38_124 ),
inference(sat_conversion,[],[f4392]) ).
cnf(s197,plain,
( spl38_101
| spl38_112
| spl38_118
| spl38_119 ),
inference(sat_conversion,[],[f4393]) ).
cnf(s198,plain,
( spl38_101
| spl38_112
| spl38_118
| spl38_120 ),
inference(sat_conversion,[],[f4394]) ).
cnf(s199,plain,
( spl38_110
| spl38_111
| spl38_112
| spl38_118 ),
inference(sat_conversion,[],[f4401]) ).
cnf(s200,plain,
( spl38_102
| spl38_111
| spl38_118
| spl38_123 ),
inference(sat_conversion,[],[f4402]) ).
cnf(s201,plain,
( spl38_102
| spl38_111
| spl38_118
| spl38_124 ),
inference(sat_conversion,[],[f4409]) ).
cnf(s202,plain,
( spl38_102
| spl38_112
| spl38_118
| spl38_121 ),
inference(sat_conversion,[],[f4410]) ).
cnf(s203,plain,
( spl38_102
| spl38_112
| spl38_118
| spl38_122 ),
inference(sat_conversion,[],[f4411]) ).
cnf(s204,plain,
( spl38_104
| spl38_110
| spl38_118
| spl38_122 ),
inference(sat_conversion,[],[f4442]) ).
cnf(s205,plain,
( spl38_104
| spl38_110
| spl38_118
| spl38_121 ),
inference(sat_conversion,[],[f4443]) ).
cnf(s206,plain,
( spl38_104
| spl38_111
| spl38_118
| spl38_120 ),
inference(sat_conversion,[],[f4448]) ).
cnf(s207,plain,
( spl38_104
| spl38_111
| spl38_118
| spl38_119 ),
inference(sat_conversion,[],[f4449]) ).
cnf(s208,plain,
( spl38_101
| spl38_109
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4450]) ).
cnf(s209,plain,
( spl38_101
| spl38_109
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4451]) ).
cnf(s210,plain,
( spl38_101
| spl38_109
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4452]) ).
cnf(s211,plain,
( spl38_101
| spl38_109
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4453]) ).
cnf(s212,plain,
( spl38_109
| spl38_110
| spl38_111
| spl38_123 ),
inference(sat_conversion,[],[f4456]) ).
cnf(s213,plain,
( spl38_109
| spl38_110
| spl38_111
| spl38_124 ),
inference(sat_conversion,[],[f4457]) ).
cnf(s214,plain,
( spl38_109
| spl38_111
| spl38_112
| spl38_120 ),
inference(sat_conversion,[],[f4460]) ).
cnf(s215,plain,
( spl38_109
| spl38_111
| spl38_112
| spl38_119 ),
inference(sat_conversion,[],[f4461]) ).
cnf(s216,plain,
( spl38_102
| spl38_109
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4462]) ).
cnf(s217,plain,
( spl38_102
| spl38_109
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4463]) ).
cnf(s218,plain,
( spl38_109
| spl38_110
| spl38_112
| spl38_121 ),
inference(sat_conversion,[],[f4472]) ).
cnf(s219,plain,
( spl38_104
| spl38_109
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4473]) ).
cnf(s220,plain,
( spl38_104
| spl38_109
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4474]) ).
cnf(s221,plain,
( spl38_102
| spl38_109
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4475]) ).
cnf(s222,plain,
( spl38_102
| spl38_109
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4476]) ).
cnf(s223,plain,
( spl38_109
| spl38_110
| spl38_112
| spl38_122 ),
inference(sat_conversion,[],[f4479]) ).
cnf(s224,plain,
( spl38_104
| spl38_109
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4486]) ).
cnf(s225,plain,
( spl38_104
| spl38_109
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4487]) ).
cnf(s226,plain,
( spl38_103
| spl38_110
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4488]) ).
cnf(s227,plain,
( spl38_103
| spl38_110
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4489]) ).
cnf(s228,plain,
( spl38_103
| spl38_110
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4490]) ).
cnf(s229,plain,
( spl38_103
| spl38_110
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4491]) ).
cnf(s230,plain,
( spl38_103
| spl38_112
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4492]) ).
cnf(s231,plain,
( spl38_103
| spl38_112
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4493]) ).
cnf(s232,plain,
( spl38_103
| spl38_112
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4494]) ).
cnf(s233,plain,
( spl38_103
| spl38_112
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4495]) ).
cnf(s234,plain,
( spl38_103
| spl38_111
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4504]) ).
cnf(s235,plain,
( spl38_103
| spl38_111
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4505]) ).
cnf(s236,plain,
( spl38_103
| spl38_111
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4506]) ).
cnf(s237,plain,
( spl38_103
| spl38_111
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4507]) ).
cnf(s238,plain,
( spl38_101
| spl38_117
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4523]) ).
cnf(s239,plain,
( spl38_101
| spl38_117
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4524]) ).
cnf(s240,plain,
( spl38_101
| spl38_117
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4525]) ).
cnf(s241,plain,
( spl38_101
| spl38_117
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4526]) ).
cnf(s242,plain,
( spl38_110
| spl38_112
| spl38_117
| spl38_121 ),
inference(sat_conversion,[],[f4531]) ).
cnf(s243,plain,
( spl38_110
| spl38_112
| spl38_117
| spl38_122 ),
inference(sat_conversion,[],[f4532]) ).
cnf(s244,plain,
( spl38_111
| spl38_112
| spl38_117
| spl38_119 ),
inference(sat_conversion,[],[f4533]) ).
cnf(s245,plain,
( spl38_111
| spl38_112
| spl38_117
| spl38_120 ),
inference(sat_conversion,[],[f4534]) ).
cnf(s246,plain,
( spl38_110
| spl38_111
| spl38_117
| spl38_124 ),
inference(sat_conversion,[],[f4539]) ).
cnf(s247,plain,
( spl38_110
| spl38_111
| spl38_117
| spl38_123 ),
inference(sat_conversion,[],[f4540]) ).
cnf(s248,plain,
( spl38_104
| spl38_117
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4557]) ).
cnf(s249,plain,
( spl38_104
| spl38_117
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4558]) ).
cnf(s250,plain,
( spl38_104
| spl38_117
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4559]) ).
cnf(s251,plain,
( spl38_104
| spl38_117
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4560]) ).
cnf(s252,plain,
( spl38_102
| spl38_117
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4561]) ).
cnf(s253,plain,
( spl38_102
| spl38_117
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4562]) ).
cnf(s254,plain,
( spl38_102
| spl38_117
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4563]) ).
cnf(s255,plain,
( spl38_102
| spl38_117
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4564]) ).
cnf(s256,plain,
( spl38_101
| spl38_118
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4565]) ).
cnf(s257,plain,
( spl38_101
| spl38_118
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4566]) ).
cnf(s258,plain,
( spl38_101
| spl38_118
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4567]) ).
cnf(s259,plain,
( spl38_101
| spl38_118
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4568]) ).
cnf(s260,plain,
( spl38_111
| spl38_112
| spl38_118
| spl38_120 ),
inference(sat_conversion,[],[f4569]) ).
cnf(s261,plain,
( spl38_111
| spl38_112
| spl38_118
| spl38_119 ),
inference(sat_conversion,[],[f4570]) ).
cnf(s262,plain,
( spl38_110
| spl38_111
| spl38_118
| spl38_123 ),
inference(sat_conversion,[],[f4571]) ).
cnf(s263,plain,
( spl38_110
| spl38_111
| spl38_118
| spl38_124 ),
inference(sat_conversion,[],[f4576]) ).
cnf(s264,plain,
( spl38_110
| spl38_112
| spl38_118
| spl38_121 ),
inference(sat_conversion,[],[f4577]) ).
cnf(s265,plain,
( spl38_110
| spl38_112
| spl38_118
| spl38_122 ),
inference(sat_conversion,[],[f4582]) ).
cnf(s266,plain,
( spl38_102
| spl38_118
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4586]) ).
cnf(s267,plain,
( spl38_102
| spl38_118
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4592]) ).
cnf(s268,plain,
( spl38_102
| spl38_118
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4593]) ).
cnf(s269,plain,
( spl38_102
| spl38_118
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4594]) ).
cnf(s270,plain,
( spl38_104
| spl38_118
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4605]) ).
cnf(s271,plain,
( spl38_104
| spl38_118
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4606]) ).
cnf(s272,plain,
( spl38_104
| spl38_118
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4607]) ).
cnf(s273,plain,
( spl38_104
| spl38_118
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4608]) ).
cnf(s274,plain,
( spl38_109
| spl38_111
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4609]) ).
cnf(s275,plain,
( spl38_109
| spl38_111
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4610]) ).
cnf(s276,plain,
( spl38_109
| spl38_111
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4611]) ).
cnf(s277,plain,
( spl38_109
| spl38_111
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4612]) ).
cnf(s278,plain,
( spl38_109
| spl38_112
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4617]) ).
cnf(s279,plain,
( spl38_109
| spl38_112
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4618]) ).
cnf(s280,plain,
( spl38_109
| spl38_110
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4619]) ).
cnf(s281,plain,
( spl38_109
| spl38_110
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4620]) ).
cnf(s282,plain,
( spl38_109
| spl38_110
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4621]) ).
cnf(s283,plain,
( spl38_109
| spl38_110
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4622]) ).
cnf(s284,plain,
( spl38_109
| spl38_112
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4627]) ).
cnf(s285,plain,
( spl38_109
| spl38_112
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4628]) ).
cnf(s286,plain,
( spl38_103
| spl38_120
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4629]) ).
cnf(s287,plain,
( spl38_103
| spl38_120
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4630]) ).
cnf(s288,plain,
( spl38_103
| spl38_120
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4631]) ).
cnf(s289,plain,
( spl38_103
| spl38_120
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4632]) ).
cnf(s290,plain,
( spl38_103
| spl38_119
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4633]) ).
cnf(s291,plain,
( spl38_103
| spl38_119
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4634]) ).
cnf(s292,plain,
( spl38_103
| spl38_119
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4635]) ).
cnf(s293,plain,
( spl38_103
| spl38_119
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4636]) ).
cnf(s294,plain,
( spl38_112
| spl38_117
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4652]) ).
cnf(s295,plain,
( spl38_112
| spl38_117
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4653]) ).
cnf(s296,plain,
( spl38_112
| spl38_117
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4654]) ).
cnf(s297,plain,
( spl38_112
| spl38_117
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4655]) ).
cnf(s298,plain,
( spl38_111
| spl38_117
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4656]) ).
cnf(s299,plain,
( spl38_111
| spl38_117
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4657]) ).
cnf(s300,plain,
( spl38_111
| spl38_117
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4658]) ).
cnf(s301,plain,
( spl38_111
| spl38_117
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4659]) ).
cnf(s302,plain,
( spl38_110
| spl38_117
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4660]) ).
cnf(s303,plain,
( spl38_110
| spl38_117
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4663]) ).
cnf(s304,plain,
( spl38_110
| spl38_117
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4666]) ).
cnf(s305,plain,
( spl38_110
| spl38_117
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4671]) ).
cnf(s306,plain,
( spl38_111
| spl38_118
| spl38_120
| spl38_123 ),
inference(sat_conversion,[],[f4672]) ).
cnf(s307,plain,
( spl38_111
| spl38_118
| spl38_119
| spl38_123 ),
inference(sat_conversion,[],[f4673]) ).
cnf(s308,plain,
( spl38_111
| spl38_118
| spl38_120
| spl38_124 ),
inference(sat_conversion,[],[f4674]) ).
cnf(s309,plain,
( spl38_111
| spl38_118
| spl38_119
| spl38_124 ),
inference(sat_conversion,[],[f4675]) ).
cnf(s310,plain,
( spl38_112
| spl38_118
| spl38_119
| spl38_121 ),
inference(sat_conversion,[],[f4676]) ).
cnf(s311,plain,
( spl38_112
| spl38_118
| spl38_120
| spl38_121 ),
inference(sat_conversion,[],[f4677]) ).
cnf(s312,plain,
( spl38_112
| spl38_118
| spl38_120
| spl38_122 ),
inference(sat_conversion,[],[f4678]) ).
cnf(s313,plain,
( spl38_112
| spl38_118
| spl38_119
| spl38_122 ),
inference(sat_conversion,[],[f4679]) ).
cnf(s314,plain,
( spl38_110
| spl38_118
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4680]) ).
cnf(s315,plain,
( spl38_110
| spl38_118
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4685]) ).
cnf(s316,plain,
( spl38_110
| spl38_118
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4686]) ).
cnf(s317,plain,
( spl38_110
| spl38_118
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4689]) ).
cnf(s318,plain,
( spl38_109
| spl38_120
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4692]) ).
cnf(s319,plain,
( spl38_109
| spl38_119
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4693]) ).
cnf(s320,plain,
( spl38_109
| spl38_119
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4694]) ).
cnf(s321,plain,
( spl38_109
| spl38_120
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4695]) ).
cnf(s322,plain,
( spl38_109
| spl38_119
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4696]) ).
cnf(s323,plain,
( spl38_109
| spl38_119
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4697]) ).
cnf(s324,plain,
( spl38_109
| spl38_120
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4698]) ).
cnf(s325,plain,
( spl38_109
| spl38_120
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4699]) ).
cnf(s326,plain,
( spl38_117
| spl38_120
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4715]) ).
cnf(s327,plain,
( spl38_117
| spl38_119
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4716]) ).
cnf(s328,plain,
( spl38_117
| spl38_119
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4717]) ).
cnf(s329,plain,
( spl38_117
| spl38_120
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4718]) ).
cnf(s330,plain,
( spl38_117
| spl38_120
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4719]) ).
cnf(s331,plain,
( spl38_117
| spl38_119
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4720]) ).
cnf(s332,plain,
( spl38_117
| spl38_120
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4721]) ).
cnf(s333,plain,
( spl38_117
| spl38_119
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4722]) ).
cnf(s334,plain,
( spl38_118
| spl38_119
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4723]) ).
cnf(s335,plain,
( spl38_118
| spl38_120
| spl38_122
| spl38_124 ),
inference(sat_conversion,[],[f4724]) ).
cnf(s336,plain,
( spl38_118
| spl38_119
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4725]) ).
cnf(s337,plain,
( spl38_118
| spl38_120
| spl38_122
| spl38_123 ),
inference(sat_conversion,[],[f4726]) ).
cnf(s338,plain,
( spl38_118
| spl38_120
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4727]) ).
cnf(s339,plain,
( spl38_118
| spl38_119
| spl38_121
| spl38_123 ),
inference(sat_conversion,[],[f4728]) ).
cnf(s340,plain,
( spl38_118
| spl38_119
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4729]) ).
cnf(s341,plain,
( spl38_118
| spl38_120
| spl38_121
| spl38_124 ),
inference(sat_conversion,[],[f4730]) ).
cnf(s347,plain,
( ~ spl38_11
| ~ spl38_13
| ~ spl38_118 ),
inference(sat_conversion,[],[f5144]) ).
cnf(s351,plain,
( ~ spl38_9
| ~ spl38_15
| ~ spl38_109 ),
inference(sat_conversion,[],[f5206]) ).
cnf(s353,plain,
( ~ spl38_34
| ~ spl38_38
| ~ spl38_110 ),
inference(sat_conversion,[],[f5282]) ).
cnf(s355,plain,
( ~ spl38_24
| ~ spl38_26
| ~ spl38_122 ),
inference(sat_conversion,[],[f5322]) ).
cnf(s359,plain,
( ~ spl38_21
| ~ spl38_27
| ~ spl38_111 ),
inference(sat_conversion,[],[f5373]) ).
cnf(s365,plain,
( ~ spl38_46
| ~ spl38_49
| ~ spl38_123 ),
inference(sat_conversion,[],[f5463]) ).
cnf(s367,plain,
( ~ spl38_47
| ~ spl38_51
| ~ spl38_124 ),
inference(sat_conversion,[],[f5493]) ).
cnf(s377,plain,
( ~ spl38_33
| ~ spl38_37
| ~ spl38_120 ),
inference(sat_conversion,[],[f5568]) ).
cnf(s381,plain,
( ~ spl38_48
| ~ spl38_50
| ~ spl38_112 ),
inference(sat_conversion,[],[f5770]) ).
cnf(s383,plain,
( ~ spl38_10
| ~ spl38_14
| ~ spl38_117 ),
inference(sat_conversion,[],[f5859]) ).
cnf(s385,plain,
( ~ spl38_12
| ~ spl38_16
| ~ spl38_103 ),
inference(sat_conversion,[],[f5904]) ).
cnf(s387,plain,
( ~ spl38_23
| ~ spl38_28
| ~ spl38_101 ),
inference(sat_conversion,[],[f5956]) ).
cnf(s389,plain,
( ~ spl38_22
| ~ spl38_25
| ~ spl38_121 ),
inference(sat_conversion,[],[f6038]) ).
cnf(s393,plain,
( ~ spl38_35
| ~ spl38_40
| ~ spl38_102 ),
inference(sat_conversion,[],[f6095]) ).
cnf(s395,plain,
( ~ spl38_36
| ~ spl38_39
| ~ spl38_119 ),
inference(sat_conversion,[],[f6159]) ).
cnf(s397,plain,
( ~ spl38_45
| ~ spl38_52
| ~ spl38_104 ),
inference(sat_conversion,[],[f6194]) ).
cnf(s398,plain,
( spl38_47
| spl38_46
| spl38_45
| ~ spl38_112 ),
inference(rat,[],[s381,s56,s54]) ).
cnf(s399,plain,
( spl38_46
| spl38_45
| ~ spl38_112
| ~ spl38_124 ),
inference(rat,[],[s381,s60,s59,s367,s398]) ).
cnf(s400,plain,
( spl38_47
| spl38_49
| spl38_45
| ~ spl38_112 ),
inference(rat,[],[s381,s55,s57]) ).
cnf(s401,plain,
( spl38_45
| ~ spl38_112
| ~ spl38_124
| ~ spl38_123 ),
inference(rat,[],[s381,s58,s61,s367,s400,s365,s399]) ).
cnf(s402,plain,
( spl38_47
| spl38_49
| spl38_52
| ~ spl38_112 ),
inference(rat,[],[s381,s63,s62]) ).
cnf(s403,plain,
( spl38_49
| spl38_52
| ~ spl38_112
| ~ spl38_124 ),
inference(rat,[],[s381,s66,s67,s367,s402]) ).
cnf(s404,plain,
( spl38_47
| spl38_46
| spl38_52
| ~ spl38_112 ),
inference(rat,[],[s381,s65,s64]) ).
cnf(s405,plain,
( spl38_119
| spl38_122
| spl38_103 ),
inference(rat,[],[s381,s69,s68,s367,s404,s365,s403,s397,s401,s174,s232,s290,s291]) ).
cnf(s406,plain,
( spl38_39
| ~ spl38_102
| spl38_34
| spl38_33 ),
inference(rat,[],[s393,s41,s48]) ).
cnf(s407,plain,
( ~ spl38_102
| spl38_34
| spl38_33
| ~ spl38_119 ),
inference(rat,[],[s393,s37,s46,s395,s406]) ).
cnf(s408,plain,
( spl38_52
| ~ spl38_112
| ~ spl38_123
| ~ spl38_124 ),
inference(rat,[],[s381,s69,s68,s367,s404,s365,s403]) ).
cnf(s409,plain,
( spl38_102
| spl38_122
| spl38_103 ),
inference(rat,[],[s397,s401,s408,s99,s130,s178,s179]) ).
cnf(s410,plain,
( spl38_39
| spl38_38
| spl38_33
| ~ spl38_102 ),
inference(rat,[],[s393,s44,s47]) ).
cnf(s411,plain,
( spl38_38
| spl38_33
| ~ spl38_102
| ~ spl38_119 ),
inference(rat,[],[s393,s40,s45,s395,s410]) ).
cnf(s412,plain,
( ~ spl38_112
| ~ spl38_124
| ~ spl38_104
| ~ spl38_123 ),
inference(rat,[],[s397,s401,s408]) ).
cnf(s413,plain,
( spl38_110
| spl38_122
| spl38_103 ),
inference(rat,[],[s169,s412,s229,s125,s228]) ).
cnf(s414,plain,
( spl38_34
| spl38_39
| ~ spl38_120
| ~ spl38_102
| ~ spl38_119 ),
inference(rat,[],[s393,s42,s49,s377,s407]) ).
cnf(s415,plain,
( spl38_39
| ~ spl38_120
| ~ spl38_110
| ~ spl38_102
| ~ spl38_119 ),
inference(rat,[],[s393,s43,s51,s377,s410,s353,s414]) ).
cnf(s416,plain,
( spl38_34
| spl38_36
| ~ spl38_120
| ~ spl38_102
| ~ spl38_119 ),
inference(rat,[],[s393,s38,s50,s377,s407]) ).
cnf(s417,plain,
( ~ spl38_120
| ~ spl38_119
| ~ spl38_110
| ~ spl38_102 ),
inference(rat,[],[s393,s39,s52,s377,s411,s353,s416,s395,s415]) ).
cnf(s418,plain,
( spl38_120
| spl38_122
| spl38_103 ),
inference(rat,[],[s231,s412,s173,s288,s289]) ).
cnf(s419,plain,
( spl38_122
| spl38_103 ),
inference(rat,[],[s418,s417,s413,s409,s405]) ).
cnf(s420,plain,
( spl38_26
| ~ spl38_101
| spl38_22
| spl38_21 ),
inference(rat,[],[s387,s23,s35]) ).
cnf(s421,plain,
( ~ spl38_101
| spl38_22
| spl38_21
| ~ spl38_122 ),
inference(rat,[],[s387,s20,s29,s355,s420]) ).
cnf(s422,plain,
( spl38_119
| ~ spl38_112
| spl38_101
| spl38_103 ),
inference(rat,[],[s412,s95,s164,s165]) ).
cnf(s423,plain,
( spl38_123
| ~ spl38_119
| spl38_101
| spl38_103 ),
inference(rat,[],[s417,s101,s120,s166]) ).
cnf(s424,plain,
( spl38_124
| ~ spl38_119
| spl38_101
| spl38_103 ),
inference(rat,[],[s417,s102,s167,s121]) ).
cnf(s425,plain,
( ~ spl38_112
| spl38_101
| spl38_103 ),
inference(rat,[],[s417,s82,s85,s96,s412,s424,s423,s422]) ).
cnf(s426,plain,
( spl38_101
| spl38_112
| spl38_103 ),
inference(rat,[],[s417,s122,s123,s87,s94]) ).
cnf(s427,plain,
( spl38_101
| spl38_103 ),
inference(rat,[],[s426,s425]) ).
cnf(s428,plain,
( spl38_26
| spl38_25
| spl38_21
| ~ spl38_101 ),
inference(rat,[],[s387,s22,s34]) ).
cnf(s429,plain,
( spl38_25
| spl38_21
| spl38_103 ),
inference(rat,[],[s387,s21,s30,s355,s428,s419,s427]) ).
cnf(s430,plain,
( spl38_119
| ~ spl38_112
| spl38_121
| spl38_103 ),
inference(rat,[],[s412,s175,s292,s293]) ).
cnf(s431,plain,
( spl38_124
| ~ spl38_119
| spl38_121
| spl38_103 ),
inference(rat,[],[s417,s181,s286,s227]) ).
cnf(s432,plain,
( spl38_104
| ~ spl38_119
| spl38_121
| spl38_103 ),
inference(rat,[],[s417,s98,s172,s126]) ).
cnf(s433,plain,
( ~ spl38_112
| spl38_121
| spl38_103 ),
inference(rat,[],[s417,s180,s287,s226,s412,s432,s431,s430]) ).
cnf(s434,plain,
( spl38_121
| spl38_112
| spl38_103 ),
inference(rat,[],[s417,s129,s168,s230,s233]) ).
cnf(s435,plain,
( spl38_121
| spl38_103 ),
inference(rat,[],[s434,s433]) ).
cnf(s436,plain,
( spl38_21
| spl38_103 ),
inference(rat,[],[s389,s421,s429,s419,s427,s435]) ).
cnf(s439,plain,
( spl38_26
| spl38_22
| spl38_27
| ~ spl38_101 ),
inference(rat,[],[s387,s25,s32]) ).
cnf(s440,plain,
( spl38_22
| spl38_27
| spl38_103 ),
inference(rat,[],[s387,s24,s28,s355,s439,s419,s427]) ).
cnf(s441,plain,
( spl38_26
| spl38_25
| spl38_27
| ~ spl38_101 ),
inference(rat,[],[s387,s27,s33]) ).
cnf(s442,plain,
( spl38_27
| spl38_103 ),
inference(rat,[],[s387,s26,s31,s355,s441,s389,s440,s419,s427,s435]) ).
cnf(s443,plain,
( spl38_119
| spl38_111
| spl38_103 ),
inference(rat,[],[s412,s127,s235,s234,s176]) ).
cnf(s444,plain,
( spl38_104
| spl38_103 ),
inference(rat,[],[s417,s86,s97,s128,s443,s359,s442,s436]) ).
cnf(s445,plain,
( spl38_123
| spl38_103 ),
inference(rat,[],[s417,s132,s170,s236,s443,s359,s442,s436]) ).
cnf(s446,plain,
( spl38_112
| spl38_103 ),
inference(rat,[],[s417,s100,s124,s177,s443,s359,s442,s436]) ).
cnf(s447,plain,
( spl38_111
| spl38_103 ),
inference(rat,[],[s417,s131,s171,s237,s412,s446,s445,s444,s443]) ).
cnf(s448,plain,
spl38_103,
inference(rat,[],[s447,s359,s442,s436]) ).
cnf(s449,plain,
( spl38_122
| ~ spl38_112
| spl38_118
| ~ spl38_124
| spl38_119 ),
inference(rat,[],[s412,s271,s336]) ).
cnf(s450,plain,
( spl38_21
| ~ spl38_101
| ~ spl38_121
| ~ spl38_122 ),
inference(rat,[],[s387,s21,s30,s355,s428,s389,s421]) ).
cnf(s451,plain,
( spl38_22
| spl38_27
| ~ spl38_101
| ~ spl38_122 ),
inference(rat,[],[s387,s24,s28,s355,s439]) ).
cnf(s452,plain,
( spl38_104
| ~ spl38_122
| spl38_118
| spl38_119 ),
inference(rat,[],[s387,s31,s26,s355,s441,s389,s451,s359,s450,s207,s145,s273]) ).
cnf(s453,plain,
( ~ spl38_112
| spl38_118
| spl38_119
| ~ spl38_124 ),
inference(rat,[],[s387,s31,s26,s355,s441,s389,s451,s359,s450,s307,s339,s257,s412,s452,s449]) ).
cnf(s454,plain,
( spl38_112
| spl38_118
| spl38_119 ),
inference(rat,[],[s387,s31,s26,s355,s441,s389,s451,s359,s450,s197,s310,s313,s261]) ).
cnf(s455,plain,
( spl38_118
| ~ spl38_124
| spl38_119 ),
inference(rat,[],[s454,s453]) ).
cnf(s456,plain,
( spl38_12
| ~ spl38_118
| spl38_10
| spl38_9 ),
inference(rat,[],[s347,s3,s4]) ).
cnf(s457,plain,
( ~ spl38_118
| spl38_10
| spl38_9 ),
inference(rat,[],[s347,s12,s14,s385,s456,s448]) ).
cnf(s458,plain,
( spl38_124
| spl38_119
| spl38_118 ),
inference(rat,[],[s387,s31,s26,s355,s441,s389,s451,s359,s450,s309,s340,s256,s334]) ).
cnf(s459,plain,
( spl38_118
| spl38_119 ),
inference(rat,[],[s458,s455]) ).
cnf(s460,plain,
( spl38_123
| spl38_122
| spl38_118 ),
inference(rat,[],[s417,s267,s315,s337,s459]) ).
cnf(s461,plain,
( spl38_104
| spl38_122
| spl38_118 ),
inference(rat,[],[s417,s270,s149,s204,s459]) ).
cnf(s462,plain,
( spl38_122
| ~ spl38_124
| spl38_118 ),
inference(rat,[],[s417,s203,s312,s265,s412,s461,s460,s459]) ).
cnf(s463,plain,
( spl38_101
| spl38_123
| spl38_118 ),
inference(rat,[],[s417,s258,s142,s195,s459]) ).
cnf(s464,plain,
( spl38_121
| spl38_123
| spl38_118 ),
inference(rat,[],[s417,s269,s316,s338,s459]) ).
cnf(s465,plain,
( spl38_27
| ~ spl38_121
| ~ spl38_101
| ~ spl38_122 ),
inference(rat,[],[s387,s31,s26,s355,s441,s389,s451]) ).
cnf(s466,plain,
( spl38_123
| ~ spl38_122
| spl38_118 ),
inference(rat,[],[s417,s306,s200,s262,s359,s465,s450,s464,s463,s459]) ).
cnf(s467,plain,
( spl38_101
| spl38_104
| spl38_118 ),
inference(rat,[],[s417,s90,s109,s144,s459]) ).
cnf(s468,plain,
( spl38_102
| spl38_104
| ~ spl38_122
| spl38_118 ),
inference(rat,[],[s359,s465,s450,s110,s148,s467]) ).
cnf(s469,plain,
( spl38_121
| ~ spl38_102
| spl38_104
| spl38_118 ),
inference(rat,[],[s417,s272,s205,s459]) ).
cnf(s470,plain,
( spl38_104
| ~ spl38_122
| spl38_118 ),
inference(rat,[],[s417,s206,s150,s359,s465,s450,s469,s468,s467,s459]) ).
cnf(s471,plain,
( spl38_101
| spl38_112
| spl38_118 ),
inference(rat,[],[s417,s108,s198,s146,s459]) ).
cnf(s472,plain,
( spl38_102
| ~ spl38_124
| spl38_118 ),
inference(rat,[],[s359,s465,s450,s202,s147,s471,s412,s470,s466,s462]) ).
cnf(s473,plain,
( spl38_121
| ~ spl38_124
| spl38_118 ),
inference(rat,[],[s417,s311,s264,s459,s412,s470,s466,s462,s472]) ).
cnf(s474,plain,
( ~ spl38_124
| spl38_118 ),
inference(rat,[],[s417,s260,s199,s359,s465,s450,s473,s472,s471,s412,s470,s466,s462,s459]) ).
cnf(s475,plain,
( spl38_122
| spl38_118 ),
inference(rat,[],[s417,s266,s314,s335,s459,s474]) ).
cnf(s476,plain,
( spl38_102
| spl38_118 ),
inference(rat,[],[s359,s465,s450,s201,s268,s143,s474,s475]) ).
cnf(s477,plain,
( spl38_101
| spl38_118 ),
inference(rat,[],[s417,s259,s196,s459,s474,s476]) ).
cnf(s478,plain,
( spl38_121
| spl38_118 ),
inference(rat,[],[s417,s317,s341,s459,s474,s476]) ).
cnf(s479,plain,
spl38_118,
inference(rat,[],[s417,s308,s263,s359,s465,s450,s478,s477,s476,s475,s474,s459]) ).
cnf(s480,plain,
( spl38_12
| spl38_14
| spl38_9 ),
inference(rat,[],[s347,s6,s5,s479]) ).
cnf(s481,plain,
( spl38_16
| spl38_14
| spl38_9 ),
inference(rat,[],[s347,s11,s13,s479]) ).
cnf(s482,plain,
( spl38_14
| spl38_9 ),
inference(rat,[],[s481,s385,s480,s448]) ).
cnf(s483,plain,
( spl38_122
| spl38_119
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s412,s251,s296,s327]) ).
cnf(s485,plain,
( spl38_123
| ~ spl38_101
| ~ spl38_122
| spl38_119
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s300,s333]) ).
cnf(s486,plain,
( spl38_104
| ~ spl38_101
| ~ spl38_122
| spl38_119
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s188,s250]) ).
cnf(s487,plain,
( ~ spl38_101
| spl38_119
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s244,s297,s412,s486,s485,s483]) ).
cnf(s488,plain,
( spl38_119
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s412,s239,s133,s183,s487]) ).
cnf(s489,plain,
( spl38_102
| ~ spl38_112
| spl38_122
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s412,s139,s252]) ).
cnf(s490,plain,
( spl38_123
| ~ spl38_102
| spl38_122
| ~ spl38_119
| spl38_117 ),
inference(rat,[],[s417,s326,s302]) ).
cnf(s491,plain,
( ~ spl38_112
| spl38_122
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s417,s249,s189,s412,s490,s489,s488]) ).
cnf(s492,plain,
( spl38_122
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s417,s295,s243,s191,s491,s488]) ).
cnf(s493,plain,
( spl38_123
| spl38_102
| ~ spl38_122
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s194,s255,s137]) ).
cnf(s494,plain,
( spl38_102
| ~ spl38_112
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s107,s140,s89,s412,s493,s492]) ).
cnf(s495,plain,
( spl38_101
| spl38_123
| ~ spl38_102
| ~ spl38_119
| spl38_117 ),
inference(rat,[],[s417,s238,s184]) ).
cnf(s496,plain,
( spl38_121
| spl38_123
| ~ spl38_102
| ~ spl38_119
| spl38_117 ),
inference(rat,[],[s417,s332,s305]) ).
cnf(s497,plain,
( spl38_123
| ~ spl38_102
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s417,s299,s247,s359,s465,s450,s496,s495,s488,s492]) ).
cnf(s498,plain,
( spl38_101
| spl38_104
| ~ spl38_102
| ~ spl38_119
| spl38_117 ),
inference(rat,[],[s417,s134,s105]) ).
cnf(s499,plain,
( spl38_110
| ~ spl38_101
| spl38_104
| ~ spl38_122
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s138,s190]) ).
cnf(s500,plain,
( ~ spl38_112
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s187,s248,s417,s499,s498,s412,s497,s494,s488,s492]) ).
cnf(s501,plain,
( spl38_102
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s141,s192,s106,s492,s500]) ).
cnf(s502,plain,
( spl38_101
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s417,s182,s135,s488,s500,s501]) ).
cnf(s503,plain,
( spl38_110
| ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s186,s242,s492,s500,s502]) ).
cnf(s504,plain,
( ~ spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s245,s294,s417,s503,s502,s501,s500,s492,s488]) ).
cnf(s505,plain,
( spl38_102
| spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s136,s193,s254,s253]) ).
cnf(s506,plain,
( spl38_101
| spl38_117 ),
inference(rat,[],[s417,s241,s185,s240,s505,s504]) ).
cnf(s507,plain,
( spl38_122
| spl38_117 ),
inference(rat,[],[s417,s303,s329,s328,s505,s504]) ).
cnf(s508,plain,
( spl38_119
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s301,s331,s504,s506,s507]) ).
cnf(s509,plain,
( spl38_110
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s246,s304,s504,s506,s507]) ).
cnf(s510,plain,
( spl38_124
| spl38_117 ),
inference(rat,[],[s359,s465,s450,s298,s330,s417,s509,s508,s507,s506,s505]) ).
cnf(s511,plain,
spl38_117,
inference(rat,[],[s510,s504]) ).
cnf(s512,plain,
spl38_9,
inference(rat,[],[s383,s457,s482,s511,s479]) ).
cnf(s513,plain,
( spl38_12
| spl38_15
| spl38_10 ),
inference(rat,[],[s347,s10,s9,s479]) ).
cnf(s514,plain,
( spl38_16
| spl38_15
| spl38_14 ),
inference(rat,[],[s347,s15,s16,s479]) ).
cnf(s516,plain,
( spl38_119
| spl38_109
| spl38_122
| ~ spl38_124 ),
inference(rat,[],[s412,s225,s284,s322]) ).
cnf(s517,plain,
( spl38_109
| spl38_102
| spl38_122
| ~ spl38_124 ),
inference(rat,[],[s412,s119,s162,s222]) ).
cnf(s518,plain,
( spl38_16
| spl38_15
| spl38_10 ),
inference(rat,[],[s347,s17,s18,s479]) ).
cnf(s519,plain,
( spl38_15
| spl38_10 ),
inference(rat,[],[s518,s385,s513,s448]) ).
cnf(s520,plain,
( spl38_104
| ~ spl38_102
| ~ spl38_119
| spl38_122
| spl38_109 ),
inference(rat,[],[s417,s224,s163]) ).
cnf(s521,plain,
( spl38_123
| ~ spl38_102
| ~ spl38_119
| spl38_122
| spl38_109 ),
inference(rat,[],[s417,s324,s283]) ).
cnf(s522,plain,
( spl38_109
| spl38_122
| ~ spl38_124 ),
inference(rat,[],[s417,s285,s223,s412,s521,s520,s517,s516]) ).
cnf(s523,plain,
( spl38_104
| spl38_119
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s158,s220,s112]) ).
cnf(s524,plain,
( spl38_123
| spl38_119
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s274,s319,s209]) ).
cnf(s525,plain,
( spl38_119
| spl38_109
| ~ spl38_124 ),
inference(rat,[],[s359,s465,s450,s215,s278,s152,s412,s524,s523,s522]) ).
cnf(s526,plain,
( spl38_102
| spl38_104
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s93,s118,s84]) ).
cnf(s527,plain,
( spl38_101
| ~ spl38_102
| spl38_104
| ~ spl38_119
| spl38_109 ),
inference(rat,[],[s417,s111,s91]) ).
cnf(s528,plain,
( spl38_121
| ~ spl38_102
| spl38_104
| ~ spl38_119
| spl38_109 ),
inference(rat,[],[s417,s219,s161]) ).
cnf(s529,plain,
( spl38_104
| ~ spl38_119
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s417,s159,s117,s359,s465,s450,s528,s527,s526]) ).
cnf(s530,plain,
( spl38_102
| spl38_123
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s155,s217,s114]) ).
cnf(s531,plain,
( spl38_101
| ~ spl38_102
| spl38_123
| ~ spl38_119
| spl38_109 ),
inference(rat,[],[s417,s208,s153]) ).
cnf(s532,plain,
( spl38_121
| ~ spl38_102
| spl38_123
| ~ spl38_119
| spl38_109 ),
inference(rat,[],[s417,s318,s281]) ).
cnf(s533,plain,
( spl38_123
| ~ spl38_119
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s417,s275,s212,s359,s465,s450,s532,s531,s530]) ).
cnf(s534,plain,
( spl38_102
| spl38_112
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s116,s160,s92]) ).
cnf(s535,plain,
( spl38_101
| ~ spl38_102
| spl38_112
| ~ spl38_119
| spl38_109 ),
inference(rat,[],[s417,s151,s113]) ).
cnf(s536,plain,
( spl38_110
| ~ spl38_101
| spl38_112
| ~ spl38_122
| spl38_109 ),
inference(rat,[],[s359,s465,s450,s218,s157]) ).
cnf(s537,plain,
( spl38_109
| ~ spl38_124 ),
inference(rat,[],[s359,s465,s450,s214,s279,s417,s536,s535,s534,s412,s533,s529,s525,s522]) ).
cnf(s538,plain,
( spl38_12
| spl38_15
| spl38_14 ),
inference(rat,[],[s347,s7,s8,s479]) ).
cnf(s539,plain,
( spl38_14
| spl38_15 ),
inference(rat,[],[s538,s385,s514,s448]) ).
cnf(s540,plain,
spl38_15,
inference(rat,[],[s539,s383,s519,s511]) ).
cnf(s541,plain,
~ spl38_109,
inference(rat,[],[s351,s512,s540]) ).
cnf(s543,plain,
~ spl38_124,
inference(rat,[],[s537,s541]) ).
cnf(s544,plain,
spl38_122,
inference(rat,[],[s417,s221,s282,s325,s323,s543,s541]) ).
cnf(s545,plain,
spl38_119,
inference(rat,[],[s359,s465,s450,s277,s320,s211,s544,s541,s543]) ).
cnf(s548,plain,
spl38_102,
inference(rat,[],[s359,s465,s450,s156,s216,s115,s544,s543,s541]) ).
cnf(s549,plain,
spl38_101,
inference(rat,[],[s417,s210,s154,s545,s548,s543,s541]) ).
cnf(s550,plain,
spl38_110,
inference(rat,[],[s359,s465,s450,s213,s280,s549,s544,s543,s541]) ).
cnf(s551,plain,
~ spl38_120,
inference(rat,[],[s417,s548,s545,s550]) ).
cnf(s552,plain,
spl38_111,
inference(rat,[],[s276,s541,s543,s551]) ).
cnf(s553,plain,
spl38_121,
inference(rat,[],[s321,s541,s543,s551]) ).
cnf(s554,plain,
spl38_21,
inference(rat,[],[s450,s544,s549,s553]) ).
cnf(s555,plain,
spl38_27,
inference(rat,[],[s465,s544,s549,s553]) ).
cnf(s556,plain,
$false,
inference(rat,[],[s359,s552,s554,s555]) ).
thf(f6197,plain,
$false,
inference(avatar_sat_refutation,[],[s556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL941^5 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 10:43:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/0.42 % (1129842)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.73/0.42 % (1129850)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3203835741:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.73/0.42 % (1129853)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.73/0.42 % (1129853)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.73/0.42 % (1129849)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3417887674:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.73/0.42 % (1129847)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3127943188:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.73/0.42 % (1129848)lrs+10_16_si=on:nwc=1.5:random_seed=1980445180:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.73/0.42 % (1129851)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3856856409:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.73/0.42 % (1129853)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4008861021:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.73/0.42 % (1129849)Instruction limit reached!
% 0.73/0.42 % (1129849)------------------------------
% 0.73/0.42 % (1129849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (1129849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (1129849)CaDiCaL version: 2.1.3
% 0.73/0.42 % (1129849)Termination reason: Instruction limit
% 0.73/0.42 % (1129849)Termination phase: shuffling
% 0.73/0.42 % (1129849)Time elapsed: 0.001 s
% 0.73/0.42 % (1129849)Peak memory usage: 10 MB
% 0.73/0.42 % (1129849)Instructions burned: 3 (million)
% 0.73/0.42 % (1129852)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2053896438:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.73/0.42 % (1129848)Instruction limit reached!
% 0.73/0.42 % (1129848)------------------------------
% 0.73/0.42 % (1129848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (1129848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (1129848)CaDiCaL version: 2.1.3
% 0.73/0.42 % (1129848)Termination reason: Instruction limit
% 0.73/0.42 % (1129848)Termination phase: shuffling
% 0.73/0.42 % (1129848)Time elapsed: 0.007 s
% 0.73/0.42 % (1129848)Peak memory usage: 10 MB
% 0.73/0.42 % (1129848)Instructions burned: 20 (million)
% 0.73/0.42 % (1129851)Instruction limit reached!
% 0.73/0.42 % (1129851)------------------------------
% 0.73/0.42 % (1129851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (1129851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (1129851)CaDiCaL version: 2.1.3
% 0.73/0.42 % (1129851)Termination reason: Instruction limit
% 0.73/0.42 % (1129851)Termination phase: shuffling
% 0.73/0.42 % (1129851)Time elapsed: 0.009 s
% 0.73/0.42 % (1129851)Peak memory usage: 10 MB
% 0.73/0.42 % (1129851)Instructions burned: 26 (million)
% 0.73/0.42 % (1129860)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=757332099:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.42 % (1129860)Instruction limit reached!
% 0.73/0.42 % (1129860)------------------------------
% 0.73/0.42 % (1129860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.42 % (1129860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.42 % (1129860)CaDiCaL version: 2.1.3
% 0.73/0.42 % (1129860)Termination reason: Instruction limit
% 0.73/0.42 % (1129860)Termination phase: shuffling
% 0.73/0.42 % (1129860)Time elapsed: 0.003 s
% 0.73/0.42 % (1129860)Peak memory usage: 10 MB
% 0.73/0.42 % (1129860)Instructions burned: 8 (million)
% 0.73/0.42 % (1129863)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.48 % (1129862)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=793848065:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.73/0.48 % (1129862)Instruction limit reached!
% 0.73/0.48 % (1129862)------------------------------
% 0.73/0.48 % (1129862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.48 % (1129862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.48 % (1129862)CaDiCaL version: 2.1.3
% 0.73/0.48 % (1129862)Termination reason: Instruction limit
% 0.73/0.48 % (1129862)Termination phase: shuffling
% 0.73/0.48 % (1129862)Time elapsed: 0.002 s
% 0.73/0.48 % (1129862)Peak memory usage: 9 MB
% 0.73/0.48 % (1129862)Instructions burned: 7 (million)
% 0.73/0.48 % (1129863)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1945377619:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.73/0.48 % (1129863)Instruction limit reached!
% 0.73/0.48 % (1129863)------------------------------
% 0.73/0.48 % (1129863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.48 % (1129863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.48 % (1129863)CaDiCaL version: 2.1.3
% 0.73/0.48 % (1129863)Termination reason: Instruction limit
% 0.73/0.48 % (1129863)Termination phase: shuffling
% 0.73/0.48 % (1129863)Time elapsed: 0.005 s
% 0.73/0.48 % (1129863)Peak memory usage: 10 MB
% 0.73/0.48 % (1129863)Instructions burned: 8 (million)
% 0.73/0.48 % (1129847)Instruction limit reached!
% 0.73/0.48 % (1129847)------------------------------
% 0.73/0.48 % (1129847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.48 % (1129847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.48 % (1129847)CaDiCaL version: 2.1.3
% 0.73/0.48 % (1129847)Termination reason: Instruction limit
% 0.73/0.48 % (1129847)Termination phase: Property scanning
% 0.73/0.48 % (1129847)Time elapsed: 0.042 s
% 0.73/0.48 % (1129847)Peak memory usage: 10 MB
% 0.73/0.48 % (1129847)Instructions burned: 88 (million)
% 0.73/0.48 % (1129865)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=895550901:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.73/0.48 % (1129865)Instruction limit reached!
% 0.73/0.48 % (1129865)------------------------------
% 0.73/0.48 % (1129865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.48 % (1129865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.48 % (1129865)CaDiCaL version: 2.1.3
% 0.73/0.48 % (1129865)Termination reason: Instruction limit
% 0.73/0.48 % (1129865)Termination phase: shuffling
% 0.73/0.48 % (1129865)Time elapsed: 0.004 s
% 0.73/0.48 % (1129865)Peak memory usage: 10 MB
% 0.73/0.48 % (1129865)Instructions burned: 13 (million)
% 0.73/0.48 % (1129868)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.73/0.48 % (1129868)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.48 % (1129852)Instruction limit reached!
% 0.73/0.48 % (1129852)------------------------------
% 0.73/0.48 % (1129852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.48 % (1129852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.48 % (1129852)CaDiCaL version: 2.1.3
% 0.73/0.48 % (1129852)Termination reason: Instruction limit
% 0.73/0.48 % (1129852)Termination phase: SInE selection
% 0.73/0.48 % (1129852)Time elapsed: 0.046 s
% 0.73/0.48 % (1129852)Peak memory usage: 10 MB
% 0.73/0.48 % (1129852)Instructions burned: 76 (million)
% 0.73/0.48 % (1129869)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=392477766:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.73/0.48 % (1129868)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=910939167:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.73/0.48 % (1129853)Instruction limit reached!
% 0.73/0.48 % (1129853)------------------------------
% 0.73/0.48 % (1129853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129853)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129853)Termination reason: Instruction limit
% 0.73/0.51 % (1129853)Termination phase: Saturation
% 0.73/0.51 % (1129853)Time elapsed: 0.058 s
% 0.73/0.51 % (1129853)Peak memory usage: 12 MB
% 0.73/0.51 % (1129853)Instructions burned: 157 (million)
% 0.73/0.51 % (1129872)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.73/0.51 % (1129872)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=160963989:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.51 % (1129872)Instruction limit reached!
% 0.73/0.51 % (1129872)------------------------------
% 0.73/0.51 % (1129872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129872)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129872)Termination reason: Instruction limit
% 0.73/0.51 % (1129872)Termination phase: shuffling
% 0.73/0.51 % (1129872)Time elapsed: 0.002 s
% 0.73/0.51 % (1129872)Peak memory usage: 10 MB
% 0.73/0.51 % (1129872)Instructions burned: 4 (million)
% 0.73/0.51 % (1129868)Instruction limit reached!
% 0.73/0.51 % (1129868)------------------------------
% 0.73/0.51 % (1129868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129868)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129868)Termination reason: Instruction limit
% 0.73/0.51 % (1129868)Termination phase: Property scanning
% 0.73/0.51 % (1129868)Time elapsed: 0.022 s
% 0.73/0.51 % (1129868)Peak memory usage: 10 MB
% 0.73/0.51 % (1129868)Instructions burned: 30 (million)
% 0.73/0.51 % (1129870)lrs+10_1_si=on:cs=on:random_seed=3250145279:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.73/0.51 % (1129873)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=780216963:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.73/0.51 % (1129870)Instruction limit reached!
% 0.73/0.51 % (1129870)------------------------------
% 0.73/0.51 % (1129870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129870)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129870)Termination reason: Instruction limit
% 0.73/0.51 % (1129870)Termination phase: shuffling
% 0.73/0.51 % (1129870)Time elapsed: 0.004 s
% 0.73/0.51 % (1129870)Peak memory usage: 10 MB
% 0.73/0.51 % (1129870)Instructions burned: 11 (million)
% 0.73/0.51 % (1129876)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1387144397:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.73/0.51 % (1129879)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=209145834:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.73/0.51 % (1129879)Instruction limit reached!
% 0.73/0.51 % (1129879)------------------------------
% 0.73/0.51 % (1129879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129879)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129879)Termination reason: Instruction limit
% 0.73/0.51 % (1129879)Termination phase: shuffling
% 0.73/0.51 % (1129879)Time elapsed: 0.009 s
% 0.73/0.51 % (1129879)Peak memory usage: 10 MB
% 0.73/0.51 % (1129879)Instructions burned: 27 (million)
% 0.73/0.51 % (1129883)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1475721050:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.73/0.51 % (1129873)Instruction limit reached!
% 0.73/0.51 % (1129873)------------------------------
% 0.73/0.51 % (1129873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.51 % (1129873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.51 % (1129873)CaDiCaL version: 2.1.3
% 0.73/0.51 % (1129873)Termination reason: Instruction limit
% 0.73/0.51 % (1129873)Termination phase: shuffling
% 0.73/0.51 % (1129873)Time elapsed: 0.023 s
% 0.73/0.51 % (1129873)Peak memory usage: 10 MB
% 1.57/0.55 % (1129873)Instructions burned: 38 (million)
% 1.57/0.55 % (1129880)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3656145630:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.57/0.55 % (1129869)Instruction limit reached!
% 1.57/0.55 % (1129869)------------------------------
% 1.57/0.55 % (1129869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129869)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129869)Termination reason: Instruction limit
% 1.57/0.55 % (1129869)Termination phase: Property scanning
% 1.57/0.55 % (1129869)Time elapsed: 0.062 s
% 1.57/0.55 % (1129869)Peak memory usage: 10 MB
% 1.57/0.55 % (1129869)Instructions burned: 87 (million)
% 1.57/0.55 % (1129880)Instruction limit reached!
% 1.57/0.55 % (1129880)------------------------------
% 1.57/0.55 % (1129880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129880)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129880)Termination reason: Instruction limit
% 1.57/0.55 % (1129880)Termination phase: shuffling
% 1.57/0.55 % (1129880)Time elapsed: 0.009 s
% 1.57/0.55 % (1129880)Peak memory usage: 10 MB
% 1.57/0.55 % (1129880)Instructions burned: 14 (million)
% 1.57/0.55 % (1129886)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3325434716:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.57/0.55 % (1129886)Instruction limit reached!
% 1.57/0.55 % (1129886)------------------------------
% 1.57/0.55 % (1129886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129886)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129886)Termination reason: Instruction limit
% 1.57/0.55 % (1129886)Termination phase: shuffling
% 1.57/0.55 % (1129886)Time elapsed: 0.005 s
% 1.57/0.55 % (1129886)Peak memory usage: 10 MB
% 1.57/0.55 % (1129886)Instructions burned: 14 (million)
% 1.57/0.55 % (1129888)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3776627708:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.57/0.55 % (1129888)Instruction limit reached!
% 1.57/0.55 % (1129888)------------------------------
% 1.57/0.55 % (1129888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129888)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129888)Termination reason: Instruction limit
% 1.57/0.55 % (1129888)Termination phase: shuffling
% 1.57/0.55 % (1129888)Time elapsed: 0.002 s
% 1.57/0.55 % (1129888)Peak memory usage: 9 MB
% 1.57/0.55 % (1129888)Instructions burned: 5 (million)
% 1.57/0.55 % (1129890)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2695134481:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.57/0.55 % (1129891)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3642032662:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.57/0.55 % (1129850)Instruction limit reached!
% 1.57/0.55 % (1129850)------------------------------
% 1.57/0.55 % (1129850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129850)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129850)Termination reason: Instruction limit
% 1.57/0.55 % (1129850)Termination phase: Saturation
% 1.57/0.55 % (1129850)Time elapsed: 0.168 s
% 1.57/0.55 % (1129850)Peak memory usage: 17 MB
% 1.57/0.55 % (1129850)Instructions burned: 636 (million)
% 1.57/0.55 % (1129893)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1148189918:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.57/0.55 % (1129891)Instruction limit reached!
% 1.57/0.55 % (1129891)------------------------------
% 1.57/0.55 % (1129891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.55 % (1129891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.55 % (1129891)CaDiCaL version: 2.1.3
% 1.57/0.55 % (1129891)Termination reason: Instruction limit
% 2.04/0.62 % (1129891)Termination phase: shuffling
% 2.04/0.62 % (1129891)Time elapsed: 0.014 s
% 2.04/0.62 % (1129891)Peak memory usage: 10 MB
% 2.04/0.62 % (1129891)Instructions burned: 23 (million)
% 2.04/0.62 % (1129900)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.04/0.62 % (1129900)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=529062536:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.04/0.62 % (1129896)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.04/0.62 % (1129896)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.04/0.62 % (1129890)Instruction limit reached!
% 2.04/0.62 % (1129890)------------------------------
% 2.04/0.62 % (1129890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.62 % (1129890)CaDiCaL version: 2.1.3
% 2.04/0.62 % (1129890)Termination reason: Instruction limit
% 2.04/0.62 % (1129890)Termination phase: Property scanning
% 2.04/0.62 % (1129890)Time elapsed: 0.023 s
% 2.04/0.62 % (1129890)Peak memory usage: 10 MB
% 2.04/0.62 % (1129890)Instructions burned: 26 (million)
% 2.04/0.62 % (1129900)Instruction limit reached!
% 2.04/0.62 % (1129900)------------------------------
% 2.04/0.62 % (1129900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.62 % (1129900)CaDiCaL version: 2.1.3
% 2.04/0.62 % (1129900)Termination reason: Instruction limit
% 2.04/0.62 % (1129900)Termination phase: shuffling
% 2.04/0.62 % (1129900)Time elapsed: 0.005 s
% 2.04/0.62 % (1129900)Peak memory usage: 9 MB
% 2.04/0.62 % (1129900)Instructions burned: 9 (million)
% 2.04/0.62 % (1129896)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3353370854:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.04/0.62 % (1129896)Instruction limit reached!
% 2.04/0.62 % (1129896)------------------------------
% 2.04/0.62 % (1129896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.62 % (1129896)CaDiCaL version: 2.1.3
% 2.04/0.62 % (1129896)Termination reason: Instruction limit
% 2.04/0.62 % (1129896)Termination phase: Property scanning
% 2.04/0.62 % (1129896)Time elapsed: 0.011 s
% 2.04/0.62 % (1129896)Peak memory usage: 10 MB
% 2.04/0.62 % (1129896)Instructions burned: 15 (million)
% 2.04/0.62 % (1129883)Refutation not found, incomplete strategy
% 2.04/0.62 % (1129883)------------------------------
% 2.04/0.62 % (1129883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.62 % (1129883)CaDiCaL version: 2.1.3
% 2.04/0.62 % (1129883)Termination reason: Refutation not found, incomplete strategy
% 2.04/0.62 % (1129883)Time elapsed: 0.087 s
% 2.04/0.62 % (1129883)Peak memory usage: 15 MB
% 2.04/0.62 % (1129883)Instructions burned: 181 (million)
% 2.04/0.62 % (1129883)------------------------------
% 2.04/0.62 % (1129883)------------------------------
% 2.04/0.62 % (1129893)Instruction limit reached!
% 2.04/0.62 % (1129893)------------------------------
% 2.04/0.62 % (1129893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.62 % (1129893)CaDiCaL version: 2.1.3
% 2.04/0.62 % (1129893)Termination reason: Instruction limit
% 2.04/0.62 % (1129893)Termination phase: Property scanning
% 2.04/0.62 % (1129893)Time elapsed: 0.035 s
% 2.04/0.62 % (1129893)Peak memory usage: 9 MB
% 2.04/0.62 % (1129893)Instructions burned: 61 (million)
% 2.04/0.62 % (1129876)Refutation not found, incomplete strategy
% 2.04/0.62 % (1129876)------------------------------
% 2.04/0.62 % (1129876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.62 % (1129876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.68 % (1129876)CaDiCaL version: 2.1.3
% 2.23/0.68 % (1129876)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.68 % (1129876)Time elapsed: 0.104 s
% 2.23/0.68 % (1129876)Peak memory usage: 15 MB
% 2.23/0.68 % (1129876)Instructions burned: 145 (million)
% 2.23/0.68 % (1129876)------------------------------
% 2.23/0.68 % (1129876)------------------------------
% 2.23/0.68 % (1129903)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2491049515:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.23/0.68 % (1129901)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=54152601:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.23/0.68 % (1129904)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=492518936:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.23/0.68 % (1129903)Instruction limit reached!
% 2.23/0.68 % (1129903)------------------------------
% 2.23/0.68 % (1129903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.68 % (1129903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.68 % (1129903)CaDiCaL version: 2.1.3
% 2.23/0.68 % (1129903)Termination reason: Instruction limit
% 2.23/0.68 % (1129903)Termination phase: shuffling
% 2.23/0.68 % (1129903)Time elapsed: 0.013 s
% 2.23/0.68 % (1129903)Peak memory usage: 10 MB
% 2.23/0.68 % (1129903)Instructions burned: 12 (million)
% 2.23/0.68 % (1129904)Instruction limit reached!
% 2.23/0.68 % (1129904)------------------------------
% 2.23/0.68 % (1129904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.68 % (1129904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.68 % (1129904)CaDiCaL version: 2.1.3
% 2.23/0.68 % (1129904)Termination reason: Instruction limit
% 2.23/0.68 % (1129904)Termination phase: Property scanning
% 2.23/0.68 % (1129904)Time elapsed: 0.012 s
% 2.23/0.68 % (1129904)Peak memory usage: 10 MB
% 2.23/0.68 % (1129904)Instructions burned: 28 (million)
% 2.23/0.68 % (1129906)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=764982478:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.23/0.68 % (1129914)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.23/0.68 % (1129908)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4253515371:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.23/0.68 % (1129914)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2549294292:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.23/0.68 % (1129907)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=786130910:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.23/0.68 % (1129914)Instruction limit reached!
% 2.23/0.68 % (1129914)------------------------------
% 2.23/0.68 % (1129914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.68 % (1129914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.68 % (1129914)CaDiCaL version: 2.1.3
% 2.23/0.68 % (1129914)Termination reason: Instruction limit
% 2.23/0.68 % (1129914)Termination phase: Property scanning
% 2.23/0.68 % (1129914)Time elapsed: 0.002 s
% 2.23/0.68 % (1129914)Peak memory usage: 10 MB
% 2.23/0.68 % (1129914)Instructions burned: 12 (million)
% 2.23/0.68 % (1129913)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=26409534:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.23/0.68 % (1129901)Instruction limit reached!
% 2.23/0.68 % (1129901)------------------------------
% 2.23/0.68 % (1129901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.68 % (1129901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.68 % (1129901)CaDiCaL version: 2.1.3
% 2.23/0.68 % (1129901)Termination reason: Instruction limit
% 2.23/0.68 % (1129901)Termination phase: Property scanning
% 2.23/0.68 % (1129901)Time elapsed: 0.034 s
% 2.23/0.68 % (1129901)Peak memory usage: 10 MB
% 2.23/0.68 % (1129901)Instructions burned: 32 (million)
% 2.23/0.68 % (1129906)Instruction limit reached!
% 2.23/0.68 % (1129906)------------------------------
% 2.47/0.74 % (1129906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.74 % (1129906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (1129906)CaDiCaL version: 2.1.3
% 2.47/0.74 % (1129906)Termination reason: Instruction limit
% 2.47/0.74 % (1129906)Termination phase: shuffling
% 2.47/0.74 % (1129906)Time elapsed: 0.012 s
% 2.47/0.74 % (1129906)Peak memory usage: 10 MB
% 2.47/0.74 % (1129906)Instructions burned: 20 (million)
% 2.47/0.74 % (1129919)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2875568658:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.47/0.74 % (1129910)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2977757588:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.47/0.74 % (1129913)Instruction limit reached!
% 2.47/0.74 % (1129913)------------------------------
% 2.47/0.74 % (1129913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.74 % (1129913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (1129913)CaDiCaL version: 2.1.3
% 2.47/0.74 % (1129913)Termination reason: Instruction limit
% 2.47/0.74 % (1129913)Termination phase: shuffling
% 2.47/0.74 % (1129913)Time elapsed: 0.019 s
% 2.47/0.74 % (1129913)Peak memory usage: 10 MB
% 2.47/0.74 % (1129913)Instructions burned: 45 (million)
% 2.47/0.74 % (1129922)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.47/0.74 % (1129922)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3194710354:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.47/0.74 % (1129921)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3105070471:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.47/0.74 % (1129922)Instruction limit reached!
% 2.47/0.74 % (1129922)------------------------------
% 2.47/0.74 % (1129922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.74 % (1129922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (1129922)CaDiCaL version: 2.1.3
% 2.47/0.74 % (1129922)Termination reason: Instruction limit
% 2.47/0.74 % (1129922)Termination phase: shuffling
% 2.47/0.74 % (1129922)Time elapsed: 0.005 s
% 2.47/0.74 % (1129922)Peak memory usage: 10 MB
% 2.47/0.74 % (1129922)Instructions burned: 6 (million)
% 2.47/0.74 % (1129919)Instruction limit reached!
% 2.47/0.74 % (1129919)------------------------------
% 2.47/0.74 % (1129919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.74 % (1129919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (1129919)CaDiCaL version: 2.1.3
% 2.47/0.74 % (1129919)Termination reason: Instruction limit
% 2.47/0.74 % (1129919)Termination phase: Saturation
% 2.47/0.74 % (1129919)Time elapsed: 0.039 s
% 2.47/0.74 % (1129919)Peak memory usage: 16 MB
% 2.47/0.74 % (1129919)Instructions burned: 182 (million)
% 2.47/0.74 % (1129929)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1467690934:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.47/0.74 % (1129925)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2383860220:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.47/0.74 % (1129928)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1509234290:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.47/0.74 % (1129908)Instruction limit reached!
% 2.47/0.74 % (1129908)------------------------------
% 2.47/0.74 % (1129908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.74 % (1129908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.74 % (1129908)CaDiCaL version: 2.1.3
% 2.47/0.74 % (1129908)Termination reason: Instruction limit
% 2.47/0.74 % (1129908)Termination phase: Saturation
% 2.47/0.74 % (1129908)Time elapsed: 0.079 s
% 2.47/0.74 % (1129908)Peak memory usage: 11 MB
% 2.47/0.74 % (1129908)Instructions burned: 143 (million)
% 2.47/0.74 % (1129925)Instruction limit reached!
% 2.47/0.80 % (1129925)------------------------------
% 2.47/0.80 % (1129925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.80 % (1129925)CaDiCaL version: 2.1.3
% 2.47/0.80 % (1129925)Termination reason: Instruction limit
% 2.47/0.80 % (1129925)Termination phase: shuffling
% 2.47/0.80 % (1129925)Time elapsed: 0.011 s
% 2.47/0.80 % (1129925)Peak memory usage: 10 MB
% 2.47/0.80 % (1129925)Instructions burned: 22 (million)
% 2.47/0.80 % (1129928)Instruction limit reached!
% 2.47/0.80 % (1129928)------------------------------
% 2.47/0.80 % (1129928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.80 % (1129928)CaDiCaL version: 2.1.3
% 2.47/0.80 % (1129928)Termination reason: Instruction limit
% 2.47/0.80 % (1129928)Termination phase: Property scanning
% 2.47/0.80 % (1129928)Time elapsed: 0.015 s
% 2.47/0.80 % (1129928)Peak memory usage: 10 MB
% 2.47/0.80 % (1129928)Instructions burned: 20 (million)
% 2.47/0.80 % (1129934)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=4166695999:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.47/0.80 % (1129933)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1858603162:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.47/0.80 % (1129935)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1852048848:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.47/0.80 % (1129934)Instruction limit reached!
% 2.47/0.80 % (1129934)------------------------------
% 2.47/0.80 % (1129934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.80 % (1129934)CaDiCaL version: 2.1.3
% 2.47/0.80 % (1129934)Termination reason: Instruction limit
% 2.47/0.80 % (1129934)Termination phase: shuffling
% 2.47/0.80 % (1129934)Time elapsed: 0.017 s
% 2.47/0.80 % (1129934)Peak memory usage: 10 MB
% 2.47/0.80 % (1129934)Instructions burned: 47 (million)
% 2.47/0.80 % (1129921)Instruction limit reached!
% 2.47/0.80 % (1129921)------------------------------
% 2.47/0.80 % (1129921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.80 % (1129921)CaDiCaL version: 2.1.3
% 2.47/0.80 % (1129921)Termination reason: Instruction limit
% 2.47/0.80 % (1129921)Termination phase: Saturation
% 2.47/0.80 % (1129921)Time elapsed: 0.080 s
% 2.47/0.80 % (1129921)Peak memory usage: 15 MB
% 2.47/0.80 % (1129921)Instructions burned: 169 (million)
% 2.47/0.80 % (1129940)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.47/0.80 % (1129939)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3429334384:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.47/0.80 % (1129940)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3702677457:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.47/0.80 % (1129910)Instruction limit reached!
% 2.47/0.80 % (1129910)------------------------------
% 2.47/0.80 % (1129910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.80 % (1129910)CaDiCaL version: 2.1.3
% 2.47/0.80 % (1129910)Termination reason: Instruction limit
% 2.47/0.80 % (1129910)Termination phase: Saturation
% 2.47/0.80 % (1129910)Time elapsed: 0.125 s
% 2.47/0.80 % (1129910)Peak memory usage: 15 MB
% 2.47/0.80 % (1129910)Instructions burned: 194 (million)
% 2.47/0.80 % (1129929)Instruction limit reached!
% 2.47/0.80 % (1129929)------------------------------
% 2.47/0.80 % (1129929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.80 % (1129929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129929)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129929)Termination reason: Instruction limit
% 3.48/0.91 % (1129929)Termination phase: Saturation
% 3.48/0.91 % (1129929)Time elapsed: 0.079 s
% 3.48/0.91 % (1129929)Peak memory usage: 15 MB
% 3.48/0.91 % (1129929)Instructions burned: 319 (million)
% 3.48/0.91 % (1129939)Instruction limit reached!
% 3.48/0.91 % (1129939)------------------------------
% 3.48/0.91 % (1129939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.91 % (1129939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129939)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129939)Termination reason: Instruction limit
% 3.48/0.91 % (1129939)Termination phase: shuffling
% 3.48/0.91 % (1129939)Time elapsed: 0.007 s
% 3.48/0.91 % (1129939)Peak memory usage: 10 MB
% 3.48/0.91 % (1129939)Instructions burned: 21 (million)
% 3.48/0.91 % (1129945)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=815644732:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.48/0.91 % (1129943)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=495141186:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.48/0.91 % (1129945)Instruction limit reached!
% 3.48/0.91 % (1129945)------------------------------
% 3.48/0.91 % (1129945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.91 % (1129945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129945)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129945)Termination reason: Instruction limit
% 3.48/0.91 % (1129945)Termination phase: shuffling
% 3.48/0.91 % (1129945)Time elapsed: 0.010 s
% 3.48/0.91 % (1129945)Peak memory usage: 10 MB
% 3.48/0.91 % (1129945)Instructions burned: 57 (million)
% 3.48/0.91 % (1129943)Instruction limit reached!
% 3.48/0.91 % (1129943)------------------------------
% 3.48/0.91 % (1129943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.91 % (1129943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129943)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129943)Termination reason: Instruction limit
% 3.48/0.91 % (1129943)Termination phase: shuffling
% 3.48/0.91 % (1129943)Time elapsed: 0.005 s
% 3.48/0.91 % (1129943)Peak memory usage: 10 MB
% 3.48/0.91 % (1129943)Instructions burned: 16 (million)
% 3.48/0.91 % (1129948)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3717529139:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.48/0.91 % (1129948)Instruction limit reached!
% 3.48/0.91 % (1129948)------------------------------
% 3.48/0.91 % (1129948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.91 % (1129935)Refutation not found, incomplete strategy
% 3.48/0.91 % (1129935)------------------------------
% 3.48/0.91 % (1129935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.91 % (1129948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.91 % (1129948)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129948)Termination reason: Instruction limit
% 3.48/0.91 % (1129948)Termination phase: Property scanning
% 3.48/0.91 % (1129948)Time elapsed: 0.007 s
% 3.48/0.91 % (1129935)CaDiCaL version: 2.1.3
% 3.48/0.91 % (1129935)Termination reason: Refutation not found, incomplete strategy
% 3.48/0.91 % (1129935)Time elapsed: 0.071 s
% 3.48/0.91 % (1129948)Peak memory usage: 10 MB
% 3.48/0.91 % (1129935)Peak memory usage: 14 MB
% 3.48/0.91 % (1129948)Instructions burned: 35 (million)
% 3.48/0.91 % (1129935)Instructions burned: 159 (million)
% 3.48/0.91 % (1129944)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=89051706:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.48/0.91 % (1129935)------------------------------
% 3.48/0.91 % (1129935)------------------------------
% 3.48/0.91 % (1129949)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1737018909:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.48/0.91 % (1129952)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1531113526:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.48/1.01 % (1129952)Instruction limit reached!
% 3.48/1.01 % (1129952)------------------------------
% 3.48/1.01 % (1129952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129952)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129952)Termination reason: Instruction limit
% 3.48/1.01 % (1129952)Termination phase: Property scanning
% 3.48/1.01 % (1129952)Time elapsed: 0.007 s
% 3.48/1.01 % (1129952)Peak memory usage: 10 MB
% 3.48/1.01 % (1129952)Instructions burned: 36 (million)
% 3.48/1.01 % (1129953)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3407729826:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.48/1.01 % (1129956)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.48/1.01 % (1129956)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3205712371:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.48/1.01 % (1129940)Instruction limit reached!
% 3.48/1.01 % (1129940)------------------------------
% 3.48/1.01 % (1129940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129940)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129940)Termination reason: Instruction limit
% 3.48/1.01 % (1129940)Termination phase: Saturation
% 3.48/1.01 % (1129940)Time elapsed: 0.074 s
% 3.48/1.01 % (1129940)Peak memory usage: 12 MB
% 3.48/1.01 % (1129940)Instructions burned: 200 (million)
% 3.48/1.01 % (1129953)Instruction limit reached!
% 3.48/1.01 % (1129953)------------------------------
% 3.48/1.01 % (1129953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129953)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129953)Termination reason: Instruction limit
% 3.48/1.01 % (1129953)Termination phase: Property scanning
% 3.48/1.01 % (1129953)Time elapsed: 0.023 s
% 3.48/1.01 % (1129953)Peak memory usage: 10 MB
% 3.48/1.01 % (1129953)Instructions burned: 68 (million)
% 3.48/1.01 % (1129959)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3085763362:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.48/1.01 % (1129944)Instruction limit reached!
% 3.48/1.01 % (1129944)------------------------------
% 3.48/1.01 % (1129944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129944)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129944)Termination reason: Instruction limit
% 3.48/1.01 % (1129944)Termination phase: Property scanning
% 3.48/1.01 % (1129944)Time elapsed: 0.051 s
% 3.48/1.01 % (1129944)Peak memory usage: 11 MB
% 3.48/1.01 % (1129944)Instructions burned: 68 (million)
% 3.48/1.01 % (1129949)Instruction limit reached!
% 3.48/1.01 % (1129949)------------------------------
% 3.48/1.01 % (1129949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129949)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129949)Termination reason: Instruction limit
% 3.48/1.01 % (1129949)Termination phase: Saturation
% 3.48/1.01 % (1129949)Time elapsed: 0.056 s
% 3.48/1.01 % (1129949)Peak memory usage: 12 MB
% 3.48/1.01 % (1129949)Instructions burned: 138 (million)
% 3.48/1.01 % (1129960)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=798262793:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 3.48/1.01 % (1129956)Instruction limit reached!
% 3.48/1.01 % (1129956)------------------------------
% 3.48/1.01 % (1129956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/1.01 % (1129956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.01 % (1129956)CaDiCaL version: 2.1.3
% 3.48/1.01 % (1129956)Termination reason: Instruction limit
% 3.48/1.01 % (1129956)Termination phase: Saturation
% 3.48/1.01 % (1129956)Time elapsed: 0.036 s
% 3.48/1.01 % (1129956)Peak memory usage: 12 MB
% 3.48/1.01 % (1129956)Instructions burned: 181 (million)
% 3.48/1.01 % (1129962)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=572574750:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 4.99/1.10 % (1129963)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2566032306:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 4.99/1.10 % (1129965)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2853660737:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 4.99/1.10 % (1129960)Instruction limit reached!
% 4.99/1.10 % (1129960)------------------------------
% 4.99/1.10 % (1129960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.99/1.10 % (1129960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.10 % (1129960)CaDiCaL version: 2.1.3
% 4.99/1.10 % (1129960)Termination reason: Instruction limit
% 4.99/1.10 % (1129960)Termination phase: Twee Goal Transformation
% 4.99/1.10 % (1129960)Time elapsed: 0.035 s
% 4.99/1.10 % (1129960)Peak memory usage: 10 MB
% 4.99/1.10 % (1129960)Instructions burned: 99 (million)
% 4.99/1.10 % (1129969)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=805081656:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 4.99/1.10 % (1129962)Refutation not found, incomplete strategy
% 4.99/1.10 % (1129962)------------------------------
% 4.99/1.10 % (1129962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.99/1.10 % (1129962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.10 % (1129962)CaDiCaL version: 2.1.3
% 4.99/1.10 % (1129962)Termination reason: Refutation not found, incomplete strategy
% 4.99/1.10 % (1129962)Time elapsed: 0.054 s
% 4.99/1.10 % (1129962)Peak memory usage: 15 MB
% 4.99/1.10 % (1129962)Instructions burned: 135 (million)
% 4.99/1.10 % (1129962)------------------------------
% 4.99/1.10 % (1129962)------------------------------
% 4.99/1.10 % (1129959)Refutation not found, incomplete strategy
% 4.99/1.10 % (1129959)------------------------------
% 4.99/1.10 % (1129959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.99/1.10 % (1129959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.10 % (1129959)CaDiCaL version: 2.1.3
% 4.99/1.10 % (1129959)Termination reason: Refutation not found, incomplete strategy
% 4.99/1.10 % (1129959)Time elapsed: 0.079 s
% 4.99/1.10 % (1129959)Peak memory usage: 15 MB
% 4.99/1.10 % (1129959)Instructions burned: 177 (million)
% 4.99/1.10 % (1129959)------------------------------
% 4.99/1.10 % (1129959)------------------------------
% 4.99/1.10 % (1129971)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2191633287:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 4.99/1.10 % (1129972)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=144474624:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 4.99/1.10 % (1129963)Refutation not found, incomplete strategy
% 4.99/1.10 % (1129963)------------------------------
% 4.99/1.10 % (1129963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.99/1.10 % (1129963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.10 % (1129963)CaDiCaL version: 2.1.3
% 4.99/1.10 % (1129963)Termination reason: Refutation not found, incomplete strategy
% 4.99/1.10 % (1129963)Time elapsed: 0.075 s
% 4.99/1.10 % (1129963)Peak memory usage: 15 MB
% 4.99/1.10 % (1129963)Instructions burned: 181 (million)
% 4.99/1.10 % (1129963)------------------------------
% 4.99/1.10 % (1129963)------------------------------
% 4.99/1.10 % (1129971)Instruction limit reached!
% 4.99/1.10 % (1129971)------------------------------
% 4.99/1.10 % (1129971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.99/1.10 % (1129971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.10 % (1129971)CaDiCaL version: 2.1.3
% 4.99/1.10 % (1129971)Termination reason: Instruction limit
% 4.99/1.10 % (1129971)Termination phase: Function definition elimination
% 4.99/1.10 % (1129971)Time elapsed: 0.017 s
% 4.99/1.10 % (1129971)Peak memory usage: 10 MB
% 4.99/1.10 % (1129971)Instructions burned: 45 (million)
% 4.99/1.10 % (1129975)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1993306247:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 4.99/1.10 % (1129976)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3216075306:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.60/1.19 % (1129969)Instruction limit reached!
% 5.60/1.19 % (1129969)------------------------------
% 5.60/1.19 % (1129969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129969)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129969)Termination reason: Instruction limit
% 5.60/1.19 % (1129969)Termination phase: Saturation
% 5.60/1.19 % (1129969)Time elapsed: 0.074 s
% 5.60/1.19 % (1129969)Peak memory usage: 14 MB
% 5.60/1.19 % (1129969)Instructions burned: 130 (million)
% 5.60/1.19 % (1129976)Instruction limit reached!
% 5.60/1.19 % (1129976)------------------------------
% 5.60/1.19 % (1129976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129976)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129976)Termination reason: Instruction limit
% 5.60/1.19 % (1129976)Termination phase: Function definition elimination
% 5.60/1.19 % (1129976)Time elapsed: 0.033 s
% 5.60/1.19 % (1129976)Peak memory usage: 10 MB
% 5.60/1.19 % (1129976)Instructions burned: 96 (million)
% 5.60/1.19 % (1129972)Refutation not found, incomplete strategy
% 5.60/1.19 % (1129972)------------------------------
% 5.60/1.19 % (1129972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129972)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129972)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.19 % (1129972)Time elapsed: 0.072 s
% 5.60/1.19 % (1129972)Peak memory usage: 14 MB
% 5.60/1.19 % (1129972)Instructions burned: 159 (million)
% 5.60/1.19 % (1129972)------------------------------
% 5.60/1.19 % (1129972)------------------------------
% 5.60/1.19 % (1129979)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=1585718670:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 5.60/1.19 % (1129980)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2425131220:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 5.60/1.19 % (1129981)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=2382415228:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 5.60/1.19 % (1129979)Instruction limit reached!
% 5.60/1.19 % (1129979)------------------------------
% 5.60/1.19 % (1129979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129979)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129979)Termination reason: Instruction limit
% 5.60/1.19 % (1129979)Termination phase: Property scanning
% 5.60/1.19 % (1129979)Time elapsed: 0.026 s
% 5.60/1.19 % (1129979)Peak memory usage: 11 MB
% 5.60/1.19 % (1129979)Instructions burned: 66 (million)
% 5.60/1.19 % (1129985)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=933300791:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 5.60/1.19 % (1129907)Instruction limit reached!
% 5.60/1.19 % (1129907)------------------------------
% 5.60/1.19 % (1129907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129907)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129907)Termination reason: Instruction limit
% 5.60/1.19 % (1129907)Termination phase: Saturation
% 5.60/1.19 % (1129907)Time elapsed: 0.465 s
% 5.60/1.19 % (1129907)Peak memory usage: 15 MB
% 5.60/1.19 % (1129907)Instructions burned: 1242 (million)
% 5.60/1.19 % (1129980)Instruction limit reached!
% 5.60/1.19 % (1129980)------------------------------
% 5.60/1.19 % (1129980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.60/1.19 % (1129980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.19 % (1129980)CaDiCaL version: 2.1.3
% 5.60/1.19 % (1129980)Termination reason: Instruction limit
% 6.39/1.35 % (1129980)Termination phase: Saturation
% 6.39/1.35 % (1129980)Time elapsed: 0.041 s
% 6.39/1.35 % (1129980)Peak memory usage: 12 MB
% 6.39/1.35 % (1129980)Instructions burned: 106 (million)
% 6.39/1.35 % (1129987)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2656886212:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.39/1.35 % (1129965)Instruction limit reached!
% 6.39/1.35 % (1129965)------------------------------
% 6.39/1.35 % (1129965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.39/1.35 % (1129965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.35 % (1129965)CaDiCaL version: 2.1.3
% 6.39/1.35 % (1129965)Termination reason: Instruction limit
% 6.39/1.35 % (1129965)Termination phase: Saturation
% 6.39/1.35 % (1129965)Time elapsed: 0.211 s
% 6.39/1.35 % (1129965)Peak memory usage: 15 MB
% 6.39/1.35 % (1129965)Instructions burned: 517 (million)
% 6.39/1.35 % (1129988)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=81446290:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.39/1.35 % (1129988)Instruction limit reached!
% 6.39/1.35 % (1129988)------------------------------
% 6.39/1.35 % (1129988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.39/1.35 % (1129988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.35 % (1129988)CaDiCaL version: 2.1.3
% 6.39/1.35 % (1129988)Termination reason: Instruction limit
% 6.39/1.35 % (1129988)Termination phase: Property scanning
% 6.39/1.35 % (1129988)Time elapsed: 0.013 s
% 6.39/1.35 % (1129988)Peak memory usage: 10 MB
% 6.39/1.35 % (1129988)Instructions burned: 34 (million)
% 6.39/1.35 % (1129990)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1380246383:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.39/1.35 % (1129992)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3930421474:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 6.39/1.35 % (1129975)Instruction limit reached!
% 6.39/1.35 % (1129975)------------------------------
% 6.39/1.35 % (1129975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.39/1.35 % (1129975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.35 % (1129975)CaDiCaL version: 2.1.3
% 6.39/1.35 % (1129975)Termination reason: Instruction limit
% 6.39/1.35 % (1129975)Termination phase: Saturation
% 6.39/1.35 % (1129975)Time elapsed: 0.174 s
% 6.39/1.35 % (1129975)Peak memory usage: 15 MB
% 6.39/1.35 % (1129975)Instructions burned: 451 (million)
% 6.39/1.35 % (1129990)Instruction limit reached!
% 6.39/1.35 % (1129990)------------------------------
% 6.39/1.35 % (1129990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.39/1.35 % (1129990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.35 % (1129990)CaDiCaL version: 2.1.3
% 6.39/1.35 % (1129990)Termination reason: Instruction limit
% 6.39/1.35 % (1129990)Termination phase: Property scanning
% 6.39/1.35 % (1129990)Time elapsed: 0.032 s
% 6.39/1.35 % (1129990)Peak memory usage: 10 MB
% 6.39/1.35 % (1129990)Instructions burned: 92 (million)
% 6.39/1.35 % (1129992)Instruction limit reached!
% 6.39/1.35 % (1129992)------------------------------
% 6.39/1.35 % (1129992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.39/1.35 % (1129992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.35 % (1129992)CaDiCaL version: 2.1.3
% 6.39/1.35 % (1129992)Termination reason: Instruction limit
% 6.39/1.35 % (1129992)Termination phase: Property scanning
% 6.39/1.35 % (1129992)Time elapsed: 0.023 s
% 6.39/1.35 % (1129992)Peak memory usage: 10 MB
% 6.39/1.35 % (1129992)Instructions burned: 67 (million)
% 6.39/1.35 % (1129995)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3287632991:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 6.39/1.35 % (1129996)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2184577991:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 6.39/1.35 % (1129995)Instruction limit reached!
% 6.39/1.35 % (1129995)------------------------------
% 6.39/1.35 % (1129995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1129995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1129995)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1129995)Termination reason: Instruction limit
% 6.87/1.45 % (1129995)Termination phase: shuffling
% 6.87/1.45 % (1129995)Time elapsed: 0.007 s
% 6.87/1.45 % (1129995)Peak memory usage: 10 MB
% 6.87/1.45 % (1129995)Instructions burned: 22 (million)
% 6.87/1.45 % (1129997)lrs+10_1_sil=128000:si=on:urr=on:random_seed=942468094:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 6.87/1.45 % (1130000)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 6.87/1.45 % (1130000)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3515696758:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 6.87/1.45 % (1129987)Instruction limit reached!
% 6.87/1.45 % (1129987)------------------------------
% 6.87/1.45 % (1129987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1129987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1129987)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1129987)Termination reason: Instruction limit
% 6.87/1.45 % (1129987)Termination phase: Saturation
% 6.87/1.45 % (1129987)Time elapsed: 0.106 s
% 6.87/1.45 % (1129987)Peak memory usage: 15 MB
% 6.87/1.45 % (1129987)Instructions burned: 496 (million)
% 6.87/1.45 % (1129997)Instruction limit reached!
% 6.87/1.45 % (1129997)------------------------------
% 6.87/1.45 % (1129997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1129997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1129997)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1129997)Termination reason: Instruction limit
% 6.87/1.45 % (1129997)Termination phase: shuffling
% 6.87/1.45 % (1129997)Time elapsed: 0.018 s
% 6.87/1.45 % (1129997)Peak memory usage: 10 MB
% 6.87/1.45 % (1129997)Instructions burned: 30 (million)
% 6.87/1.45 % (1130004)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1583858834:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 6.87/1.45 % (1130003)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=1601004454:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 6.87/1.45 % (1130000)Instruction limit reached!
% 6.87/1.45 % (1130000)------------------------------
% 6.87/1.45 % (1130000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1130000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1130000)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1130000)Termination reason: Instruction limit
% 6.87/1.45 % (1130000)Termination phase: Saturation
% 6.87/1.45 % (1130000)Time elapsed: 0.053 s
% 6.87/1.45 % (1130000)Peak memory usage: 12 MB
% 6.87/1.45 % (1130000)Instructions burned: 139 (million)
% 6.87/1.45 % (1129985)Instruction limit reached!
% 6.87/1.45 % (1129985)------------------------------
% 6.87/1.45 % (1129985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1129985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1129985)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1129985)Termination reason: Instruction limit
% 6.87/1.45 % (1129985)Termination phase: Saturation
% 6.87/1.45 % (1129985)Time elapsed: 0.185 s
% 6.87/1.45 % (1129985)Peak memory usage: 14 MB
% 6.87/1.45 % (1129985)Instructions burned: 377 (million)
% 6.87/1.45 % (1130004)Refutation not found, incomplete strategy
% 6.87/1.45 % (1130004)------------------------------
% 6.87/1.45 % (1130004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.45 % (1130004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.45 % (1130004)CaDiCaL version: 2.1.3
% 6.87/1.45 % (1130004)Termination reason: Refutation not found, incomplete strategy
% 6.87/1.45 % (1130004)Time elapsed: 0.046 s
% 6.87/1.45 % (1130004)Peak memory usage: 17 MB
% 6.87/1.45 % (1130004)Instructions burned: 181 (million)
% 6.87/1.45 % (1130004)------------------------------
% 6.87/1.45 % (1130004)------------------------------
% 6.87/1.45 % (1130007)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 8.00/1.63 % (1130007)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3935956984:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 8.00/1.63 % (1129933)Instruction limit reached!
% 8.00/1.63 % (1129933)------------------------------
% 8.00/1.63 % (1129933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.00/1.63 % (1129933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.00/1.63 % (1129933)CaDiCaL version: 2.1.3
% 8.00/1.63 % (1129933)Termination reason: Instruction limit
% 8.00/1.63 % (1129933)Termination phase: Saturation
% 8.00/1.63 % (1129933)Time elapsed: 0.554 s
% 8.00/1.63 % (1129933)Peak memory usage: 19 MB
% 8.00/1.63 % (1129933)Instructions burned: 854 (million)
% 8.00/1.63 % (1130009)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=990491023:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 8.00/1.63 % (1130008)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3243130472:i=116:ep=RSTC:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/116Mi)
% 8.00/1.63 % (1130011)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=885582714:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2990 on theBenchmark for (2990ds/270Mi)
% 8.00/1.63 % (1129996)Instruction limit reached!
% 8.00/1.63 % (1129996)------------------------------
% 8.00/1.63 % (1129996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.00/1.63 % (1129996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.00/1.63 % (1129996)CaDiCaL version: 2.1.3
% 8.00/1.63 % (1129996)Termination reason: Instruction limit
% 8.00/1.63 % (1129996)Termination phase: Saturation
% 8.00/1.63 % (1129996)Time elapsed: 0.142 s
% 8.00/1.63 % (1129996)Peak memory usage: 17 MB
% 8.00/1.63 % (1129996)Instructions burned: 339 (million)
% 8.00/1.63 % (1130015)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=694319485:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/9840Mi)
% 8.00/1.63 % (1130008)Instruction limit reached!
% 8.00/1.63 % (1130008)------------------------------
% 8.00/1.63 % (1130008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.00/1.63 % (1130008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.00/1.63 % (1130008)CaDiCaL version: 2.1.3
% 8.00/1.63 % (1130008)Termination reason: Instruction limit
% 8.00/1.63 % (1130008)Termination phase: Property scanning
% 8.00/1.63 % (1130008)Time elapsed: 0.075 s
% 8.00/1.63 % (1130008)Peak memory usage: 10 MB
% 8.00/1.63 % (1130008)Instructions burned: 116 (million)
% 8.00/1.63 % (1130003)Instruction limit reached!
% 8.00/1.63 % (1130003)------------------------------
% 8.00/1.63 % (1130003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.00/1.63 % (1130003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.00/1.63 % (1130003)CaDiCaL version: 2.1.3
% 8.00/1.63 % (1130003)Termination reason: Instruction limit
% 8.00/1.63 % (1130003)Termination phase: Saturation
% 8.00/1.63 % (1130003)Time elapsed: 0.141 s
% 8.00/1.63 % (1130003)Peak memory usage: 14 MB
% 8.00/1.63 % (1130003)Instructions burned: 340 (million)
% 8.00/1.63 % (1130018)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.00/1.63 % (1130018)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3270612469:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.00/1.63 % (1130017)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2160215328:i=421:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/421Mi)
% 8.00/1.63 % (1130007)Instruction limit reached!
% 8.00/1.63 % (1130007)------------------------------
% 8.00/1.63 % (1130007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.00/1.63 % (1130007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.00/1.63 % (1130007)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130007)Termination reason: Instruction limit
% 8.89/2.00 % (1130007)Termination phase: Saturation
% 8.89/2.00 % (1130007)Time elapsed: 0.157 s
% 8.89/2.00 % (1130007)Peak memory usage: 13 MB
% 8.89/2.00 % (1130007)Instructions burned: 374 (million)
% 8.89/2.00 % (1130011)Instruction limit reached!
% 8.89/2.00 % (1130011)------------------------------
% 8.89/2.00 % (1130011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.89/2.00 % (1130011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.00 % (1130011)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130011)Termination reason: Instruction limit
% 8.89/2.00 % (1130011)Termination phase: Saturation
% 8.89/2.00 % (1130011)Time elapsed: 0.134 s
% 8.89/2.00 % (1130011)Peak memory usage: 13 MB
% 8.89/2.00 % (1130011)Instructions burned: 270 (million)
% 8.89/2.00 % (1130021)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3421464935:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/31Mi)
% 8.89/2.00 % (1130022)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 8.89/2.00 % (1130022)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.89/2.00 % (1130022)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2380548149:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2988 on theBenchmark for (2988ds/1440Mi)
% 8.89/2.00 % (1130021)Instruction limit reached!
% 8.89/2.00 % (1130021)------------------------------
% 8.89/2.00 % (1130021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.89/2.00 % (1130021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.00 % (1130021)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130021)Termination reason: Instruction limit
% 8.89/2.00 % (1130021)Termination phase: Property scanning
% 8.89/2.00 % (1130021)Time elapsed: 0.012 s
% 8.89/2.00 % (1130021)Peak memory usage: 10 MB
% 8.89/2.00 % (1130021)Instructions burned: 32 (million)
% 8.89/2.00 % (1130025)dis+10_2_sil=128000:si=on:random_seed=483073991:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2988 on theBenchmark for (2988ds/339Mi)
% 8.89/2.00 % (1130017)Refutation not found, incomplete strategy
% 8.89/2.00 % (1130017)------------------------------
% 8.89/2.00 % (1130017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.89/2.00 % (1130017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.00 % (1130017)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130017)Termination reason: Refutation not found, incomplete strategy
% 8.89/2.00 % (1130017)Time elapsed: 0.094 s
% 8.89/2.00 % (1130017)Peak memory usage: 15 MB
% 8.89/2.00 % (1130017)Instructions burned: 142 (million)
% 8.89/2.00 % (1130017)------------------------------
% 8.89/2.00 % (1130017)------------------------------
% 8.89/2.00 % (1130018)Instruction limit reached!
% 8.89/2.00 % (1130018)------------------------------
% 8.89/2.00 % (1130018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.89/2.00 % (1130018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.00 % (1130018)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130018)Termination reason: Instruction limit
% 8.89/2.00 % (1130018)Termination phase: Saturation
% 8.89/2.00 % (1130018)Time elapsed: 0.127 s
% 8.89/2.00 % (1130018)Peak memory usage: 12 MB
% 8.89/2.00 % (1130018)Instructions burned: 272 (million)
% 8.89/2.00 % (1130009)Instruction limit reached!
% 8.89/2.00 % (1130009)------------------------------
% 8.89/2.00 % (1130009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.89/2.00 % (1130009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.89/2.00 % (1130009)CaDiCaL version: 2.1.3
% 8.89/2.00 % (1130009)Termination reason: Instruction limit
% 8.89/2.00 % (1130009)Termination phase: Saturation
% 8.89/2.00 % (1130009)Time elapsed: 0.239 s
% 8.89/2.00 % (1130009)Peak memory usage: 17 MB
% 8.89/2.00 % (1130009)Instructions burned: 576 (million)
% 8.89/2.00 % (1130028)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2345334349:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/122Mi)
% 8.89/2.00 % (1130027)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=291073269:i=111:add=on:fgj=on:rtra=on:fdi=1024_2988 on theBenchmark for (2988ds/111Mi)
% 11.78/2.14 % (1130029)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=3828753083:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/136Mi)
% 11.78/2.14 % (1130028)Instruction limit reached!
% 11.78/2.14 % (1130028)------------------------------
% 11.78/2.14 % (1130028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.78/2.14 % (1130028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.78/2.14 % (1130028)CaDiCaL version: 2.1.3
% 11.78/2.14 % (1130028)Termination reason: Instruction limit
% 11.78/2.14 % (1130028)Termination phase: Saturation
% 11.78/2.14 % (1130028)Time elapsed: 0.048 s
% 11.78/2.14 % (1130028)Peak memory usage: 13 MB
% 11.78/2.14 % (1130028)Instructions burned: 122 (million)
% 11.78/2.14 % (1130029)Instruction limit reached!
% 11.78/2.14 % (1130029)------------------------------
% 11.78/2.14 % (1130029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.78/2.14 % (1130029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.78/2.14 % (1130029)CaDiCaL version: 2.1.3
% 11.78/2.14 % (1130029)Termination reason: Instruction limit
% 11.78/2.14 % (1130029)Termination phase: Property scanning
% 11.78/2.14 % (1130029)Time elapsed: 0.048 s
% 11.78/2.14 % (1130029)Peak memory usage: 10 MB
% 11.78/2.14 % (1130029)Instructions burned: 136 (million)
% 11.78/2.14 % (1130033)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2590974322:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2987 on theBenchmark for (2987ds/232Mi)
% 11.78/2.14 % (1130027)Instruction limit reached!
% 11.78/2.14 % (1130027)------------------------------
% 11.78/2.14 % (1130027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.78/2.14 % (1130027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.78/2.14 % (1130027)CaDiCaL version: 2.1.3
% 11.78/2.14 % (1130027)Termination reason: Instruction limit
% 11.78/2.14 % (1130027)Termination phase: Property scanning
% 11.78/2.14 % (1130027)Time elapsed: 0.071 s
% 11.78/2.14 % (1130027)Peak memory usage: 10 MB
% 11.78/2.14 % (1130027)Instructions burned: 111 (million)
% 11.78/2.14 % (1130034)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2419390604:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2987 on theBenchmark for (2987ds/1254Mi)
% 11.78/2.14 % (1130025)Instruction limit reached!
% 11.78/2.14 % (1130025)------------------------------
% 11.78/2.14 % (1130025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.78/2.14 % (1130025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.78/2.14 % (1130025)CaDiCaL version: 2.1.3
% 11.78/2.14 % (1130025)Termination reason: Instruction limit
% 11.78/2.14 % (1130025)Termination phase: Saturation
% 11.78/2.14 % (1130025)Time elapsed: 0.134 s
% 11.78/2.14 % (1130025)Peak memory usage: 15 MB
% 11.78/2.14 % (1130025)Instructions burned: 341 (million)
% 11.78/2.14 % (1130036)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 11.78/2.14 % (1130038)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1871862172:i=619:add=on:rtra=on_2987 on theBenchmark for (2987ds/619Mi)
% 11.78/2.14 % (1130036)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=3426502004:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2987 on theBenchmark for (2987ds/281Mi)
% 11.78/2.14 % (1130033)Refutation not found, incomplete strategy
% 11.78/2.14 % (1130033)------------------------------
% 11.78/2.14 % (1130033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.78/2.14 % (1130033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.78/2.14 % (1130033)CaDiCaL version: 2.1.3
% 11.78/2.14 % (1130033)Termination reason: Refutation not found, incomplete strategy
% 11.78/2.14 % (1130033)Time elapsed: 0.090 s
% 11.78/2.14 % (1130033)Peak memory usage: 14 MB
% 11.78/2.14 % (1130033)Instructions burned: 203 (million)
% 11.78/2.14 % (1130033)------------------------------
% 11.78/2.14 % (1130033)------------------------------
% 11.78/2.14 % (1130041)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1783924268:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/865Mi)
% 12.53/2.24 % (1130036)Instruction limit reached!
% 12.53/2.24 % (1130036)------------------------------
% 12.53/2.24 % (1130036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130036)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130036)Termination reason: Instruction limit
% 12.53/2.24 % (1130036)Termination phase: Saturation
% 12.53/2.24 % (1130036)Time elapsed: 0.168 s
% 12.53/2.24 % (1130036)Peak memory usage: 12 MB
% 12.53/2.24 % (1130036)Instructions burned: 281 (million)
% 12.53/2.24 % (1130038)Refutation not found, incomplete strategy
% 12.53/2.24 % (1130038)------------------------------
% 12.53/2.24 % (1130038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130038)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130038)Termination reason: Refutation not found, incomplete strategy
% 12.53/2.24 % (1130038)Time elapsed: 0.171 s
% 12.53/2.24 % (1130038)Peak memory usage: 16 MB
% 12.53/2.24 % (1130038)Instructions burned: 431 (million)
% 12.53/2.24 % (1130038)------------------------------
% 12.53/2.24 % (1130038)------------------------------
% 12.53/2.24 % (1130044)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2546065811:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/130Mi)
% 12.53/2.24 % (1130043)lrs+10_1_sil=128000:si=on:urr=on:random_seed=950681711:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/212Mi)
% 12.53/2.24 % (1130044)Instruction limit reached!
% 12.53/2.24 % (1130044)------------------------------
% 12.53/2.24 % (1130044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130044)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130044)Termination reason: Instruction limit
% 12.53/2.24 % (1130044)Termination phase: Saturation
% 12.53/2.24 % (1130044)Time elapsed: 0.051 s
% 12.53/2.24 % (1130044)Peak memory usage: 13 MB
% 12.53/2.24 % (1130044)Instructions burned: 130 (million)
% 12.53/2.24 % (1130047)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3528759932:st=1.5:i=346:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/346Mi)
% 12.53/2.24 % (1130047)Refutation not found, incomplete strategy
% 12.53/2.24 % (1130047)------------------------------
% 12.53/2.24 % (1130047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130047)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130047)Termination reason: Refutation not found, incomplete strategy
% 12.53/2.24 % (1130047)Time elapsed: 0.087 s
% 12.53/2.24 % (1130047)Peak memory usage: 15 MB
% 12.53/2.24 % (1130047)Instructions burned: 137 (million)
% 12.53/2.24 % (1130047)------------------------------
% 12.53/2.24 % (1130047)------------------------------
% 12.53/2.24 % (1130043)Instruction limit reached!
% 12.53/2.24 % (1130043)------------------------------
% 12.53/2.24 % (1130043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130043)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130043)Termination reason: Instruction limit
% 12.53/2.24 % (1130043)Termination phase: Saturation
% 12.53/2.24 % (1130043)Time elapsed: 0.157 s
% 12.53/2.24 % (1130043)Peak memory usage: 12 MB
% 12.53/2.24 % (1130043)Instructions burned: 212 (million)
% 12.53/2.24 % (1130057)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=966266952:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2983 on theBenchmark for (2983ds/152Mi)
% 12.53/2.24 % (1130058)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=429760588:i=75:ep=R:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/75Mi)
% 12.53/2.24 % (1130057)Instruction limit reached!
% 12.53/2.24 % (1130057)------------------------------
% 12.53/2.24 % (1130057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.53/2.24 % (1130057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.53/2.24 % (1130057)CaDiCaL version: 2.1.3
% 12.53/2.24 % (1130057)Termination reason: Instruction limit
% 13.25/2.48 % (1130057)Termination phase: Saturation
% 13.25/2.48 % (1130057)Time elapsed: 0.056 s
% 13.25/2.48 % (1130057)Peak memory usage: 12 MB
% 13.25/2.48 % (1130057)Instructions burned: 152 (million)
% 13.25/2.48 % (1130058)Instruction limit reached!
% 13.25/2.48 % (1130058)------------------------------
% 13.25/2.48 % (1130058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.25/2.48 % (1130058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.48 % (1130058)CaDiCaL version: 2.1.3
% 13.25/2.48 % (1130058)Termination reason: Instruction limit
% 13.25/2.48 % (1130058)Termination phase: Property scanning
% 13.25/2.48 % (1130058)Time elapsed: 0.040 s
% 13.25/2.48 % (1130058)Peak memory usage: 10 MB
% 13.25/2.48 % (1130058)Instructions burned: 76 (million)
% 13.25/2.48 % (1130041)Instruction limit reached!
% 13.25/2.48 % (1130041)------------------------------
% 13.25/2.48 % (1130041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.25/2.48 % (1130041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.48 % (1130041)CaDiCaL version: 2.1.3
% 13.25/2.48 % (1130041)Termination reason: Instruction limit
% 13.25/2.48 % (1130041)Termination phase: Saturation
% 13.25/2.48 % (1130041)Time elapsed: 0.396 s
% 13.25/2.48 % (1130041)Peak memory usage: 20 MB
% 13.25/2.48 % (1130041)Instructions burned: 867 (million)
% 13.25/2.48 % (1130062)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=23321345:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2982 on theBenchmark for (2982ds/148Mi)
% 13.25/2.48 % (1130063)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3966713157:i=161:piset=and:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/161Mi)
% 13.25/2.48 % (1130022)Instruction limit reached!
% 13.25/2.48 % (1130022)------------------------------
% 13.25/2.48 % (1130022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.25/2.48 % (1130022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.48 % (1130022)CaDiCaL version: 2.1.3
% 13.25/2.48 % (1130022)Termination reason: Instruction limit
% 13.25/2.48 % (1130022)Termination phase: Saturation
% 13.25/2.48 % (1130022)Time elapsed: 0.653 s
% 13.25/2.48 % (1130022)Peak memory usage: 22 MB
% 13.25/2.48 % (1130022)Instructions burned: 1441 (million)
% 13.25/2.48 % (1130061)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=499578780:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/387Mi)
% 13.25/2.48 % (1130067)lrs+10_1_sil=128000:si=on:random_seed=3138972071:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/888Mi)
% 13.25/2.48 % (1130063)Instruction limit reached!
% 13.25/2.48 % (1130063)------------------------------
% 13.25/2.48 % (1130063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.25/2.48 % (1130063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.48 % (1130063)CaDiCaL version: 2.1.3
% 13.25/2.48 % (1130063)Termination reason: Instruction limit
% 13.25/2.48 % (1130063)Termination phase: Saturation
% 13.25/2.48 % (1130063)Time elapsed: 0.032 s
% 13.25/2.48 % (1130063)Peak memory usage: 12 MB
% 13.25/2.48 % (1130063)Instructions burned: 167 (million)
% 13.25/2.48 % (1130069)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=927195063:i=136:add=on:ins=4:rtra=on:sup=off_2981 on theBenchmark for (2981ds/136Mi)
% 13.25/2.48 % (1130069)Instruction limit reached!
% 13.25/2.48 % (1130069)------------------------------
% 13.25/2.48 % (1130069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.25/2.48 % (1130069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.48 % (1130069)CaDiCaL version: 2.1.3
% 13.25/2.48 % (1130069)Termination reason: Instruction limit
% 13.25/2.48 % (1130069)Termination phase: Property scanning
% 13.25/2.48 % (1130069)Time elapsed: 0.026 s
% 13.25/2.48 % (1130069)Peak memory usage: 11 MB
% 13.25/2.48 % (1130069)Instructions burned: 139 (million)
% 13.25/2.48 % (1130071)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=4184139231:i=88:s2at=3:nm=2:rtra=on:rawr=on_2981 on theBenchmark for (2981ds/88Mi)
% 13.25/2.48 % (1130071)Instruction limit reached!
% 13.25/2.48 % (1130071)------------------------------
% 13.25/2.48 % (1130071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130071)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130071)Termination reason: Instruction limit
% 15.02/2.76 % (1130071)Termination phase: Property scanning
% 15.02/2.76 % (1130071)Time elapsed: 0.018 s
% 15.02/2.76 % (1130071)Peak memory usage: 11 MB
% 15.02/2.76 % (1130071)Instructions burned: 92 (million)
% 15.02/2.76 % (1130034)Instruction limit reached!
% 15.02/2.76 % (1130034)------------------------------
% 15.02/2.76 % (1130034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130034)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130034)Termination reason: Instruction limit
% 15.02/2.76 % (1130034)Termination phase: Saturation
% 15.02/2.76 % (1130034)Time elapsed: 0.607 s
% 15.02/2.76 % (1130034)Peak memory usage: 21 MB
% 15.02/2.76 % (1130034)Instructions burned: 1255 (million)
% 15.02/2.76 % (1130073)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=4244821096:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2981 on theBenchmark for (2981ds/93Mi)
% 15.02/2.76 % (1130061)Refutation not found, incomplete strategy
% 15.02/2.76 % (1130061)------------------------------
% 15.02/2.76 % (1130061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130061)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130061)Termination reason: Refutation not found, incomplete strategy
% 15.02/2.76 % (1130061)Time elapsed: 0.123 s
% 15.02/2.76 % (1130062)Instruction limit reached!
% 15.02/2.76 % (1130062)------------------------------
% 15.02/2.76 % (1130062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130062)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130062)Termination reason: Instruction limit
% 15.02/2.76 % (1130062)Termination phase: Saturation
% 15.02/2.76 % (1130062)Time elapsed: 0.128 s
% 15.02/2.76 % (1130061)Peak memory usage: 15 MB
% 15.02/2.76 % (1130062)Peak memory usage: 12 MB
% 15.02/2.76 % (1130061)Instructions burned: 145 (million)
% 15.02/2.76 % (1130062)Instructions burned: 151 (million)
% 15.02/2.76 % (1130061)------------------------------
% 15.02/2.76 % (1130061)------------------------------
% 15.02/2.76 % (1130073)Instruction limit reached!
% 15.02/2.76 % (1130073)------------------------------
% 15.02/2.76 % (1130073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130073)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130073)Termination reason: Instruction limit
% 15.02/2.76 % (1130073)Termination phase: Property scanning
% 15.02/2.76 % (1130073)Time elapsed: 0.019 s
% 15.02/2.76 % (1130073)Peak memory usage: 11 MB
% 15.02/2.76 % (1130073)Instructions burned: 97 (million)
% 15.02/2.76 % (1130078)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 15.02/2.76 % (1130078)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=1307136646:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2980 on theBenchmark for (2980ds/391Mi)
% 15.02/2.76 % (1130074)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3375018523:i=2186:rtra=on:ixr=off_2981 on theBenchmark for (2981ds/2186Mi)
% 15.02/2.76 % (1130076)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1104021167:s2a=on:i=240:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/240Mi)
% 15.02/2.76 % (1130077)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2787352684:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2980 on theBenchmark for (2980ds/805Mi)
% 15.02/2.76 % (1130078)Refutation not found, incomplete strategy
% 15.02/2.76 % (1130078)------------------------------
% 15.02/2.76 % (1130078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.02/2.76 % (1130078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.02/2.76 % (1130078)CaDiCaL version: 2.1.3
% 15.02/2.76 % (1130078)Termination reason: Refutation not found, incomplete strategy
% 16.19/2.91 % (1130078)Time elapsed: 0.054 s
% 16.19/2.91 % (1130078)Peak memory usage: 14 MB
% 16.19/2.91 % (1130078)Instructions burned: 253 (million)
% 16.19/2.91 % (1130078)------------------------------
% 16.19/2.91 % (1130078)------------------------------
% 16.19/2.91 % (1130083)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=4105202856:i=355:av=off:fsr=off:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/355Mi)
% 16.19/2.91 % (1130083)Instruction limit reached!
% 16.19/2.91 % (1130083)------------------------------
% 16.19/2.91 % (1130083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.19/2.91 % (1130083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/2.91 % (1130083)CaDiCaL version: 2.1.3
% 16.19/2.91 % (1130083)Termination reason: Instruction limit
% 16.19/2.91 % (1130083)Termination phase: Saturation
% 16.19/2.91 % (1130083)Time elapsed: 0.074 s
% 16.19/2.91 % (1130083)Peak memory usage: 14 MB
% 16.19/2.91 % (1130083)Instructions burned: 357 (million)
% 16.19/2.91 % (1130085)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3786429968:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/314Mi)
% 16.19/2.91 % (1130076)Instruction limit reached!
% 16.19/2.91 % (1130076)------------------------------
% 16.19/2.91 % (1130076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.19/2.91 % (1130076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/2.91 % (1130076)CaDiCaL version: 2.1.3
% 16.19/2.91 % (1130076)Termination reason: Instruction limit
% 16.19/2.91 % (1130076)Termination phase: Saturation
% 16.19/2.91 % (1130076)Time elapsed: 0.138 s
% 16.19/2.91 % (1130076)Peak memory usage: 13 MB
% 16.19/2.91 % (1130076)Instructions burned: 241 (million)
% 16.19/2.91 % (1130087)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=857104955:s2a=on:i=251:fsr=off:rtra=on_2979 on theBenchmark for (2979ds/251Mi)
% 16.19/2.91 % (1130085)Refutation not found, incomplete strategy
% 16.19/2.91 % (1130085)------------------------------
% 16.19/2.91 % (1130085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.19/2.91 % (1130085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/2.91 % (1130085)CaDiCaL version: 2.1.3
% 16.19/2.91 % (1130085)Termination reason: Refutation not found, incomplete strategy
% 16.19/2.91 % (1130085)Time elapsed: 0.032 s
% 16.19/2.91 % (1130085)Peak memory usage: 14 MB
% 16.19/2.91 % (1130085)Instructions burned: 152 (million)
% 16.19/2.91 % (1130085)------------------------------
% 16.19/2.91 % (1130085)------------------------------
% 16.19/2.91 % (1130089)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1008914970:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2978 on theBenchmark for (2978ds/2470Mi)
% 16.19/2.91 % (1130067)Instruction limit reached!
% 16.19/2.91 % (1130067)------------------------------
% 16.19/2.91 % (1130067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.19/2.91 % (1130067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/2.91 % (1130067)CaDiCaL version: 2.1.3
% 16.19/2.91 % (1130067)Termination reason: Instruction limit
% 16.19/2.91 % (1130067)Termination phase: Saturation
% 16.19/2.91 % (1130067)Time elapsed: 0.361 s
% 16.19/2.91 % (1130067)Peak memory usage: 15 MB
% 16.19/2.91 % (1130067)Instructions burned: 889 (million)
% 16.19/2.91 % (1130091)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=1466407099:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2978 on theBenchmark for (2978ds/673Mi)
% 16.19/2.91 % (1130087)Instruction limit reached!
% 16.19/2.91 % (1130087)------------------------------
% 16.19/2.91 % (1130087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.19/2.91 % (1130087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/2.91 % (1130087)CaDiCaL version: 2.1.3
% 16.19/2.91 % (1130087)Termination reason: Instruction limit
% 16.19/2.91 % (1130087)Termination phase: Saturation
% 16.19/2.91 % (1130087)Time elapsed: 0.093 s
% 16.19/2.91 % (1130087)Peak memory usage: 12 MB
% 16.19/2.91 % (1130087)Instructions burned: 252 (million)
% 16.19/2.91 % (1130093)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2234219830:i=116:ep=RSTC:rtra=on:ntd=on_2978 on theBenchmark for (2978ds/116Mi)
% 18.68/3.15 % (1130093)Instruction limit reached!
% 18.68/3.15 % (1130093)------------------------------
% 18.68/3.15 % (1130093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.15 % (1130093)CaDiCaL version: 2.1.3
% 18.68/3.15 % (1130093)Termination reason: Instruction limit
% 18.68/3.15 % (1130093)Termination phase: Property scanning
% 18.68/3.15 % (1130093)Time elapsed: 0.041 s
% 18.68/3.15 % (1130093)Peak memory usage: 10 MB
% 18.68/3.15 % (1130093)Instructions burned: 116 (million)
% 18.68/3.15 % (1130095)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2108967115:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2977 on theBenchmark for (2977ds/270Mi)
% 18.68/3.15 % (1130077)Instruction limit reached!
% 18.68/3.15 % (1130077)------------------------------
% 18.68/3.15 % (1130077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.15 % (1130077)CaDiCaL version: 2.1.3
% 18.68/3.15 % (1130077)Termination reason: Instruction limit
% 18.68/3.15 % (1130077)Termination phase: Saturation
% 18.68/3.15 % (1130077)Time elapsed: 0.412 s
% 18.68/3.15 % (1130077)Peak memory usage: 17 MB
% 18.68/3.15 % (1130077)Instructions burned: 806 (million)
% 18.68/3.15 % (1130095)Instruction limit reached!
% 18.68/3.15 % (1130095)------------------------------
% 18.68/3.15 % (1130095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.15 % (1130095)CaDiCaL version: 2.1.3
% 18.68/3.15 % (1130095)Termination reason: Instruction limit
% 18.68/3.15 % (1130095)Termination phase: Saturation
% 18.68/3.15 % (1130095)Time elapsed: 0.104 s
% 18.68/3.15 % (1130095)Peak memory usage: 13 MB
% 18.68/3.15 % (1130095)Instructions burned: 272 (million)
% 18.68/3.15 % (1130097)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=796479086:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2976 on theBenchmark for (2976ds/30Mi)
% 18.68/3.15 % (1130098)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 18.68/3.15 % (1130097)Instruction limit reached!
% 18.68/3.15 % (1130097)------------------------------
% 18.68/3.15 % (1130097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.15 % (1130097)CaDiCaL version: 2.1.3
% 18.68/3.15 % (1130097)Termination reason: Instruction limit
% 18.68/3.15 % (1130097)Termination phase: shuffling
% 18.68/3.15 % (1130097)Time elapsed: 0.012 s
% 18.68/3.15 % (1130097)Peak memory usage: 10 MB
% 18.68/3.15 % (1130097)Instructions burned: 32 (million)
% 18.68/3.15 % (1130098)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=1526085946:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2976 on theBenchmark for (2976ds/39Mi)
% 18.68/3.15 % (1130100)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2310890630:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2976 on theBenchmark for (2976ds/365Mi)
% 18.68/3.15 % (1130098)Instruction limit reached!
% 18.68/3.15 % (1130098)------------------------------
% 18.68/3.15 % (1130098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.15 % (1130098)CaDiCaL version: 2.1.3
% 18.68/3.15 % (1130098)Termination reason: Instruction limit
% 18.68/3.15 % (1130098)Termination phase: Function definition elimination
% 18.68/3.15 % (1130098)Time elapsed: 0.016 s
% 18.68/3.15 % (1130098)Peak memory usage: 10 MB
% 18.68/3.15 % (1130098)Instructions burned: 41 (million)
% 18.68/3.15 % (1130103)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=895866482:i=158:av=off:rtra=on_2975 on theBenchmark for (2975ds/158Mi)
% 18.68/3.15 % (1130103)Instruction limit reached!
% 18.68/3.15 % (1130103)------------------------------
% 18.68/3.15 % (1130103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.68/3.15 % (1130103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130103)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130103)Termination reason: Instruction limit
% 20.13/3.34 % (1130103)Termination phase: Saturation
% 20.13/3.34 % (1130103)Time elapsed: 0.063 s
% 20.13/3.34 % (1130103)Peak memory usage: 12 MB
% 20.13/3.34 % (1130103)Instructions burned: 160 (million)
% 20.13/3.34 % (1130105)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 20.13/3.34 % (1130105)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3070042514:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/252Mi)
% 20.13/3.34 % (1130091)Instruction limit reached!
% 20.13/3.34 % (1130091)------------------------------
% 20.13/3.34 % (1130091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.13/3.34 % (1130091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130091)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130091)Termination reason: Instruction limit
% 20.13/3.34 % (1130091)Termination phase: Saturation
% 20.13/3.34 % (1130091)Time elapsed: 0.374 s
% 20.13/3.34 % (1130091)Peak memory usage: 15 MB
% 20.13/3.34 % (1130091)Instructions burned: 674 (million)
% 20.13/3.34 % (1130100)Instruction limit reached!
% 20.13/3.34 % (1130100)------------------------------
% 20.13/3.34 % (1130100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.13/3.34 % (1130100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130100)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130100)Termination reason: Instruction limit
% 20.13/3.34 % (1130100)Termination phase: Saturation
% 20.13/3.34 % (1130100)Time elapsed: 0.143 s
% 20.13/3.34 % (1130100)Peak memory usage: 14 MB
% 20.13/3.34 % (1130100)Instructions burned: 368 (million)
% 20.13/3.34 % (1130107)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=110348023:i=213:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/213Mi)
% 20.13/3.34 % (1130108)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=2253648490:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2974 on theBenchmark for (2974ds/160Mi)
% 20.13/3.34 % (1130105)Instruction limit reached!
% 20.13/3.34 % (1130105)------------------------------
% 20.13/3.34 % (1130105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.13/3.34 % (1130105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130105)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130105)Termination reason: Instruction limit
% 20.13/3.34 % (1130105)Termination phase: Saturation
% 20.13/3.34 % (1130105)Time elapsed: 0.095 s
% 20.13/3.34 % (1130105)Peak memory usage: 12 MB
% 20.13/3.34 % (1130105)Instructions burned: 254 (million)
% 20.13/3.34 % (1130111)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3438649740:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2973 on theBenchmark for (2973ds/763Mi)
% 20.13/3.34 % (1130107)Refutation not found, incomplete strategy
% 20.13/3.34 % (1130107)------------------------------
% 20.13/3.34 % (1130107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.13/3.34 % (1130107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130107)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130107)Termination reason: Refutation not found, incomplete strategy
% 20.13/3.34 % (1130107)Time elapsed: 0.054 s
% 20.13/3.34 % (1130107)Peak memory usage: 14 MB
% 20.13/3.34 % (1130107)Instructions burned: 139 (million)
% 20.13/3.34 % (1130107)------------------------------
% 20.13/3.34 % (1130107)------------------------------
% 20.13/3.34 % (1130108)Instruction limit reached!
% 20.13/3.34 % (1130108)------------------------------
% 20.13/3.34 % (1130108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.13/3.34 % (1130108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.13/3.34 % (1130108)CaDiCaL version: 2.1.3
% 20.13/3.34 % (1130108)Termination reason: Instruction limit
% 20.13/3.34 % (1130108)Termination phase: Saturation
% 20.13/3.34 % (1130108)Time elapsed: 0.062 s
% 20.13/3.34 % (1130108)Peak memory usage: 13 MB
% 20.13/3.34 % (1130108)Instructions burned: 161 (million)
% 20.13/3.34 % (1130113)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 20.61/3.43 % (1130113)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1366663618:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2973 on theBenchmark for (2973ds/237Mi)
% 20.61/3.43 % (1130114)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=665050871:s2a=on:i=386:rtra=on:ntd=on_2973 on theBenchmark for (2973ds/386Mi)
% 20.61/3.43 % (1130089)Instruction limit reached!
% 20.61/3.43 % (1130089)------------------------------
% 20.61/3.43 % (1130089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.61/3.43 % (1130089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.61/3.43 % (1130089)CaDiCaL version: 2.1.3
% 20.61/3.43 % (1130089)Termination reason: Instruction limit
% 20.61/3.43 % (1130089)Termination phase: Saturation
% 20.61/3.43 % (1130089)Time elapsed: 0.604 s
% 20.61/3.43 % (1130089)Peak memory usage: 18 MB
% 20.61/3.43 % (1130089)Instructions burned: 2470 (million)
% 20.61/3.43 % (1130117)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=4220867430:i=300:piset=and:nm=32:rtra=on_2972 on theBenchmark for (2972ds/300Mi)
% 20.61/3.43 % (1130113)Refutation not found, incomplete strategy
% 20.61/3.43 % (1130113)------------------------------
% 20.61/3.43 % (1130113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.61/3.43 % (1130113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.61/3.43 % (1130113)CaDiCaL version: 2.1.3
% 20.61/3.43 % (1130113)Termination reason: Refutation not found, incomplete strategy
% 20.61/3.43 % (1130113)Time elapsed: 0.095 s
% 20.61/3.43 % (1130113)Peak memory usage: 16 MB
% 20.61/3.43 % (1130113)Instructions burned: 219 (million)
% 20.61/3.43 % (1130113)------------------------------
% 20.61/3.43 % (1130113)------------------------------
% 20.61/3.43 % (1130117)Instruction limit reached!
% 20.61/3.43 % (1130117)------------------------------
% 20.61/3.43 % (1130117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.61/3.43 % (1130117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.61/3.43 % (1130117)CaDiCaL version: 2.1.3
% 20.61/3.43 % (1130117)Termination reason: Instruction limit
% 20.61/3.43 % (1130117)Termination phase: Saturation
% 20.61/3.43 % (1130117)Time elapsed: 0.061 s
% 20.61/3.43 % (1130117)Peak memory usage: 13 MB
% 20.61/3.43 % (1130117)Instructions burned: 303 (million)
% 20.61/3.43 % (1130119)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=4188225086:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/567Mi)
% 20.61/3.43 % (1130121)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=479453895:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2972 on theBenchmark for (2972ds/379Mi)
% 20.61/3.43 % (1130111)Refutation not found, incomplete strategy
% 20.61/3.43 % (1130111)------------------------------
% 20.61/3.43 % (1130111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.61/3.43 % (1130111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.61/3.43 % (1130111)CaDiCaL version: 2.1.3
% 20.61/3.43 % (1130111)Termination reason: Refutation not found, incomplete strategy
% 20.61/3.43 % (1130111)Time elapsed: 0.207 s
% 20.61/3.43 % (1130111)Peak memory usage: 17 MB
% 20.61/3.43 % (1130111)Instructions burned: 449 (million)
% 20.61/3.43 % (1130111)------------------------------
% 20.61/3.43 % (1130111)------------------------------
% 20.61/3.43 % (1130123)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2077852673:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2971 on theBenchmark for (2971ds/429Mi)
% 20.61/3.43 % (1130114)Instruction limit reached!
% 20.61/3.43 % (1130114)------------------------------
% 20.61/3.43 % (1130114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.61/3.43 % (1130114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.61/3.43 % (1130114)CaDiCaL version: 2.1.3
% 20.61/3.43 % (1130114)Termination reason: Instruction limit
% 20.61/3.43 % (1130114)Termination phase: Saturation
% 20.61/3.43 % (1130114)Time elapsed: 0.203 s
% 20.61/3.43 % (1130114)Peak memory usage: 13 MB
% 20.61/3.43 % (1130114)Instructions burned: 386 (million)
% 20.61/3.43 % (1130125)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=2599509391:i=478:bd=all:rtra=on_2971 on theBenchmark for (2971ds/478Mi)
% 21.90/3.61 % (1130119)Refutation not found, incomplete strategy
% 21.90/3.61 % (1130119)------------------------------
% 21.90/3.61 % (1130119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.90/3.61 % (1130119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.90/3.61 % (1130119)CaDiCaL version: 2.1.3
% 21.90/3.61 % (1130119)Termination reason: Refutation not found, incomplete strategy
% 21.90/3.61 % (1130119)Time elapsed: 0.145 s
% 21.90/3.61 % (1130119)Peak memory usage: 14 MB
% 21.90/3.61 % (1130119)Instructions burned: 349 (million)
% 21.90/3.61 % (1130119)------------------------------
% 21.90/3.61 % (1130119)------------------------------
% 21.90/3.61 % (1130127)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1876573813:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2970 on theBenchmark for (2970ds/445Mi)
% 21.90/3.61 % (1130121)Instruction limit reached!
% 21.90/3.61 % (1130121)------------------------------
% 21.90/3.61 % (1130121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.90/3.61 % (1130121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.90/3.61 % (1130121)CaDiCaL version: 2.1.3
% 21.90/3.61 % (1130121)Termination reason: Instruction limit
% 21.90/3.61 % (1130121)Termination phase: Saturation
% 21.90/3.61 % (1130121)Time elapsed: 0.149 s
% 21.90/3.61 % (1130121)Peak memory usage: 14 MB
% 21.90/3.61 % (1130121)Instructions burned: 381 (million)
% 21.90/3.61 % (1130129)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3260003365:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2970 on theBenchmark for (2970ds/71Mi)
% 21.90/3.61 % (1130129)Instruction limit reached!
% 21.90/3.61 % (1130129)------------------------------
% 21.90/3.61 % (1130129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.90/3.61 % (1130129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.90/3.61 % (1130129)CaDiCaL version: 2.1.3
% 21.90/3.61 % (1130129)Termination reason: Instruction limit
% 21.90/3.61 % (1130129)Termination phase: Property scanning
% 21.90/3.61 % (1130129)Time elapsed: 0.027 s
% 21.90/3.61 % (1130129)Peak memory usage: 10 MB
% 21.90/3.61 % (1130129)Instructions burned: 71 (million)
% 21.90/3.61 % (1130131)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3280125764:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2969 on theBenchmark for (2969ds/302Mi)
% 21.90/3.61 % (1130123)Instruction limit reached!
% 21.90/3.61 % (1130123)------------------------------
% 21.90/3.61 % (1130123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.90/3.61 % (1130123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.90/3.61 % (1130123)CaDiCaL version: 2.1.3
% 21.90/3.61 % (1130123)Termination reason: Instruction limit
% 21.90/3.61 % (1130123)Termination phase: Saturation
% 21.90/3.61 % (1130123)Time elapsed: 0.172 s
% 21.90/3.61 % (1130123)Peak memory usage: 15 MB
% 21.90/3.61 % (1130123)Instructions burned: 430 (million)
% 21.90/3.61 % (1130127)Instruction limit reached!
% 21.90/3.61 % (1130127)------------------------------
% 21.90/3.61 % (1130127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.90/3.61 % (1130127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.90/3.61 % (1130127)CaDiCaL version: 2.1.3
% 21.90/3.61 % (1130127)Termination reason: Instruction limit
% 21.90/3.61 % (1130127)Termination phase: Saturation
% 21.90/3.61 % (1130127)Time elapsed: 0.090 s
% 21.90/3.61 % (1130127)Peak memory usage: 15 MB
% 21.90/3.61 % (1130127)Instructions burned: 446 (million)
% 21.90/3.61 % (1130134)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 21.90/3.61 % (1130134)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 21.90/3.61 % (1130133)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=3398717176:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2969 on theBenchmark for (2969ds/4980Mi)
% 21.90/3.61 % (1130134)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=734043341:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2969 on theBenchmark for (2969ds/100Mi)
% 21.90/3.61 % (1130134)Instruction limit reached!
% 21.90/3.61 % (1130134)------------------------------
% 23.11/3.72 % (1130134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130134)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130134)Termination reason: Instruction limit
% 23.11/3.72 % (1130134)Termination phase: Saturation
% 23.11/3.72 % (1130134)Time elapsed: 0.021 s
% 23.11/3.72 % (1130134)Peak memory usage: 11 MB
% 23.11/3.72 % (1130134)Instructions burned: 105 (million)
% 23.11/3.72 % (1130137)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2395825779:i=76:piset=equals:rtra=on:ntd=on_2969 on theBenchmark for (2969ds/76Mi)
% 23.11/3.72 % (1130137)Instruction limit reached!
% 23.11/3.72 % (1130137)------------------------------
% 23.11/3.72 % (1130137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130137)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130137)Termination reason: Instruction limit
% 23.11/3.72 % (1130137)Termination phase: Property scanning
% 23.11/3.72 % (1130137)Time elapsed: 0.015 s
% 23.11/3.72 % (1130137)Peak memory usage: 10 MB
% 23.11/3.72 % (1130137)Instructions burned: 77 (million)
% 23.11/3.72 % (1130139)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=3986427378:i=289:rtra=on_2968 on theBenchmark for (2968ds/289Mi)
% 23.11/3.72 % (1130074)Instruction limit reached!
% 23.11/3.72 % (1130074)------------------------------
% 23.11/3.72 % (1130074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130074)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130074)Termination reason: Instruction limit
% 23.11/3.72 % (1130074)Termination phase: Saturation
% 23.11/3.72 % (1130074)Time elapsed: 1.202 s
% 23.11/3.72 % (1130074)Peak memory usage: 18 MB
% 23.11/3.72 % (1130074)Instructions burned: 2186 (million)
% 23.11/3.72 % (1130131)Refutation not found, incomplete strategy
% 23.11/3.72 % (1130131)------------------------------
% 23.11/3.72 % (1130131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130131)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130131)Termination reason: Refutation not found, incomplete strategy
% 23.11/3.72 % (1130131)Time elapsed: 0.115 s
% 23.11/3.72 % (1130131)Peak memory usage: 17 MB
% 23.11/3.72 % (1130131)Instructions burned: 218 (million)
% 23.11/3.72 % (1130141)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=3255668923:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2968 on theBenchmark for (2968ds/493Mi)
% 23.11/3.72 % (1130131)------------------------------
% 23.11/3.72 % (1130131)------------------------------
% 23.11/3.72 % (1130133)Refutation not found, incomplete strategy
% 23.11/3.72 % (1130133)------------------------------
% 23.11/3.72 % (1130133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130133)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130133)Termination reason: Refutation not found, incomplete strategy
% 23.11/3.72 % (1130133)Time elapsed: 0.096 s
% 23.11/3.72 % (1130133)Peak memory usage: 16 MB
% 23.11/3.72 % (1130133)Instructions burned: 223 (million)
% 23.11/3.72 % (1130125)Instruction limit reached!
% 23.11/3.72 % (1130125)------------------------------
% 23.11/3.72 % (1130125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.11/3.72 % (1130125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.11/3.72 % (1130125)CaDiCaL version: 2.1.3
% 23.11/3.72 % (1130125)Termination reason: Instruction limit
% 23.11/3.72 % (1130125)Termination phase: Saturation
% 23.11/3.72 % (1130125)Time elapsed: 0.260 s
% 23.11/3.72 % (1130125)Peak memory usage: 18 MB
% 23.11/3.72 % (1130125)Instructions burned: 480 (million)
% 23.11/3.72 % (1130133)------------------------------
% 23.11/3.72 % (1130133)------------------------------
% 23.11/3.72 % (1130144)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 23.11/3.72 % (1130143)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1784280819:cond=on:i=34:hud=10:nm=10:rtra=on_2968 on theBenchmark for (2968ds/34Mi)
% 23.86/3.95 % (1130144)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=3815667515:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2968 on theBenchmark for (2968ds/372Mi)
% 23.86/3.95 % (1130145)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=1456836517:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2968 on theBenchmark for (2968ds/670Mi)
% 23.86/3.95 % (1130139)Instruction limit reached!
% 23.86/3.95 % (1130139)------------------------------
% 23.86/3.95 % (1130139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.95 % (1130139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.95 % (1130139)CaDiCaL version: 2.1.3
% 23.86/3.95 % (1130139)Termination reason: Instruction limit
% 23.86/3.95 % (1130139)Termination phase: Saturation
% 23.86/3.95 % (1130139)Time elapsed: 0.059 s
% 23.86/3.95 % (1130139)Peak memory usage: 14 MB
% 23.86/3.95 % (1130139)Instructions burned: 291 (million)
% 23.86/3.95 % (1130143)Instruction limit reached!
% 23.86/3.95 % (1130143)------------------------------
% 23.86/3.95 % (1130143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.95 % (1130143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.95 % (1130143)CaDiCaL version: 2.1.3
% 23.86/3.95 % (1130143)Termination reason: Instruction limit
% 23.86/3.95 % (1130143)Termination phase: Property scanning
% 23.86/3.95 % (1130143)Time elapsed: 0.014 s
% 23.86/3.95 % (1130143)Peak memory usage: 10 MB
% 23.86/3.95 % (1130143)Instructions burned: 35 (million)
% 23.86/3.95 % (1130149)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=597359402:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2968 on theBenchmark for (2968ds/647Mi)
% 23.86/3.95 % (1130150)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=4012354090:i=857:add=off:kws=frequency:rtra=on:ntd=on_2968 on theBenchmark for (2968ds/857Mi)
% 23.86/3.95 % (1130149)Refutation not found, incomplete strategy
% 23.86/3.95 % (1130149)------------------------------
% 23.86/3.95 % (1130149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.95 % (1130149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.95 % (1130149)CaDiCaL version: 2.1.3
% 23.86/3.95 % (1130149)Termination reason: Refutation not found, incomplete strategy
% 23.86/3.95 % (1130149)Time elapsed: 0.046 s
% 23.86/3.95 % (1130149)Peak memory usage: 14 MB
% 23.86/3.95 % (1130149)Instructions burned: 203 (million)
% 23.86/3.95 % (1130149)------------------------------
% 23.86/3.95 % (1130149)------------------------------
% 23.86/3.95 % (1130153)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=2495590836:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2967 on theBenchmark for (2967ds/693Mi)
% 23.86/3.95 % (1130144)Instruction limit reached!
% 23.86/3.95 % (1130144)------------------------------
% 23.86/3.95 % (1130144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.95 % (1130144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.95 % (1130144)CaDiCaL version: 2.1.3
% 23.86/3.95 % (1130144)Termination reason: Instruction limit
% 23.86/3.95 % (1130144)Termination phase: Saturation
% 23.86/3.95 % (1130144)Time elapsed: 0.150 s
% 23.86/3.95 % (1130144)Peak memory usage: 15 MB
% 23.86/3.95 % (1130144)Instructions burned: 372 (million)
% 23.86/3.95 % (1130155)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=48656246:i=285:hud=10:bd=all:rtra=on:ss=axioms_2966 on theBenchmark for (2966ds/285Mi)
% 23.86/3.95 % (1130141)Instruction limit reached!
% 23.86/3.95 % (1130141)------------------------------
% 23.86/3.95 % (1130141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.86/3.95 % (1130141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.86/3.95 % (1130141)CaDiCaL version: 2.1.3
% 23.86/3.95 % (1130141)Termination reason: Instruction limit
% 23.86/3.95 % (1130141)Termination phase: Saturation
% 23.86/3.95 % (1130141)Time elapsed: 0.201 s
% 23.86/3.95 % (1130141)Peak memory usage: 14 MB
% 23.86/3.95 % (1130141)Instructions burned: 495 (million)
% 26.72/4.28 % (1130150)Refutation not found, incomplete strategy
% 26.72/4.28 % (1130150)------------------------------
% 26.72/4.28 % (1130150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.72/4.28 % (1130150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.72/4.28 % (1130150)CaDiCaL version: 2.1.3
% 26.72/4.28 % (1130150)Termination reason: Refutation not found, incomplete strategy
% 26.72/4.28 % (1130150)Time elapsed: 0.160 s
% 26.72/4.28 % (1130150)Peak memory usage: 16 MB
% 26.72/4.28 % (1130150)Instructions burned: 407 (million)
% 26.72/4.28 % (1130150)------------------------------
% 26.72/4.28 % (1130150)------------------------------
% 26.72/4.28 % (1130157)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 26.72/4.28 % (1130157)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1154159602:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2966 on theBenchmark for (2966ds/52Mi)
% 26.72/4.28 % (1130158)dis+10_1_si=on:random_seed=985800814:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2966 on theBenchmark for (2966ds/407Mi)
% 26.72/4.28 % (1130157)Instruction limit reached!
% 26.72/4.28 % (1130157)------------------------------
% 26.72/4.28 % (1130157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.72/4.28 % (1130157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.72/4.28 % (1130157)CaDiCaL version: 2.1.3
% 26.72/4.28 % (1130157)Termination reason: Instruction limit
% 26.72/4.28 % (1130157)Termination phase: shuffling
% 26.72/4.28 % (1130157)Time elapsed: 0.018 s
% 26.72/4.28 % (1130157)Peak memory usage: 10 MB
% 26.72/4.28 % (1130157)Instructions burned: 55 (million)
% 26.72/4.28 % (1130161)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2183249377:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/2240Mi)
% 26.72/4.28 % (1130153)Instruction limit reached!
% 26.72/4.28 % (1130153)------------------------------
% 26.72/4.28 % (1130153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.72/4.28 % (1130153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.72/4.28 % (1130153)CaDiCaL version: 2.1.3
% 26.72/4.28 % (1130153)Termination reason: Instruction limit
% 26.72/4.28 % (1130153)Termination phase: Saturation
% 26.72/4.28 % (1130153)Time elapsed: 0.165 s
% 26.72/4.28 % (1130153)Peak memory usage: 15 MB
% 26.72/4.28 % (1130153)Instructions burned: 696 (million)
% 26.72/4.28 % (1130155)Refutation not found, incomplete strategy
% 26.72/4.28 % (1130155)------------------------------
% 26.72/4.28 % (1130155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.72/4.28 % (1130155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.72/4.28 % (1130155)CaDiCaL version: 2.1.3
% 26.72/4.28 % (1130155)Termination reason: Refutation not found, incomplete strategy
% 26.72/4.28 % (1130155)Time elapsed: 0.067 s
% 26.72/4.28 % (1130155)Peak memory usage: 16 MB
% 26.72/4.28 % (1130155)Instructions burned: 154 (million)
% 26.72/4.28 % (1130155)------------------------------
% 26.72/4.28 % (1130155)------------------------------
% 26.72/4.28 % (1130163)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=2250427674:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2965 on theBenchmark for (2965ds/336Mi)
% 26.72/4.28 % (1130145)Instruction limit reached!
% 26.72/4.28 % (1130145)------------------------------
% 26.72/4.28 % (1130145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.72/4.28 % (1130145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.72/4.28 % (1130145)CaDiCaL version: 2.1.3
% 26.72/4.28 % (1130145)Termination reason: Instruction limit
% 26.72/4.28 % (1130145)Termination phase: Saturation
% 26.72/4.28 % (1130145)Time elapsed: 0.260 s
% 26.72/4.28 % (1130145)Peak memory usage: 16 MB
% 26.72/4.28 % (1130145)Instructions burned: 670 (million)
% 26.72/4.28 % (1130164)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=151844448:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2965 on theBenchmark for (2965ds/1142Mi)
% 26.72/4.28 % (1130167)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1527767062:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2965 on theBenchmark for (2965ds/376Mi)
% 26.72/4.28 % (1130163)Refutation not found, incomplete strategy
% 27.92/4.47 % (1130163)------------------------------
% 27.92/4.47 % (1130163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.92/4.47 % (1130163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.92/4.47 % (1130163)CaDiCaL version: 2.1.3
% 27.92/4.47 % (1130163)Termination reason: Refutation not found, incomplete strategy
% 27.92/4.47 % (1130163)Time elapsed: 0.039 s
% 27.92/4.47 % (1130163)Peak memory usage: 14 MB
% 27.92/4.47 % (1130163)Instructions burned: 190 (million)
% 27.92/4.47 % (1130163)------------------------------
% 27.92/4.47 % (1130163)------------------------------
% 27.92/4.47 % (1130170)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=2611825891:i=766:bd=all:rtra=on_2965 on theBenchmark for (2965ds/766Mi)
% 27.92/4.47 % (1130167)Refutation not found, incomplete strategy
% 27.92/4.47 % (1130167)------------------------------
% 27.92/4.47 % (1130167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.92/4.47 % (1130167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.92/4.47 % (1130167)CaDiCaL version: 2.1.3
% 27.92/4.47 % (1130167)Termination reason: Refutation not found, incomplete strategy
% 27.92/4.47 % (1130167)Time elapsed: 0.088 s
% 27.92/4.47 % (1130167)Peak memory usage: 14 MB
% 27.92/4.47 % (1130167)Instructions burned: 202 (million)
% 27.92/4.47 % (1130167)------------------------------
% 27.92/4.47 % (1130167)------------------------------
% 27.92/4.47 % (1130158)Instruction limit reached!
% 27.92/4.47 % (1130158)------------------------------
% 27.92/4.47 % (1130158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.92/4.47 % (1130158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.92/4.47 % (1130158)CaDiCaL version: 2.1.3
% 27.92/4.47 % (1130158)Termination reason: Instruction limit
% 27.92/4.47 % (1130158)Termination phase: Saturation
% 27.92/4.47 % (1130158)Time elapsed: 0.162 s
% 27.92/4.47 % (1130158)Peak memory usage: 15 MB
% 27.92/4.47 % (1130158)Instructions burned: 408 (million)
% 27.92/4.47 % (1130172)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 27.92/4.47 % (1130172)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=2687173857:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2964 on theBenchmark for (2964ds/959Mi)
% 27.92/4.47 % (1130173)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=2058929100:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2964 on theBenchmark for (2964ds/6359Mi)
% 27.92/4.47 % (1130170)Instruction limit reached!
% 27.92/4.47 % (1130170)------------------------------
% 27.92/4.47 % (1130170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.92/4.47 % (1130170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.92/4.47 % (1130170)CaDiCaL version: 2.1.3
% 27.92/4.47 % (1130170)Termination reason: Instruction limit
% 27.92/4.47 % (1130170)Termination phase: Saturation
% 27.92/4.47 % (1130170)Time elapsed: 0.177 s
% 27.92/4.47 % (1130170)Peak memory usage: 19 MB
% 27.92/4.47 % (1130170)Instructions burned: 769 (million)
% 27.92/4.47 % (1130176)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3207210289:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2963 on theBenchmark for (2963ds/35Mi)
% 27.92/4.47 % (1130176)Instruction limit reached!
% 27.92/4.47 % (1130176)------------------------------
% 27.92/4.47 % (1130176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.92/4.47 % (1130176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.92/4.47 % (1130176)CaDiCaL version: 2.1.3
% 27.92/4.47 % (1130176)Termination reason: Instruction limit
% 27.92/4.47 % (1130176)Termination phase: shuffling
% 27.92/4.47 % (1130176)Time elapsed: 0.006 s
% 27.92/4.47 % (1130176)Peak memory usage: 10 MB
% 27.92/4.47 % (1130176)Instructions burned: 37 (million)
% 27.92/4.47 % (1130178)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=1462227355:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2963 on theBenchmark for (2963ds/53Mi)
% 27.92/4.47 % (1130178)Instruction limit reached!
% 27.92/4.47 % (1130178)------------------------------
% 27.92/4.47 % (1130178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130178)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130178)Termination reason: Instruction limit
% 29.43/4.64 % (1130178)Termination phase: Property scanning
% 29.43/4.64 % (1130178)Time elapsed: 0.011 s
% 29.43/4.64 % (1130178)Peak memory usage: 10 MB
% 29.43/4.64 % (1130178)Instructions burned: 55 (million)
% 29.43/4.64 % (1130180)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=2051405981:s2a=on:i=876:s2at=6:nm=2:rtra=on_2963 on theBenchmark for (2963ds/876Mi)
% 29.43/4.64 % (1130172)Refutation not found, incomplete strategy
% 29.43/4.64 % (1130172)------------------------------
% 29.43/4.64 % (1130172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130172)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130172)Termination reason: Refutation not found, incomplete strategy
% 29.43/4.64 % (1130172)Time elapsed: 0.304 s
% 29.43/4.64 % (1130172)Peak memory usage: 17 MB
% 29.43/4.64 % (1130172)Instructions burned: 760 (million)
% 29.43/4.64 % (1130172)------------------------------
% 29.43/4.64 % (1130172)------------------------------
% 29.43/4.64 % (1130182)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3490834228:i=57:ep=R:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/57Mi)
% 29.43/4.64 % (1130180)Instruction limit reached!
% 29.43/4.64 % (1130180)------------------------------
% 29.43/4.64 % (1130180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130180)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130180)Termination reason: Instruction limit
% 29.43/4.64 % (1130180)Termination phase: Saturation
% 29.43/4.64 % (1130180)Time elapsed: 0.196 s
% 29.43/4.64 % (1130180)Peak memory usage: 17 MB
% 29.43/4.64 % (1130180)Instructions burned: 880 (million)
% 29.43/4.64 % (1130184)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 29.43/4.64 % (1130182)Instruction limit reached!
% 29.43/4.64 % (1130182)------------------------------
% 29.43/4.64 % (1130182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130182)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130182)Termination reason: Instruction limit
% 29.43/4.64 % (1130182)Termination phase: Property scanning
% 29.43/4.64 % (1130182)Time elapsed: 0.022 s
% 29.43/4.64 % (1130182)Peak memory usage: 10 MB
% 29.43/4.64 % (1130182)Instructions burned: 58 (million)
% 29.43/4.64 % (1130184)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=587596823:i=306:bd=all:rtra=on_2961 on theBenchmark for (2961ds/306Mi)
% 29.43/4.64 % (1130186)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=4022057965:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2960 on theBenchmark for (2960ds/262Mi)
% 29.43/4.64 % (1130184)Instruction limit reached!
% 29.43/4.64 % (1130184)------------------------------
% 29.43/4.64 % (1130184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130184)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130184)Termination reason: Instruction limit
% 29.43/4.64 % (1130184)Termination phase: Saturation
% 29.43/4.64 % (1130184)Time elapsed: 0.064 s
% 29.43/4.64 % (1130184)Peak memory usage: 16 MB
% 29.43/4.64 % (1130184)Instructions burned: 310 (million)
% 29.43/4.64 % (1130188)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 29.43/4.64 % (1130188)ott+1002_16_sil=128000:si=on:random_seed=1451732395:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2960 on theBenchmark for (2960ds/409Mi)
% 29.43/4.64 % (1130186)Refutation not found, incomplete strategy
% 29.43/4.64 % (1130186)------------------------------
% 29.43/4.64 % (1130186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.43/4.64 % (1130186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.43/4.64 % (1130186)CaDiCaL version: 2.1.3
% 29.43/4.64 % (1130186)Termination reason: Refutation not found, incomplete strategy
% 29.43/4.64 % (1130186)Time elapsed: 0.093 s
% 30.48/4.84 % (1130186)Peak memory usage: 16 MB
% 30.48/4.84 % (1130186)Instructions burned: 221 (million)
% 30.48/4.84 % (1130186)------------------------------
% 30.48/4.84 % (1130186)------------------------------
% 30.48/4.84 % (1130164)Instruction limit reached!
% 30.48/4.84 % (1130164)------------------------------
% 30.48/4.84 % (1130164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.48/4.84 % (1130164)CaDiCaL version: 2.1.3
% 30.48/4.84 % (1130164)Termination reason: Instruction limit
% 30.48/4.84 % (1130164)Termination phase: Saturation
% 30.48/4.84 % (1130164)Time elapsed: 0.585 s
% 30.48/4.84 % (1130164)Peak memory usage: 18 MB
% 30.48/4.84 % (1130164)Instructions burned: 1142 (million)
% 30.48/4.84 % (1130190)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=1752198223:s2a=on:i=381:rtra=on_2959 on theBenchmark for (2959ds/381Mi)
% 30.48/4.84 % (1130191)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1671638057:cond=on:i=324:rtra=on:ntd=on_2959 on theBenchmark for (2959ds/324Mi)
% 30.48/4.84 % (1130188)Instruction limit reached!
% 30.48/4.84 % (1130188)------------------------------
% 30.48/4.84 % (1130188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.48/4.84 % (1130188)CaDiCaL version: 2.1.3
% 30.48/4.84 % (1130188)Termination reason: Instruction limit
% 30.48/4.84 % (1130188)Termination phase: Saturation
% 30.48/4.84 % (1130188)Time elapsed: 0.083 s
% 30.48/4.84 % (1130188)Peak memory usage: 14 MB
% 30.48/4.84 % (1130188)Instructions burned: 410 (million)
% 30.48/4.84 % (1130194)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=970228924:i=240:kws=inv_precedence:rtra=on_2959 on theBenchmark for (2959ds/240Mi)
% 30.48/4.84 % (1130194)Refutation not found, incomplete strategy
% 30.48/4.84 % (1130194)------------------------------
% 30.48/4.84 % (1130194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.48/4.84 % (1130194)CaDiCaL version: 2.1.3
% 30.48/4.84 % (1130194)Termination reason: Refutation not found, incomplete strategy
% 30.48/4.84 % (1130194)Time elapsed: 0.057 s
% 30.48/4.84 % (1130194)Peak memory usage: 15 MB
% 30.48/4.84 % (1130194)Instructions burned: 146 (million)
% 30.48/4.84 % (1130194)------------------------------
% 30.48/4.84 % (1130194)------------------------------
% 30.48/4.84 % (1130196)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 30.48/4.84 % (1130196)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2765494528:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2958 on theBenchmark for (2958ds/124Mi)
% 30.48/4.84 % (1130190)Instruction limit reached!
% 30.48/4.84 % (1130190)------------------------------
% 30.48/4.84 % (1130190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.48/4.84 % (1130190)CaDiCaL version: 2.1.3
% 30.48/4.84 % (1130190)Termination reason: Instruction limit
% 30.48/4.84 % (1130190)Termination phase: Saturation
% 30.48/4.84 % (1130190)Time elapsed: 0.146 s
% 30.48/4.84 % (1130190)Peak memory usage: 14 MB
% 30.48/4.84 % (1130190)Instructions burned: 381 (million)
% 30.48/4.84 % (1130191)Instruction limit reached!
% 30.48/4.84 % (1130191)------------------------------
% 30.48/4.84 % (1130191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.48/4.84 % (1130191)CaDiCaL version: 2.1.3
% 30.48/4.84 % (1130191)Termination reason: Instruction limit
% 30.48/4.84 % (1130191)Termination phase: Saturation
% 30.48/4.84 % (1130191)Time elapsed: 0.150 s
% 30.48/4.84 % (1130191)Peak memory usage: 14 MB
% 30.48/4.84 % (1130191)Instructions burned: 325 (million)
% 30.48/4.84 % (1130198)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=2715734827:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2958 on theBenchmark for (2958ds/223Mi)
% 30.48/4.84 % (1130196)Instruction limit reached!
% 30.48/4.84 % (1130196)------------------------------
% 30.48/4.84 % (1130196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.48/4.84 % (1130196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.68/5.20 % (1130196)CaDiCaL version: 2.1.3
% 33.68/5.20 % (1130196)Termination reason: Instruction limit
% 33.68/5.20 % (1130196)Termination phase: Property scanning
% 33.68/5.20 % (1130196)Time elapsed: 0.044 s
% 33.68/5.20 % (1130196)Peak memory usage: 10 MB
% 33.68/5.20 % (1130196)Instructions burned: 124 (million)
% 33.68/5.20 % (1130199)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3873372324:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2958 on theBenchmark for (2958ds/282Mi)
% 33.68/5.20 % (1130201)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=3479303466:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2957 on theBenchmark for (2957ds/464Mi)
% 33.68/5.20 % (1129981)Instruction limit reached!
% 33.68/5.20 % (1129981)------------------------------
% 33.68/5.20 % (1129981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.68/5.20 % (1129981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.68/5.20 % (1129981)CaDiCaL version: 2.1.3
% 33.68/5.20 % (1129981)Termination reason: Instruction limit
% 33.68/5.20 % (1129981)Termination phase: Saturation
% 33.68/5.20 % (1129981)Time elapsed: 3.559 s
% 33.68/5.20 % (1129981)Peak memory usage: 42 MB
% 33.68/5.20 % (1129981)Instructions burned: 5759 (million)
% 33.68/5.20 % (1130204)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1169779996:i=88:s2at=3:nm=2:rtra=on:rawr=on_2957 on theBenchmark for (2957ds/88Mi)
% 33.68/5.20 % (1130198)Instruction limit reached!
% 33.68/5.20 % (1130198)------------------------------
% 33.68/5.20 % (1130198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.68/5.20 % (1130198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.68/5.20 % (1130198)CaDiCaL version: 2.1.3
% 33.68/5.20 % (1130198)Termination reason: Instruction limit
% 33.68/5.20 % (1130198)Termination phase: Saturation
% 33.68/5.20 % (1130198)Time elapsed: 0.083 s
% 33.68/5.20 % (1130198)Peak memory usage: 12 MB
% 33.68/5.20 % (1130198)Instructions burned: 224 (million)
% 33.68/5.20 % (1130204)Instruction limit reached!
% 33.68/5.20 % (1130204)------------------------------
% 33.68/5.20 % (1130204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.68/5.20 % (1130204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.68/5.20 % (1130204)CaDiCaL version: 2.1.3
% 33.68/5.20 % (1130204)Termination reason: Instruction limit
% 33.68/5.20 % (1130204)Termination phase: Property scanning
% 33.68/5.20 % (1130204)Time elapsed: 0.018 s
% 33.68/5.20 % (1130204)Peak memory usage: 11 MB
% 33.68/5.20 % (1130204)Instructions burned: 89 (million)
% 33.68/5.20 % (1130208)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 33.68/5.20 % (1130208)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1656111202:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2956 on theBenchmark for (2956ds/4386Mi)
% 33.68/5.20 % (1130207)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=831765080:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2957 on theBenchmark for (2957ds/280Mi)
% 33.68/5.20 % (1130199)Instruction limit reached!
% 33.68/5.20 % (1130199)------------------------------
% 33.68/5.20 % (1130199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.68/5.20 % (1130199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.68/5.20 % (1130199)CaDiCaL version: 2.1.3
% 33.68/5.20 % (1130199)Termination reason: Instruction limit
% 33.68/5.20 % (1130199)Termination phase: Saturation
% 33.68/5.20 % (1130199)Time elapsed: 0.118 s
% 33.68/5.20 % (1130199)Peak memory usage: 17 MB
% 33.68/5.20 % (1130199)Instructions burned: 283 (million)
% 33.68/5.20 % (1130211)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 33.68/5.20 % (1130211)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 33.68/5.20 % (1130211)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=3256308589:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2956 on theBenchmark for (2956ds/483Mi)
% 33.68/5.20 % (1130201)Refutation not found, incomplete strategy
% 33.68/5.20 % (1130201)------------------------------
% 35.37/5.50 % (1130201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130201)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130201)Termination reason: Refutation not found, incomplete strategy
% 35.37/5.50 % (1130201)Time elapsed: 0.148 s
% 35.37/5.50 % (1130201)Peak memory usage: 16 MB
% 35.37/5.50 % (1130201)Instructions burned: 213 (million)
% 35.37/5.50 % (1130201)------------------------------
% 35.37/5.50 % (1130201)------------------------------
% 35.37/5.50 % (1130213)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1862915869:i=73:rtra=on_2956 on theBenchmark for (2956ds/73Mi)
% 35.37/5.50 % (1130207)Instruction limit reached!
% 35.37/5.50 % (1130207)------------------------------
% 35.37/5.50 % (1130207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130207)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130207)Termination reason: Instruction limit
% 35.37/5.50 % (1130207)Termination phase: Saturation
% 35.37/5.50 % (1130207)Time elapsed: 0.109 s
% 35.37/5.50 % (1130207)Peak memory usage: 13 MB
% 35.37/5.50 % (1130207)Instructions burned: 282 (million)
% 35.37/5.50 % (1130215)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2835798422:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2955 on theBenchmark for (2955ds/176Mi)
% 35.37/5.50 % (1130213)Instruction limit reached!
% 35.37/5.50 % (1130213)------------------------------
% 35.37/5.50 % (1130213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130213)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130213)Termination reason: Instruction limit
% 35.37/5.50 % (1130213)Termination phase: Property scanning
% 35.37/5.50 % (1130213)Time elapsed: 0.044 s
% 35.37/5.50 % (1130213)Peak memory usage: 10 MB
% 35.37/5.50 % (1130213)Instructions burned: 73 (million)
% 35.37/5.50 % (1130217)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 35.37/5.50 % (1130217)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=32768735:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2955 on theBenchmark for (2955ds/39Mi)
% 35.37/5.50 % (1130217)Instruction limit reached!
% 35.37/5.50 % (1130217)------------------------------
% 35.37/5.50 % (1130217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130217)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130217)Termination reason: Instruction limit
% 35.37/5.50 % (1130217)Termination phase: Property scanning
% 35.37/5.50 % (1130217)Time elapsed: 0.017 s
% 35.37/5.50 % (1130217)Peak memory usage: 10 MB
% 35.37/5.50 % (1130217)Instructions burned: 40 (million)
% 35.37/5.50 % (1130220)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4011550657:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2954 on theBenchmark for (2954ds/708Mi)
% 35.37/5.50 % (1130215)Instruction limit reached!
% 35.37/5.50 % (1130215)------------------------------
% 35.37/5.50 % (1130215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130215)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130215)Termination reason: Instruction limit
% 35.37/5.50 % (1130215)Termination phase: Saturation
% 35.37/5.50 % (1130215)Time elapsed: 0.109 s
% 35.37/5.50 % (1130215)Peak memory usage: 12 MB
% 35.37/5.50 % (1130215)Instructions burned: 177 (million)
% 35.37/5.50 % (1130211)Instruction limit reached!
% 35.37/5.50 % (1130211)------------------------------
% 35.37/5.50 % (1130211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.37/5.50 % (1130211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.37/5.50 % (1130211)CaDiCaL version: 2.1.3
% 35.37/5.50 % (1130211)Termination reason: Instruction limit
% 35.37/5.50 % (1130211)Termination phase: Saturation
% 35.37/5.50 % (1130211)Time elapsed: 0.218 s
% 35.37/5.50 % (1130211)Peak memory usage: 17 MB
% 35.37/5.50 % (1130211)Instructions burned: 484 (million)
% 35.37/5.50 % (1130222)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 36.50/5.73 % (1130222)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3977243022:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2954 on theBenchmark for (2954ds/252Mi)
% 36.50/5.73 % (1130223)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=2323229366:i=823:fsr=off:rtra=on_2954 on theBenchmark for (2954ds/823Mi)
% 36.50/5.73 % (1130222)Instruction limit reached!
% 36.50/5.73 % (1130222)------------------------------
% 36.50/5.73 % (1130222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.50/5.73 % (1130222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.50/5.73 % (1130222)CaDiCaL version: 2.1.3
% 36.50/5.73 % (1130222)Termination reason: Instruction limit
% 36.50/5.73 % (1130222)Termination phase: Saturation
% 36.50/5.73 % (1130222)Time elapsed: 0.094 s
% 36.50/5.73 % (1130222)Peak memory usage: 12 MB
% 36.50/5.73 % (1130222)Instructions burned: 254 (million)
% 36.50/5.73 % (1130226)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 36.50/5.73 % (1130226)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=1509709475:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2953 on theBenchmark for (2953ds/16202Mi)
% 36.50/5.73 % (1130161)Instruction limit reached!
% 36.50/5.73 % (1130161)------------------------------
% 36.50/5.73 % (1130161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.50/5.73 % (1130161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.50/5.73 % (1130161)CaDiCaL version: 2.1.3
% 36.50/5.73 % (1130161)Termination reason: Instruction limit
% 36.50/5.73 % (1130161)Termination phase: Saturation
% 36.50/5.73 % (1130161)Time elapsed: 1.354 s
% 36.50/5.73 % (1130161)Peak memory usage: 29 MB
% 36.50/5.73 % (1130161)Instructions burned: 2241 (million)
% 36.50/5.73 % (1130228)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2667363898:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2952 on theBenchmark for (2952ds/300Mi)
% 36.50/5.73 % (1130226)Refutation not found, incomplete strategy
% 36.50/5.73 % (1130226)------------------------------
% 36.50/5.73 % (1130226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.50/5.73 % (1130226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.50/5.73 % (1130226)CaDiCaL version: 2.1.3
% 36.50/5.73 % (1130226)Termination reason: Refutation not found, incomplete strategy
% 36.50/5.73 % (1130226)Time elapsed: 0.106 s
% 36.50/5.73 % (1130226)Peak memory usage: 15 MB
% 36.50/5.73 % (1130226)Instructions burned: 249 (million)
% 36.50/5.73 % (1130226)------------------------------
% 36.50/5.73 % (1130226)------------------------------
% 36.50/5.73 % (1130230)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 36.50/5.73 % (1130230)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 36.50/5.73 % (1130230)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=2737848755:i=177:add=on:bd=preordered:rtra=on:rawr=on_2951 on theBenchmark for (2951ds/177Mi)
% 36.50/5.73 % (1130230)Instruction limit reached!
% 36.50/5.73 % (1130230)------------------------------
% 36.50/5.73 % (1130230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.50/5.73 % (1130230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.50/5.73 % (1130230)CaDiCaL version: 2.1.3
% 36.50/5.73 % (1130230)Termination reason: Instruction limit
% 36.50/5.73 % (1130230)Termination phase: Saturation
% 36.50/5.73 % (1130230)Time elapsed: 0.066 s
% 36.50/5.73 % (1130230)Peak memory usage: 12 MB
% 36.50/5.73 % (1130230)Instructions burned: 178 (million)
% 36.50/5.73 % (1130232)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=1074610118:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2951 on theBenchmark for (2951ds/715Mi)
% 36.50/5.73 % (1130220)Instruction limit reached!
% 36.50/5.73 % (1130220)------------------------------
% 36.50/5.73 % (1130220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.50/5.73 % (1130220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.44/6.14 % (1130220)CaDiCaL version: 2.1.3
% 40.44/6.14 % (1130220)Termination reason: Instruction limit
% 40.44/6.14 % (1130220)Termination phase: Saturation
% 40.44/6.14 % (1130220)Time elapsed: 0.411 s
% 40.44/6.14 % (1130220)Peak memory usage: 16 MB
% 40.44/6.14 % (1130220)Instructions burned: 708 (million)
% 40.44/6.14 % (1130234)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 40.44/6.14 % (1130234)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 40.44/6.14 % (1130228)Instruction limit reached!
% 40.44/6.14 % (1130228)------------------------------
% 40.44/6.14 % (1130228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.44/6.14 % (1130228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.44/6.14 % (1130228)CaDiCaL version: 2.1.3
% 40.44/6.14 % (1130228)Termination reason: Instruction limit
% 40.44/6.14 % (1130228)Termination phase: Saturation
% 40.44/6.14 % (1130228)Time elapsed: 0.188 s
% 40.44/6.14 % (1130228)Peak memory usage: 13 MB
% 40.44/6.14 % (1130228)Instructions burned: 302 (million)
% 40.44/6.14 % (1130234)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1835969350:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2950 on theBenchmark for (2950ds/230Mi)
% 40.44/6.14 % (1130232)Refutation not found, incomplete strategy
% 40.44/6.14 % (1130232)------------------------------
% 40.44/6.14 % (1130232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.44/6.14 % (1130232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.44/6.14 % (1130232)CaDiCaL version: 2.1.3
% 40.44/6.14 % (1130232)Termination reason: Refutation not found, incomplete strategy
% 40.44/6.14 % (1130232)Time elapsed: 0.079 s
% 40.44/6.14 % (1130232)Peak memory usage: 15 MB
% 40.44/6.14 % (1130232)Instructions burned: 164 (million)
% 40.44/6.14 % (1130232)------------------------------
% 40.44/6.14 % (1130232)------------------------------
% 40.44/6.14 % (1130235)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1170267422:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2950 on theBenchmark for (2950ds/606Mi)
% 40.44/6.14 % (1130237)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 40.44/6.14 % (1130237)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=2809036002:lrd=on:i=841:nm=0:rtra=on_2949 on theBenchmark for (2949ds/841Mi)
% 40.44/6.14 % (1130234)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 40.44/6.14 % (1130234)Instruction limit reached!
% 40.44/6.14 % (1130234)------------------------------
% 40.44/6.14 % (1130234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.44/6.14 % (1130234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.44/6.14 % (1130234)CaDiCaL version: 2.1.3
% 40.44/6.14 % (1130234)Termination reason: Instruction limit
% 40.44/6.14 % (1130234)Termination phase: Saturation
% 40.44/6.14 % (1130234)Time elapsed: 0.152 s
% 40.44/6.14 % (1130234)Peak memory usage: 12 MB
% 40.44/6.14 % (1130234)Instructions burned: 230 (million)
% 40.44/6.14 % (1130240)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3292452447:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2948 on theBenchmark for (2948ds/445Mi)
% 40.44/6.14 % (1130223)Instruction limit reached!
% 40.44/6.14 % (1130223)------------------------------
% 40.44/6.14 % (1130223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.44/6.14 % (1130223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.44/6.14 % (1130223)CaDiCaL version: 2.1.3
% 40.44/6.14 % (1130223)Termination reason: Instruction limit
% 40.44/6.14 % (1130223)Termination phase: Saturation
% 40.44/6.14 % (1130223)Time elapsed: 0.581 s
% 40.44/6.14 % (1130223)Peak memory usage: 16 MB
% 40.44/6.14 % (1130223)Instructions burned: 823 (million)
% 40.44/6.14 % (1130242)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3278969311:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2948 on theBenchmark for (2948ds/71Mi)
% 40.44/6.14 % (1130242)Instruction limit reached!
% 40.44/6.14 % (1130242)------------------------------
% 40.44/6.14 % (1130242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.89/6.26 % (1130242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.89/6.26 % (1130242)CaDiCaL version: 2.1.3
% 40.89/6.26 % (1130242)Termination reason: Instruction limit
% 40.89/6.26 % (1130242)Termination phase: Property scanning
% 40.89/6.26 % (1130242)Time elapsed: 0.031 s
% 40.89/6.26 % (1130242)Peak memory usage: 10 MB
% 40.89/6.26 % (1130242)Instructions burned: 71 (million)
% 40.89/6.26 % (1130244)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 40.89/6.26 % (1130244)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 40.89/6.26 % (1130244)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=118566813:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2947 on theBenchmark for (2947ds/100Mi)
% 40.89/6.26 % (1130235)Instruction limit reached!
% 40.89/6.26 % (1130235)------------------------------
% 40.89/6.26 % (1130235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.89/6.26 % (1130235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.89/6.26 % (1130235)CaDiCaL version: 2.1.3
% 40.89/6.26 % (1130235)Termination reason: Instruction limit
% 40.89/6.26 % (1130235)Termination phase: Saturation
% 40.89/6.26 % (1130235)Time elapsed: 0.254 s
% 40.89/6.26 % (1130235)Peak memory usage: 15 MB
% 40.89/6.26 % (1130235)Instructions burned: 606 (million)
% 40.89/6.26 % (1130247)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 40.89/6.26 % (1130247)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=2458173385:i=1352:add=on:aac=none:rtra=on_2947 on theBenchmark for (2947ds/1352Mi)
% 40.89/6.26 % (1130244)Instruction limit reached!
% 40.89/6.26 % (1130244)------------------------------
% 40.89/6.26 % (1130244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.89/6.26 % (1130244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.89/6.26 % (1130244)CaDiCaL version: 2.1.3
% 40.89/6.26 % (1130244)Termination reason: Instruction limit
% 40.89/6.26 % (1130244)Termination phase: Saturation
% 40.89/6.26 % (1130244)Time elapsed: 0.044 s
% 40.89/6.26 % (1130244)Peak memory usage: 11 MB
% 40.89/6.26 % (1130244)Instructions burned: 100 (million)
% 40.89/6.26 % (1130208)Instruction limit reached!
% 40.89/6.26 % (1130208)------------------------------
% 40.89/6.26 % (1130208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.89/6.26 % (1130208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.89/6.26 % (1130208)CaDiCaL version: 2.1.3
% 40.89/6.26 % (1130208)Termination reason: Instruction limit
% 40.89/6.26 % (1130208)Termination phase: Saturation
% 40.89/6.26 % (1130208)Time elapsed: 0.994 s
% 40.89/6.26 % (1130208)Peak memory usage: 17 MB
% 40.89/6.26 % (1130208)Instructions burned: 4390 (million)
% 40.89/6.26 % (1130253)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=2024532871:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2946 on theBenchmark for (2946ds/1924Mi)
% 40.89/6.26 % (1130252)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=150107861:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2946 on theBenchmark for (2946ds/646Mi)
% 40.89/6.26 % (1130240)Instruction limit reached!
% 40.89/6.26 % (1130240)------------------------------
% 40.89/6.26 % (1130240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 40.89/6.26 % (1130240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 40.89/6.26 % (1130240)CaDiCaL version: 2.1.3
% 40.89/6.26 % (1130240)Termination reason: Instruction limit
% 40.89/6.26 % (1130240)Termination phase: Saturation
% 40.89/6.26 % (1130240)Time elapsed: 0.213 s
% 40.89/6.26 % (1130240)Peak memory usage: 15 MB
% 40.89/6.26 % (1130240)Instructions burned: 445 (million)
% 40.89/6.26 % (1130257)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3031214500:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2946 on theBenchmark for (2946ds/984Mi)
% 40.89/6.26 % (1130237)Instruction limit reached!
% 40.89/6.26 % (1130237)------------------------------
% 41.59/6.36 % (1130237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.59/6.36 % (1130237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.59/6.36 % (1130237)CaDiCaL version: 2.1.3
% 41.59/6.36 % (1130237)Termination reason: Instruction limit
% 41.59/6.36 % (1130237)Termination phase: Saturation
% 41.59/6.36 % (1130237)Time elapsed: 0.443 s
% 41.59/6.36 % (1130237)Peak memory usage: 17 MB
% 41.59/6.36 % (1130237)Instructions burned: 841 (million)
% 41.59/6.36 % (1130259)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=955850004:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2945 on theBenchmark for (2945ds/592Mi)
% 41.59/6.36 % (1130247)Refutation not found, incomplete strategy
% 41.59/6.36 % (1130247)------------------------------
% 41.59/6.36 % (1130247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.59/6.36 % (1130247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.59/6.36 % (1130247)CaDiCaL version: 2.1.3
% 41.59/6.36 % (1130247)Termination reason: Refutation not found, incomplete strategy
% 41.59/6.36 % (1130247)Time elapsed: 0.299 s
% 41.59/6.36 % (1130247)Peak memory usage: 17 MB
% 41.59/6.36 % (1130247)Instructions burned: 714 (million)
% 41.59/6.36 % (1130247)------------------------------
% 41.59/6.36 % (1130247)------------------------------
% 41.59/6.36 % (1130262)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=2772219393:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2944 on theBenchmark for (2944ds/872Mi)
% 41.59/6.36 % (1130252)Instruction limit reached!
% 41.59/6.36 % (1130252)------------------------------
% 41.59/6.36 % (1130252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.59/6.36 % (1130252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.59/6.36 % (1130252)CaDiCaL version: 2.1.3
% 41.59/6.36 % (1130252)Termination reason: Instruction limit
% 41.59/6.36 % (1130252)Termination phase: Saturation
% 41.59/6.36 % (1130252)Time elapsed: 0.277 s
% 41.59/6.36 % (1130252)Peak memory usage: 17 MB
% 41.59/6.36 % (1130252)Instructions burned: 647 (million)
% 41.59/6.36 % (1130264)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 41.59/6.36 % (1130264)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3581162033:i=999:add=on:rtra=on_2943 on theBenchmark for (2943ds/999Mi)
% 41.59/6.36 % (1130262)Refutation not found, incomplete strategy
% 41.59/6.36 % (1130262)------------------------------
% 41.59/6.36 % (1130262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.59/6.36 % (1130262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.59/6.36 % (1130262)CaDiCaL version: 2.1.3
% 41.59/6.36 % (1130262)Termination reason: Refutation not found, incomplete strategy
% 41.59/6.36 % (1130262)Time elapsed: 0.119 s
% 41.59/6.36 % (1130262)Peak memory usage: 15 MB
% 41.59/6.36 % (1130262)Instructions burned: 198 (million)
% 41.59/6.36 % (1130262)------------------------------
% 41.59/6.36 % (1130262)------------------------------
% 41.59/6.36 % (1130266)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 41.59/6.36 % (1130266)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=2084710628:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2942 on theBenchmark for (2942ds/244Mi)
% 41.59/6.36 % (1130259)Instruction limit reached!
% 41.59/6.36 % (1130259)------------------------------
% 41.59/6.36 % (1130259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.59/6.36 % (1130259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.59/6.36 % (1130259)CaDiCaL version: 2.1.3
% 41.59/6.36 % (1130259)Termination reason: Instruction limit
% 41.59/6.36 % (1130259)Termination phase: Saturation
% 41.59/6.36 % (1130259)Time elapsed: 0.353 s
% 41.59/6.36 % (1130259)Peak memory usage: 13 MB
% 41.59/6.36 % (1130259)Instructions burned: 592 (million)
% 41.59/6.36 % (1130268)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=3050928773:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2941 on theBenchmark for (2941ds/113Mi)
% 41.59/6.36 % (1130266)Instruction limit reached!
% 41.59/6.36 % (1130266)------------------------------
% 42.46/6.55 % (1130266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.46/6.55 % (1130266)CaDiCaL version: 2.1.3
% 42.46/6.55 % (1130266)Termination reason: Instruction limit
% 42.46/6.55 % (1130266)Termination phase: Saturation
% 42.46/6.55 % (1130266)Time elapsed: 0.119 s
% 42.46/6.55 % (1130266)Peak memory usage: 14 MB
% 42.46/6.55 % (1130266)Instructions burned: 246 (million)
% 42.46/6.55 % (1130270)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2063523457:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2941 on theBenchmark for (2941ds/7795Mi)
% 42.46/6.55 % (1130268)Instruction limit reached!
% 42.46/6.55 % (1130268)------------------------------
% 42.46/6.55 % (1130268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.46/6.55 % (1130268)CaDiCaL version: 2.1.3
% 42.46/6.55 % (1130268)Termination reason: Instruction limit
% 42.46/6.55 % (1130268)Termination phase: Property scanning
% 42.46/6.55 % (1130268)Time elapsed: 0.043 s
% 42.46/6.55 % (1130268)Peak memory usage: 10 MB
% 42.46/6.55 % (1130268)Instructions burned: 113 (million)
% 42.46/6.55 % (1130272)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3223519747:st=2:i=5026:sd=1:rtra=on:ss=axioms_2940 on theBenchmark for (2940ds/5026Mi)
% 42.46/6.55 % (1130257)Instruction limit reached!
% 42.46/6.55 % (1130257)------------------------------
% 42.46/6.55 % (1130257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.46/6.55 % (1130257)CaDiCaL version: 2.1.3
% 42.46/6.55 % (1130257)Termination reason: Instruction limit
% 42.46/6.55 % (1130257)Termination phase: Saturation
% 42.46/6.55 % (1130257)Time elapsed: 0.552 s
% 42.46/6.55 % (1130257)Peak memory usage: 16 MB
% 42.46/6.55 % (1130257)Instructions burned: 986 (million)
% 42.46/6.55 % (1130253)Instruction limit reached!
% 42.46/6.55 % (1130253)------------------------------
% 42.46/6.55 % (1130253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.46/6.55 % (1130253)CaDiCaL version: 2.1.3
% 42.46/6.55 % (1130253)Termination reason: Instruction limit
% 42.46/6.55 % (1130253)Termination phase: Saturation
% 42.46/6.55 % (1130253)Time elapsed: 0.640 s
% 42.46/6.55 % (1130253)Peak memory usage: 20 MB
% 42.46/6.55 % (1130253)Instructions burned: 1928 (million)
% 42.46/6.55 % (1130270)Refutation not found, incomplete strategy
% 42.46/6.55 % (1130270)------------------------------
% 42.46/6.55 % (1130270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.46/6.55 % (1130270)CaDiCaL version: 2.1.3
% 42.46/6.55 % (1130270)Termination reason: Refutation not found, incomplete strategy
% 42.46/6.55 % (1130270)Time elapsed: 0.060 s
% 42.46/6.55 % (1130270)Peak memory usage: 15 MB
% 42.46/6.55 % (1130270)Instructions burned: 138 (million)
% 42.46/6.55 % (1130270)------------------------------
% 42.46/6.55 % (1130270)------------------------------
% 42.46/6.55 % (1130275)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 42.46/6.55 % (1130275)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=1870463812:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2940 on theBenchmark for (2940ds/763Mi)
% 42.46/6.55 % (1130276)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2286773193:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2940 on theBenchmark for (2940ds/1144Mi)
% 42.46/6.55 % (1130277)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 42.46/6.55 % (1130277)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1205829893:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2940 on theBenchmark for (2940ds/52Mi)
% 42.46/6.55 % (1130272)Refutation not found, incomplete strategy
% 42.46/6.55 % (1130272)------------------------------
% 42.46/6.55 % (1130272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.46/6.55 % (1130272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.57/6.82 % (1130272)CaDiCaL version: 2.1.3
% 43.57/6.82 % (1130272)Termination reason: Refutation not found, incomplete strategy
% 43.57/6.82 % (1130272)Time elapsed: 0.056 s
% 43.57/6.82 % (1130272)Peak memory usage: 14 MB
% 43.57/6.82 % (1130272)Instructions burned: 141 (million)
% 43.57/6.82 % (1130277)Instruction limit reached!
% 43.57/6.82 % (1130277)------------------------------
% 43.57/6.82 % (1130277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.57/6.82 % (1130277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.57/6.82 % (1130277)CaDiCaL version: 2.1.3
% 43.57/6.82 % (1130277)Termination reason: Instruction limit
% 43.57/6.82 % (1130277)Termination phase: shuffling
% 43.57/6.82 % (1130277)Time elapsed: 0.017 s
% 43.57/6.82 % (1130277)Peak memory usage: 10 MB
% 43.57/6.82 % (1130277)Instructions burned: 52 (million)
% 43.57/6.82 % (1130272)------------------------------
% 43.57/6.82 % (1130272)------------------------------
% 43.57/6.82 % (1130281)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=3632000718:i=1724:fsr=off:rtra=on:fe=abstraction_2940 on theBenchmark for (2940ds/1724Mi)
% 43.57/6.82 % (1130282)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=1520736341:i=439:add=on:slsql=off:rtra=on:ntd=on_2940 on theBenchmark for (2940ds/439Mi)
% 43.57/6.82 % (1130276)Refutation not found, incomplete strategy
% 43.57/6.82 % (1130276)------------------------------
% 43.57/6.82 % (1130276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.57/6.82 % (1130276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.57/6.82 % (1130276)CaDiCaL version: 2.1.3
% 43.57/6.82 % (1130276)Termination reason: Refutation not found, incomplete strategy
% 43.57/6.82 % (1130276)Time elapsed: 0.047 s
% 43.57/6.82 % (1130276)Peak memory usage: 14 MB
% 43.57/6.82 % (1130276)Instructions burned: 203 (million)
% 43.57/6.82 % (1130276)------------------------------
% 43.57/6.82 % (1130276)------------------------------
% 43.57/6.82 % (1130285)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2537490106:i=6395:sd=1:rtra=on:ss=axioms_2939 on theBenchmark for (2939ds/6395Mi)
% 43.57/6.82 % (1130275)Refutation not found, incomplete strategy
% 43.57/6.82 % (1130275)------------------------------
% 43.57/6.82 % (1130275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.57/6.82 % (1130275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.57/6.82 % (1130275)CaDiCaL version: 2.1.3
% 43.57/6.82 % (1130275)Termination reason: Refutation not found, incomplete strategy
% 43.57/6.82 % (1130275)Time elapsed: 0.064 s
% 43.57/6.82 % (1130275)Peak memory usage: 16 MB
% 43.57/6.82 % (1130275)Instructions burned: 147 (million)
% 43.57/6.82 % (1130275)------------------------------
% 43.57/6.82 % (1130275)------------------------------
% 43.57/6.82 % (1130287)WARNING Broken Constraint: if ho_split_queue_lambda_weight(5) has been set then ho_split_queue(off) is equal to on
% 43.57/6.82 % (1130287)ott+2_16:1_sil=128000:si=on:hsqlw=5:sos=on:urr=on:bce=on:uwa=off:random_seed=2397716560:i=6762:add=off:bd=all:rtra=on:ss=axioms:ntd=on_2939 on theBenchmark for (2939ds/6762Mi)
% 43.57/6.82 % (1130285)Refutation not found, incomplete strategy
% 43.57/6.82 % (1130285)------------------------------
% 43.57/6.82 % (1130285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.57/6.82 % (1130285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.57/6.82 % (1130285)CaDiCaL version: 2.1.3
% 43.57/6.82 % (1130285)Termination reason: Refutation not found, incomplete strategy
% 43.57/6.82 % (1130285)Time elapsed: 0.028 s
% 43.57/6.82 % (1130285)Peak memory usage: 15 MB
% 43.57/6.82 % (1130285)Instructions burned: 134 (million)
% 43.57/6.82 % (1130285)------------------------------
% 43.57/6.82 % (1130285)------------------------------
% 43.57/6.82 % (1130289)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 43.57/6.82 % (1130289)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2025696199:s2a=on:i=376:add=on:rtra=on:fe=axiom:fdi=1024_2939 on theBenchmark for (2939ds/376Mi)
% 43.57/6.82 % (1130264)Instruction limit reached!
% 43.57/6.82 % (1130264)------------------------------
% 43.57/6.82 % (1130264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.80/7.10 % (1130264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.80/7.10 % (1130264)CaDiCaL version: 2.1.3
% 46.80/7.10 % (1130264)Termination reason: Instruction limit
% 46.80/7.10 % (1130264)Termination phase: Saturation
% 46.80/7.10 % (1130264)Time elapsed: 0.466 s
% 46.80/7.10 % (1130264)Peak memory usage: 16 MB
% 46.80/7.10 % (1130264)Instructions burned: 999 (million)
% 46.80/7.10 % (1130291)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2405667276:i=965:bd=all:ins=4:rtra=on_2939 on theBenchmark for (2939ds/965Mi)
% 46.80/7.10 % (1130287)Refutation not found, incomplete strategy
% 46.80/7.10 % (1130287)------------------------------
% 46.80/7.10 % (1130287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.80/7.10 % (1130287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.80/7.10 % (1130287)CaDiCaL version: 2.1.3
% 46.80/7.10 % (1130287)Termination reason: Refutation not found, incomplete strategy
% 46.80/7.10 % (1130287)Time elapsed: 0.071 s
% 46.80/7.10 % (1130287)Peak memory usage: 16 MB
% 46.80/7.10 % (1130287)Instructions burned: 178 (million)
% 46.80/7.10 % (1130287)------------------------------
% 46.80/7.10 % (1130287)------------------------------
% 46.80/7.10 % (1130289)Instruction limit reached!
% 46.80/7.10 % (1130289)------------------------------
% 46.80/7.10 % (1130289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.80/7.10 % (1130289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.80/7.10 % (1130289)CaDiCaL version: 2.1.3
% 46.80/7.10 % (1130289)Termination reason: Instruction limit
% 46.80/7.10 % (1130289)Termination phase: Saturation
% 46.80/7.10 % (1130289)Time elapsed: 0.076 s
% 46.80/7.10 % (1130289)Peak memory usage: 13 MB
% 46.80/7.10 % (1130289)Instructions burned: 379 (million)
% 46.80/7.10 % (1130293)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1446400864:i=5013:sd=1:rtra=on:ss=axioms:sgt=64_2938 on theBenchmark for (2938ds/5013Mi)
% 46.80/7.10 % (1130294)dis+2_1_tgt=full:si=on:uwa=one_side_interpreted:random_seed=1398590209:i=1583:kws=inv_frequency:bd=preordered:nm=0:rtra=on_2938 on theBenchmark for (2938ds/1583Mi)
% 46.80/7.10 % (1130282)Instruction limit reached!
% 46.80/7.10 % (1130282)------------------------------
% 46.80/7.10 % (1130282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.80/7.10 % (1130282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.80/7.10 % (1130282)CaDiCaL version: 2.1.3
% 46.80/7.10 % (1130282)Termination reason: Instruction limit
% 46.80/7.10 % (1130282)Termination phase: Saturation
% 46.80/7.10 % (1130282)Time elapsed: 0.171 s
% 46.80/7.10 % (1130282)Peak memory usage: 14 MB
% 46.80/7.10 % (1130282)Instructions burned: 441 (million)
% 46.80/7.10 % (1130305)WARNING Broken Constraint: if sine_level_split_queue_ratios(1,32) has been set then sine_level_split_queue(off) is equal to on
% 46.80/7.10 % (1130305)WARNING Broken Constraint: if ho_split_queue_cutoffs(2) has been set then ho_split_queue(off) is equal to on
% 46.80/7.10 % (1130305)WARNING Broken Constraint: if sine_to_age_generality_threshold(16) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 46.80/7.10 % (1130305)WARNING Broken Constraint: if ho_split_queue_ratios(4,1) has been set then ho_split_queue(off) is equal to on
% 46.80/7.10 % (1130305)ott+1002_1_slsqr=1,32:sil=128000:fde=none:e2e=on:hsqc=2:si=on:sp=const_min:sos=on:uwa=interpreted_only:s2agt=16:chr=on:random_seed=692333814:hsqr=4,1:avsq=on:cond=on:i=1774:add=on:avsqr=1,16:kws=arity_squared:nm=120:rtra=on:fe=abstraction:ss=axioms_2938 on theBenchmark for (2938ds/1774Mi)
% 46.80/7.10 % (1130305)Refutation not found, incomplete strategy
% 46.80/7.10 % (1130305)------------------------------
% 46.80/7.10 % (1130305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.80/7.10 % (1130305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.80/7.10 % (1130305)CaDiCaL version: 2.1.3
% 46.80/7.10 % (1130305)Termination reason: Refutation not found, incomplete strategy
% 46.80/7.10 % (1130305)Time elapsed: 0.056 s
% 46.80/7.10 % (1130305)Peak memory usage: 15 MB
% 46.80/7.10 % (1130305)Instructions burned: 140 (million)
% 46.80/7.10 % (1130305)------------------------------
% 46.80/7.10 % (1130305)------------------------------
% 46.80/7.10 % (1130339)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1966916381:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2937 on theBenchmark for (2937ds/515Mi)
% 48.35/7.30 % (1130015)Instruction limit reached!
% 48.35/7.30 % (1130015)------------------------------
% 48.35/7.30 % (1130015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/7.30 % (1130015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/7.30 % (1130015)CaDiCaL version: 2.1.3
% 48.35/7.30 % (1130015)Termination reason: Instruction limit
% 48.35/7.30 % (1130015)Termination phase: Saturation
% 48.35/7.30 % (1130015)Time elapsed: 5.364 s
% 48.35/7.30 % (1130015)Peak memory usage: 48 MB
% 48.35/7.30 % (1130015)Instructions burned: 9841 (million)
% 48.35/7.30 % (1130383)WARNING Broken Constraint: if sine_to_age_generality_threshold(60) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 48.35/7.30 % (1130383)lrs-30_5:1_sil=128000:drc=off:sas=cadical:si=on:lma=off:cbe=off:uwa=one_side_interpreted:s2agt=60:lwlo=on:random_seed=145272286:avsq=on:i=1297:add=on:avsqr=1,8:rtra=on:fsd=on_2936 on theBenchmark for (2936ds/1297Mi)
% 48.35/7.30 % (1130294)Instruction limit reached!
% 48.35/7.30 % (1130294)------------------------------
% 48.35/7.30 % (1130294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/7.30 % (1130294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/7.30 % (1130294)CaDiCaL version: 2.1.3
% 48.35/7.30 % (1130294)Termination reason: Instruction limit
% 48.35/7.30 % (1130294)Termination phase: Saturation
% 48.35/7.30 % (1130294)Time elapsed: 0.331 s
% 48.35/7.30 % (1130294)Peak memory usage: 24 MB
% 48.35/7.30 % (1130294)Instructions burned: 1587 (million)
% 48.35/7.30 % (1130339)Instruction limit reached!
% 48.35/7.30 % (1130339)------------------------------
% 48.35/7.30 % (1130339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/7.30 % (1130339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/7.30 % (1130339)CaDiCaL version: 2.1.3
% 48.35/7.30 % (1130339)Termination reason: Instruction limit
% 48.35/7.30 % (1130339)Termination phase: Saturation
% 48.35/7.30 % (1130339)Time elapsed: 0.206 s
% 48.35/7.30 % (1130339)Peak memory usage: 15 MB
% 48.35/7.30 % (1130339)Instructions burned: 515 (million)
% 48.35/7.30 % (1130426)dis+1002_1_to=lpo:drc=ordering:fde=none:bsd=on:si=on:ser=on:sp=const_min:cbe=off:uwa=off:flr=on:random_seed=4192043087:s2a=on:i=611:rtra=on:gsp=on_2935 on theBenchmark for (2935ds/611Mi)
% 48.35/7.30 % (1130430)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 48.35/7.30 % (1130430)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=2458706682:i=72:bd=all:rtra=on_2935 on theBenchmark for (2935ds/72Mi)
% 48.35/7.30 % (1130426)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 48.35/7.30 % (1130291)Instruction limit reached!
% 48.35/7.30 % (1130291)------------------------------
% 48.35/7.30 % (1130291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/7.30 % (1130291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/7.30 % (1130291)CaDiCaL version: 2.1.3
% 48.35/7.30 % (1130291)Termination reason: Instruction limit
% 48.35/7.30 % (1130291)Termination phase: Saturation
% 48.35/7.30 % (1130291)Time elapsed: 0.420 s
% 48.35/7.30 % (1130291)Peak memory usage: 20 MB
% 48.35/7.30 % (1130291)Instructions burned: 966 (million)
% 48.35/7.30 % (1130430)Instruction limit reached!
% 48.35/7.30 % (1130430)------------------------------
% 48.35/7.30 % (1130430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.35/7.30 % (1130430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.35/7.30 % (1130430)CaDiCaL version: 2.1.3
% 48.35/7.30 % (1130430)Termination reason: Instruction limit
% 48.35/7.30 % (1130430)Termination phase: Property scanning
% 48.35/7.30 % (1130430)Time elapsed: 0.026 s
% 48.35/7.30 % (1130430)Peak memory usage: 10 MB
% 48.35/7.30 % (1130430)Instructions burned: 74 (million)
% 48.35/7.30 % (1130455)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3411391139:hsq=on:hsqr=16,1:s2a=on:i=6580:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2934 on theBenchmark for (2934ds/6580Mi)
% 48.35/7.30 % (1130456)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=1771345272:i=6209:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2934 on theBenchmark for (2934ds/6209Mi)
% 50.06/7.65 % (1130456)Refutation not found, incomplete strategy
% 50.06/7.65 % (1130456)------------------------------
% 50.06/7.65 % (1130456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130456)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130456)Termination reason: Refutation not found, incomplete strategy
% 50.06/7.65 % (1130456)Time elapsed: 0.093 s
% 50.06/7.65 % (1130456)Peak memory usage: 16 MB
% 50.06/7.65 % (1130456)Instructions burned: 220 (million)
% 50.06/7.65 % (1130456)------------------------------
% 50.06/7.65 % (1130456)------------------------------
% 50.06/7.65 % (1130426)Instruction limit reached!
% 50.06/7.65 % (1130426)------------------------------
% 50.06/7.65 % (1130426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130426)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130426)Termination reason: Instruction limit
% 50.06/7.65 % (1130426)Termination phase: Saturation
% 50.06/7.65 % (1130426)Time elapsed: 0.155 s
% 50.06/7.65 % (1130426)Peak memory usage: 17 MB
% 50.06/7.65 % (1130426)Instructions burned: 612 (million)
% 50.06/7.65 % (1130465)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 50.06/7.65 % (1130465)ott+1002_16_sil=128000:si=on:random_seed=1247980174:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2933 on theBenchmark for (2933ds/409Mi)
% 50.06/7.65 % (1130464)lrs+1002_14_sil=128000:e2e=on:si=on:urr=on:nwc=1.2:random_seed=3240390359:cond=fast:i=1003:bd=all:fsr=off:rtra=on:sup=off_2933 on theBenchmark for (2933ds/1003Mi)
% 50.06/7.65 % (1130465)Instruction limit reached!
% 50.06/7.65 % (1130465)------------------------------
% 50.06/7.65 % (1130465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130465)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130465)Termination reason: Instruction limit
% 50.06/7.65 % (1130465)Termination phase: Saturation
% 50.06/7.65 % (1130465)Time elapsed: 0.084 s
% 50.06/7.65 % (1130465)Peak memory usage: 14 MB
% 50.06/7.65 % (1130465)Instructions burned: 414 (million)
% 50.06/7.65 % (1130468)ott+10_1024_sil=128000:tgt=ground:cnfonf=lazy_pi_sigma_gen:si=on:sp=const_frequency:sos=on:lma=off:bsr=on:uwa=one_side_interpreted:nwc=20:random_seed=90034091:cond=on:i=403:kws=precedence:erml=3:bs=unit_only:bd=all:rtra=on:ss=axioms:er=known:ntd=on_2932 on theBenchmark for (2932ds/403Mi)
% 50.06/7.65 % (1130468)Refutation not found, incomplete strategy
% 50.06/7.65 % (1130468)------------------------------
% 50.06/7.65 % (1130468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130468)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130468)Termination reason: Refutation not found, incomplete strategy
% 50.06/7.65 % (1130468)Time elapsed: 0.034 s
% 50.06/7.65 % (1130468)Peak memory usage: 16 MB
% 50.06/7.65 % (1130468)Instructions burned: 149 (million)
% 50.06/7.65 % (1130468)------------------------------
% 50.06/7.65 % (1130468)------------------------------
% 50.06/7.65 % (1130470)lrs+10_1_sil=128000:fde=none:cnfonf=lazy_pi_sigma_gen:si=on:random_seed=3680299582:st=2:i=6843:sd=2:bd=all:rtra=on:sup=off:ss=axioms_2932 on theBenchmark for (2932ds/6843Mi)
% 50.06/7.65 % (1130281)Instruction limit reached!
% 50.06/7.65 % (1130281)------------------------------
% 50.06/7.65 % (1130281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130281)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130281)Termination reason: Instruction limit
% 50.06/7.65 % (1130281)Termination phase: Saturation
% 50.06/7.65 % (1130281)Time elapsed: 0.814 s
% 50.06/7.65 % (1130281)Peak memory usage: 19 MB
% 50.06/7.65 % (1130281)Instructions burned: 1724 (million)
% 50.06/7.65 % (1130470)Refutation not found, incomplete strategy
% 50.06/7.65 % (1130470)------------------------------
% 50.06/7.65 % (1130470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130470)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130470)Termination reason: Refutation not found, incomplete strategy
% 50.06/7.65 % (1130470)Time elapsed: 0.025 s
% 50.06/7.65 % (1130470)Peak memory usage: 15 MB
% 50.06/7.65 % (1130470)Instructions burned: 105 (million)
% 50.06/7.65 % (1130470)------------------------------
% 50.06/7.65 % (1130470)------------------------------
% 50.06/7.65 % (1130473)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4010611813:uwa_fpi=on:i=888:doe=on:bd=preordered:rtra=on:fsd=on_2931 on theBenchmark for (2931ds/888Mi)
% 50.06/7.65 % (1130472)lrs+10_2:1_si=on:random_seed=3915940065:s2a=on:i=506:rtra=on:fe=abstraction_2931 on theBenchmark for (2931ds/506Mi)
% 50.06/7.65 % (1130464)Refutation not found, incomplete strategy
% 50.06/7.65 % (1130464)------------------------------
% 50.06/7.65 % (1130464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130464)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130464)Termination reason: Refutation not found, incomplete strategy
% 50.06/7.65 % (1130464)Time elapsed: 0.186 s
% 50.06/7.65 % (1130464)Peak memory usage: 15 MB
% 50.06/7.65 % (1130464)Instructions burned: 466 (million)
% 50.06/7.65 % (1130464)------------------------------
% 50.06/7.65 % (1130464)------------------------------
% 50.06/7.65 % (1130476)WARNING Broken Constraint: if positive_literal_split_queue_ratios(32,1) has been set then positive_literal_split_queue(off) is equal to on
% 50.06/7.65 % (1130476)ott+1002_3:2_to=kbo:sil=128000:cnfonf=lazy_gen:si=on:sp=reverse_frequency:lma=off:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=1.5:random_seed=3715986209:cond=fast:i=416:fgj=on:bd=preordered:rtra=on_2931 on theBenchmark for (2931ds/416Mi)
% 50.06/7.65 % (1130383)Instruction limit reached!
% 50.06/7.65 % (1130383)------------------------------
% 50.06/7.65 % (1130383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130383)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130383)Termination reason: Instruction limit
% 50.06/7.65 % (1130383)Termination phase: Saturation
% 50.06/7.65 % (1130383)Time elapsed: 0.509 s
% 50.06/7.65 % (1130383)Peak memory usage: 15 MB
% 50.06/7.65 % (1130383)Instructions burned: 1299 (million)
% 50.06/7.65 % (1130478)dis+10_3:2_sfv=off:to=kbo:plsq=on:fde=unused:e2e=on:si=on:sp=reverse_frequency:acc=on:uwa=off:fd=preordered:slsqc=1:pe=on:slsq=on:random_seed=1064314537:hsq=on:hsqr=16,1:avsq=on:s2a=on:i=13534:hsql=off:nm=16:nicw=on:ins=20:rtra=on:ss=axioms:ntd=on_2931 on theBenchmark for (2931ds/13534Mi)
% 50.06/7.65 % (1130478)Refutation not found, incomplete strategy
% 50.06/7.65 % (1130478)------------------------------
% 50.06/7.65 % (1130478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130478)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130478)Termination reason: Refutation not found, incomplete strategy
% 50.06/7.65 % (1130478)Time elapsed: 0.095 s
% 50.06/7.65 % (1130478)Peak memory usage: 15 MB
% 50.06/7.65 % (1130478)Instructions burned: 220 (million)
% 50.06/7.65 % (1130478)------------------------------
% 50.06/7.65 % (1130478)------------------------------
% 50.06/7.65 % (1130473)Instruction limit reached!
% 50.06/7.65 % (1130473)------------------------------
% 50.06/7.65 % (1130473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130473)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130473)Termination reason: Instruction limit
% 50.06/7.65 % (1130473)Termination phase: Saturation
% 50.06/7.65 % (1130473)Time elapsed: 0.180 s
% 50.06/7.65 % (1130473)Peak memory usage: 13 MB
% 50.06/7.65 % (1130473)Instructions burned: 893 (million)
% 50.06/7.65 % (1130480)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(10) has been set then forward_subsumption_demodulation(off) is equal to on
% 50.06/7.65 % (1130480)dis+1002_3_tgt=ground:cnfonf=lazy_simp:si=on:sp=unary_first:cbe=off:uwa=ground:updr=off:random_seed=2052382117:i=206:fgj=on:hud=10:nm=30:rtra=on:fsdmm=10_2929 on theBenchmark for (2929ds/206Mi)
% 50.06/7.65 % (1130481)dis+1010_1_sfv=off:slsqr=2,1:to=kbo:plsq=on:cnfonf=lazy_simp:si=on:cbe=off:uwa=hol:nwc=2:s2agt=16:slsq=on:random_seed=1170708091:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2295:avsqr=1,16:aac=none:hud=3:rtra=on_2929 on theBenchmark for (2929ds/2295Mi)
% 50.06/7.65 % (1130476)Instruction limit reached!
% 50.06/7.65 % (1130476)------------------------------
% 50.06/7.65 % (1130476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130476)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130476)Termination reason: Instruction limit
% 50.06/7.65 % (1130476)Termination phase: Saturation
% 50.06/7.65 % (1130476)Time elapsed: 0.173 s
% 50.06/7.65 % (1130476)Peak memory usage: 16 MB
% 50.06/7.65 % (1130476)Instructions burned: 416 (million)
% 50.06/7.65 % (1130472)Instruction limit reached!
% 50.06/7.65 % (1130472)------------------------------
% 50.06/7.65 % (1130472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130472)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130472)Termination reason: Instruction limit
% 50.06/7.65 % (1130472)Termination phase: Saturation
% 50.06/7.65 % (1130472)Time elapsed: 0.203 s
% 50.06/7.65 % (1130472)Peak memory usage: 15 MB
% 50.06/7.65 % (1130472)Instructions burned: 506 (million)
% 50.06/7.65 % (1130484)ott+1010_1_to=lpo:sil=128000:fde=none:si=on:sp=unary_first:uwa=off:nwc=1:random_seed=2870908018:i=637:piset=not:ep=RST:bd=all:av=off:rtra=on_2929 on theBenchmark for (2929ds/637Mi)
% 50.06/7.65 % (1130485)dis+1002_15:31_sil=128000:cnfonf=lazy_not_gen:si=on:cbe=off:uwa=off:random_seed=894790231:hsq=on:i=667:rtra=on:ixr=off_2929 on theBenchmark for (2929ds/667Mi)
% 50.06/7.65 % (1130480)Instruction limit reached!
% 50.06/7.65 % (1130480)------------------------------
% 50.06/7.65 % (1130480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130480)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130480)Termination reason: Instruction limit
% 50.06/7.65 % (1130480)Termination phase: Saturation
% 50.06/7.65 % (1130480)Time elapsed: 0.079 s
% 50.06/7.65 % (1130480)Peak memory usage: 12 MB
% 50.06/7.65 % (1130480)Instructions burned: 207 (million)
% 50.06/7.65 % (1130488)lrs-1004_16_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:lma=off:uwa=off:random_seed=2366220189:i=1801:bd=preordered:nm=32:rtra=on:fdi=1024_2928 on theBenchmark for (2928ds/1801Mi)
% 50.06/7.65 % (1130481) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1129842-1130481"...
% 50.06/7.65 % (1130485)Instruction limit reached!
% 50.06/7.65 % (1130485)------------------------------
% 50.06/7.65 % (1130485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130485)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130485)Termination reason: Instruction limit
% 50.06/7.65 % (1130485)Termination phase: Saturation
% 50.06/7.65 % (1130485)Time elapsed: 0.259 s
% 50.06/7.65 % (1130485)Peak memory usage: 14 MB
% 50.06/7.65 % (1130485)Instructions burned: 669 (million)
% 50.06/7.65 % (1130490)lrs+1002_1024_anc=all_dependent:sil=128000:drc=off:cnfonf=lazy_not_be_gen:si=on:cbe=off:cs=on:random_seed=1871302568:i=555:aac=none:rtra=on:fe=abstraction:ntd=on_2926 on theBenchmark for (2926ds/555Mi)
% 50.06/7.65 % (1130484)Instruction limit reached!
% 50.06/7.65 % (1130484)------------------------------
% 50.06/7.65 % (1130484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 50.06/7.65 % (1130484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 50.06/7.65 % (1130484)CaDiCaL version: 2.1.3
% 50.06/7.65 % (1130484)Termination reason: Instruction limit
% 50.06/7.65 % (1130484)Termination phase: Saturation
% 50.06/7.65 % (1130484)Time elapsed: 0.285 s
% 50.06/7.65 % (1130484)Peak memory usage: 18 MB
% 50.06/7.65 % (1130484)Instructions burned: 637 (million)
% 50.06/7.65 % (1130481)...printing done.
% 50.06/7.65 % (1130481)Refutation found. Thanks to Tanya!
% 50.06/7.65 % SZS status Theorem for theBenchmark
% 50.06/7.65 % SZS output start Proof for theBenchmark
% See solution above
% 51.26/7.71 % (1130481)------------------------------
% 51.26/7.71 % (1130481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.26/7.71 % (1130481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.26/7.71 % (1130481)CaDiCaL version: 2.1.3
% 51.26/7.71 % (1130481)Termination reason: Refutation
% 51.26/7.71 % (1130481)Time elapsed: 0.338 s
% 51.26/7.71 % (1130481)Peak memory usage: 16 MB
% 51.26/7.71 % (1130481)Instructions burned: 1553 (million)
% 51.26/7.71 % (1129842)Success in time 7.427 s
% 51.26/7.71 % Vampire exiting
%------------------------------------------------------------------------------