%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL960^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:14:56 AM UTC 2026
% Result : Theorem 0.56s 0.32s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 199 ( 48 unt; 0 typ; 8 def)
% Number of atoms : 3761 ( 727 equ; 0 cnn)
% Maximal formula atoms : 38 ( 18 avg)
% Number of connectives : 6837 ( 220 ~; 688 |; 119 &;4815 @)
% ( 7 <=>; 538 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 169 ( 169 >; 0 *; 0 +; 0 <<)
% Number of symbols : 127 ( 122 usr; 16 con; 0-4 aty)
% ( 422 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 1296 ( 0 sgn 513 !; 2 ?;1296 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
f: $i > $i > mworld > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
sK0: mworld > $i ).
thf(func_def_29,type,
sF1: $o ).
thf(func_def_30,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
sK2: mworld > mworld ).
thf(func_def_35,type,
sK3: $i > mworld > mworld ).
thf(func_def_36,type,
sK4: $i > mworld > $i ).
thf(func_def_37,type,
sK5: $i > mworld > mworld ).
thf(func_def_38,type,
sK6: mworld > $i ).
thf(func_def_39,type,
sK7: $i > mworld > mworld ).
thf(func_def_40,type,
sK8: $i > mworld > $i ).
thf(func_def_41,type,
sK9: $i > mworld > mworld ).
thf(func_def_42,type,
sK10: $i > mworld > mworld ).
thf(func_def_43,type,
sK11: mworld > $i > mworld ).
thf(func_def_44,type,
sK12: mworld > $i > $i ).
thf(func_def_45,type,
sK13: mworld > $i > mworld ).
thf(func_def_46,type,
sK14: mworld > $i > mworld ).
thf(func_def_47,type,
sK15: mworld > mworld > $i > mworld ).
thf(func_def_48,type,
sK16: mworld > $i > mworld ).
thf(func_def_49,type,
sK17: mworld > $i > mworld ).
thf(func_def_50,type,
sK18: mworld > $i > mworld ).
thf(func_def_51,type,
sK19: mworld > mworld > $i > mworld ).
thf(func_def_52,type,
sK20: mworld > $i > mworld ).
thf(func_def_53,type,
sK21: mworld > $i > mworld ).
thf(func_def_54,type,
sK22: mworld > $i > mworld ).
thf(func_def_55,type,
sK23: mworld > mworld > $i > mworld ).
thf(func_def_56,type,
sK24: mworld > mworld > $i > mworld ).
thf(func_def_57,type,
sK25: mworld > mworld > $i > mworld ).
thf(func_def_58,type,
sK26: mworld > mworld > $i > mworld ).
thf(func_def_59,type,
sK27: mworld > $i > mworld ).
thf(func_def_60,type,
sK28: mworld > $i > mworld ).
thf(func_def_61,type,
sK29: mworld > $i > mworld ).
thf(func_def_62,type,
sK30: mworld > $i > mworld ).
thf(func_def_63,type,
sK31: mworld > $i > mworld ).
thf(func_def_64,type,
sK32: $i > mworld > $i ).
thf(func_def_65,type,
sK33: $i > mworld > mworld ).
thf(func_def_66,type,
sK34: mworld > $i > $i ).
thf(func_def_67,type,
sK35: mworld > $i > mworld ).
thf(func_def_68,type,
sK36: mworld > $i > mworld ).
thf(func_def_69,type,
sK37: mworld > $i > mworld ).
thf(func_def_70,type,
sK38: mworld > $i > mworld ).
thf(func_def_71,type,
sK39: mworld > mworld > $i > mworld ).
thf(func_def_72,type,
sK40: mworld > $i > mworld ).
thf(func_def_73,type,
sK41: mworld > $i > mworld > mworld ).
thf(func_def_74,type,
sK42: mworld > $i > mworld ).
thf(func_def_75,type,
sK43: mworld > $i > mworld ).
thf(func_def_76,type,
sK44: mworld > $i > mworld ).
thf(func_def_77,type,
sK45: mworld > mworld > $i > mworld ).
thf(func_def_78,type,
sK46: mworld > mworld > $i > mworld ).
thf(func_def_79,type,
sK47: mworld > $i > mworld ).
thf(func_def_80,type,
sK48: $i > mworld > mworld ).
thf(func_def_81,type,
sK49: mworld > $i > mworld ).
thf(func_def_82,type,
sK50: mworld > $i > mworld ).
thf(func_def_83,type,
sK51: mworld > $i > mworld ).
thf(func_def_84,type,
sK52: mworld > $i > mworld ).
thf(func_def_85,type,
sK53: mworld > mworld > $i > mworld ).
thf(func_def_86,type,
sK54: mworld > mworld > $i > mworld ).
thf(func_def_87,type,
sK55: mworld > $i > mworld ).
thf(func_def_88,type,
sK56: mworld > $i > mworld ).
thf(func_def_89,type,
sK57: mworld > mworld > $i > mworld ).
thf(func_def_90,type,
sK58: mworld > $i > mworld ).
thf(func_def_91,type,
sK59: mworld > $i > mworld ).
thf(func_def_92,type,
sK60: mworld > $i > mworld ).
thf(func_def_93,type,
sK61: mworld > $i > mworld ).
thf(func_def_94,type,
sK62: mworld > $i > mworld ).
thf(func_def_95,type,
sK63: mworld > $i > mworld ).
thf(func_def_96,type,
sK64: mworld > $i > mworld ).
thf(func_def_97,type,
sK65: mworld > $i > mworld ).
thf(func_def_98,type,
sK66: mworld > mworld > $i > mworld ).
thf(func_def_99,type,
sK67: mworld > $i > mworld ).
thf(func_def_100,type,
sK68: mworld > $i > mworld > mworld ).
thf(func_def_101,type,
sK69: mworld > $i > mworld ).
thf(func_def_102,type,
sK70: mworld > $i > mworld ).
thf(func_def_103,type,
sK71: mworld > $i > mworld ).
thf(func_def_104,type,
sK72: mworld > $i > mworld ).
thf(func_def_105,type,
sK73: mworld > mworld > $i > mworld ).
thf(func_def_106,type,
sK74: mworld > mworld > $i > mworld ).
thf(func_def_107,type,
sK75: mworld > $i > mworld ).
thf(func_def_108,type,
sK76: mworld ).
thf(func_def_109,type,
sK77: mworld > $i > $i ).
thf(func_def_110,type,
sK78: $i > mworld > $i > mworld ).
thf(func_def_111,type,
sK79: mworld > $i > mworld ).
thf(func_def_112,type,
sK80: $i > mworld > mworld > $i > mworld ).
thf(func_def_113,type,
sK81: $i > mworld > mworld ).
thf(func_def_114,type,
sK82: $i > mworld > mworld ).
thf(func_def_115,type,
sK83: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) )
= mexists_di ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f13,conjecture,
( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mbox
@ ( mforall_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ X2 @ X1 ) ) @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) @ ( mbox @ ( f @ X2 @ X1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mbox @ ( f @ X4 @ X3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish256) ).
thf(f14,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mbox
@ ( mforall_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ X2 @ X1 ) ) @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) @ ( mbox @ ( f @ X2 @ X1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mbox @ ( f @ X4 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
thf(f15,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f16,plain,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mbox
@ ( mforall_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ X2 @ X1 ) ) @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ X2 @ X0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ X2 @ X2 ) ) ) ) ) @ ( mbox @ ( f @ X2 @ X1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mbox @ ( f @ X4 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f17,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mbox
@ ( mforall_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ Y2 @ Y1 ) ) @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) @ ( mbox @ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f20,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[],[f12]) ).
thf(f21,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f23,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f27,plain,
! [X1: mworld,X0: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f35,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f40,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mbox
@ ( mforall_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ Y2 @ Y1 ) ) @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) @ ( mbox @ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f41,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X1 @ X0 )
= $true ),
inference(rectify,[],[f27]) ).
thf(f43,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f46,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X1 @ X0 )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f47,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f48,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f52,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f53,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mbox
@ ( mforall_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( f @ Y2 @ Y1 ) ) @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( f @ Y2 @ Y0 ) ) @ ( mbox @ ( mnot @ ( mbox @ ( f @ Y2 @ Y2 ) ) ) ) ) @ ( mbox @ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mexists_di
@ ^ [Y0: $i] :
( mbox
@ ( mforall_di
@ ^ [Y1: $i] : ( mbox @ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f55,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f58,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
& ( eiw_di @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f53,f48,f51,f52,f51,f55,f44,f51,f55,f43,f51,f52,f51,f43,f51,f51,f47,f51,f51,f52,f43,f51,f51,f47,f51,f51,f51,f47,f44,f51,f55,f51]) ).
thf(f59,definition,
( sF1
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
& ( eiw_di @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f60,plain,
$true != sF1,
inference(definition_folding,[],[f58,f59]) ).
thf(f61,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
& ( eiw_di @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y0 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y2 ) ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( f @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( f @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f59]) ).
thf(f821,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) ) )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( f @ Y4 @ Y2 @ Y5 ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f822,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) ) )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( f @ Y4 @ Y2 @ Y5 ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK76 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f821]) ).
thf(f823,plain,
( ( ( ( mrel @ mactual @ sK76 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f822]) ).
thf(f824,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f823]) ).
thf(f826,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f824]) ).
thf(f827,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y0 ) ) ) ) ) ) )
= $true )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f824]) ).
thf(f828,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f827]) ).
thf(f829,plain,
! [X1: mworld] :
( ( $true = sF1 )
| ( $true
= ( ( mrel @ sK76 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f828]) ).
thf(f830,plain,
! [X1: mworld] :
( ( $true = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ X1 ) ) ) ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f829]) ).
thf(f831,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ X1 ) ) ) )
@ X2 ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f830]) ).
thf(f832,plain,
! [X2: $i,X1: mworld] :
( ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ X1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f831]) ).
thf(f833,plain,
! [X2: $i,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ X1 ) ) )
= $true )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f832]) ).
thf(f834,plain,
! [X2: $i,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ X1 ) )
@ ( sK77 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f833]) ).
thf(f835,plain,
! [X2: $i,X1: mworld] :
( ( $true = sF1 )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
& ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f834]) ).
thf(f836,plain,
! [X2: $i,X1: mworld] :
( ( $true = sF1 )
| ( $true
= ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f835]) ).
thf(f838,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK77 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f837]) ).
thf(f839,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f838]) ).
thf(f840,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f839]) ).
thf(f841,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK77 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f840]) ).
thf(f842,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( ( eiw_di @ X4 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f841]) ).
thf(f843,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f842]) ).
thf(f844,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f843]) ).
thf(f845,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f843]) ).
thf(f846,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) ) ) )
@ X5 )
= $true )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f845]) ).
thf(f847,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( ( mrel @ X3 @ X5 )
=> ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) ) ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f846]) ).
thf(f848,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f847]) ).
thf(f849,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f848]) ).
thf(f850,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( $true = sF1 )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f849]) ).
thf(f851,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f850]) ).
thf(f852,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) )
@ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f851]) ).
thf(f853,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) )
@ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ ( sK79 @ X5 @ X4 ) )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f852]) ).
thf(f854,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
= $true )
| ( $true = sF1 )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( ( mrel @ X5 @ ( sK78 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( ( mrel @ X5 @ ( sK79 @ X5 @ X4 ) )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f853]) ).
thf(f855,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( ( mrel @ X5 @ ( sK79 @ X5 @ X4 ) )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( ( mrel @ X5 @ ( sK78 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f854]) ).
thf(f856,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) )
= $false )
| ( ( ( mrel @ X5 @ ( sK78 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
= $false )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f855]) ).
thf(f860,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( ( mrel @ X5 @ ( sK78 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f856]) ).
thf(f861,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f860]) ).
thf(f866,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( $true = sF1 )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK79 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ X7 ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f861]) ).
thf(f867,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true
= ( ( mrel @ ( sK79 @ X5 @ X4 ) @ X7 )
=> ( f @ X4 @ X4 @ X7 ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ X3 @ X5 )
= $false ) ),
inference(beta-eta_normalization,[],[f866]) ).
thf(f868,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ ( sK79 @ X5 @ X4 ) @ X7 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f867]) ).
thf(f869,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = sF1 )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) ) ) ) )
@ X5 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f844]) ).
thf(f870,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $true
= ( ( mrel @ X3 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f869]) ).
thf(f871,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) ) )
| ( $true = sF1 )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f872,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) ) )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f871]) ).
thf(f873,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f872]) ).
thf(f875,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $true = sF1 )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f873]) ).
thf(f876,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ X6 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ Y0 ) )
@ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f875]) ).
thf(f877,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( ( mrel @ X5 @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) )
=> ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f876]) ).
thf(f878,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true
= ( ( mrel @ X5 @ X6 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ sK76 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f877]) ).
thf(f886,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true = sF1 )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f878]) ).
thf(f887,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false ) ),
inference(not_proxy_clausification,[],[f886]) ).
thf(f888,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = sF1 )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f887]) ).
thf(f889,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( ( mrel @ X6 @ ( sK82 @ X4 @ X6 ) )
=> ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f888]) ).
thf(f890,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f889]) ).
thf(f898,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK76 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) )
@ sK83 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f826]) ).
thf(f899,plain,
( ( $true = sF1 )
| ( ( ( mrel @ sK76 @ sK83 )
=> ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK83 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ sK83 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f898]) ).
thf(f900,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK83 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ sK83 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f899]) ).
thf(f902,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK83 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ sK83 ) ) ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f900]) ).
thf(f903,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK83 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) )
& ( eiw_di @ Y0 @ sK83 ) )
@ sK84 )
= $true )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f902]) ).
thf(f904,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK83 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK84 @ Y2 ) ) ) ) ) ) )
& ( eiw_di @ sK84 @ sK83 ) )
= $true )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f903]) ).
thf(f905,plain,
( ( $true = sF1 )
| ( $true
= ( eiw_di @ sK84 @ sK83 ) ) ),
inference(and_proxy_clausification,[],[f904]) ).
thf(f906,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK83 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK84 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f904]) ).
thf(f907,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK83 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK84 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f906]) ).
thf(f908,plain,
! [X1: mworld] :
( ( $true = sF1 )
| ( $true
= ( ( mrel @ sK83 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK84 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f907]) ).
thf(f909,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK83 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK84 @ Y1 ) ) ) ) )
= $true )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f908]) ).
thf(f910,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK83 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK84 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f909]) ).
thf(f911,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK84 @ Y0 ) ) ) ) )
| ( $true = sF1 )
| ( $false
= ( mrel @ sK83 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f910]) ).
thf(f912,plain,
! [X2: $i,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK84 @ Y0 ) ) )
= $true )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true = sF1 )
| ( $false
= ( mrel @ sK83 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f911]) ).
thf(f913,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK84 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ sK83 @ X1 ) )
| ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f912]) ).
thf(f914,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $true = sF1 )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ sK84 @ X3 ) )
= $true )
| ( $false
= ( mrel @ sK83 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f913]) ).
thf(f915,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ sK83 @ X1 ) )
| ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f914]) ).
thf(f1561,definition,
( spl85_162
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl85_162])],[avatar_definition]) ).
thf(f1582,definition,
( spl85_167
<=> ! [X5: mworld,X4: $i,X2: $i,X7: mworld,X6: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ ( sK79 @ X5 @ X4 ) @ X7 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X3 @ X5 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl85_167])],[avatar_definition]) ).
thf(f1583,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ ( sK79 @ X5 @ X4 ) @ X7 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false ) )
| ~ spl85_167 ),
inference(avatar_component_clause,[],[f1582]) ).
thf(f1584,plain,
( spl85_167
| spl85_162 ),
inference(avatar_split_clause,[],[f868,f1561,f1582]) ).
thf(f1598,definition,
( spl85_171
<=> ! [X5: mworld,X4: $i,X2: $i,X6: mworld,X3: mworld,X1: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl85_171])],[avatar_definition]) ).
thf(f1599,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false ) )
| ~ spl85_171 ),
inference(avatar_component_clause,[],[f1598]) ).
thf(f1600,plain,
( spl85_162
| spl85_171 ),
inference(avatar_split_clause,[],[f890,f1598,f1561]) ).
thf(f1610,definition,
( spl85_174
<=> ! [X2: $i,X1: mworld] :
( ( $true
= ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl85_174])],[avatar_definition]) ).
thf(f1611,plain,
( ! [X2: $i,X1: mworld] :
( ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_174 ),
inference(avatar_component_clause,[],[f1610]) ).
thf(f1612,plain,
( spl85_162
| spl85_174 ),
inference(avatar_split_clause,[],[f836,f1610,f1561]) ).
thf(f1619,definition,
( spl85_176
<=> ! [X2: $i,X1: mworld,X3: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( $false
= ( mrel @ sK83 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl85_176])],[avatar_definition]) ).
thf(f1620,plain,
( ! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ sK83 @ X1 ) ) )
| ~ spl85_176 ),
inference(avatar_component_clause,[],[f1619]) ).
thf(f1621,plain,
( spl85_176
| spl85_162 ),
inference(avatar_split_clause,[],[f915,f1561,f1619]) ).
thf(f1623,definition,
( spl85_177
<=> ( $true
= ( eiw_di @ sK84 @ sK83 ) ) ),
introduced(definition,[new_symbols(definition,[spl85_177])],[avatar_definition]) ).
thf(f1625,plain,
( ( $true
= ( eiw_di @ sK84 @ sK83 ) )
| ~ spl85_177 ),
inference(avatar_component_clause,[],[f1623]) ).
thf(f1626,plain,
( spl85_162
| spl85_177 ),
inference(avatar_split_clause,[],[f905,f1623,f1561]) ).
thf(f1627,plain,
~ spl85_162,
inference(avatar_split_clause,[],[f60,f1561]) ).
thf(f1641,plain,
( ! [X2: $i,X1: mworld] :
( ( $true
= ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) )
| ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_174 ),
inference(forward_demodulation,[],[f1611,f46]) ).
thf(f1642,plain,
( ! [X2: $i,X1: mworld] :
( ( $true
= ( eiw_di @ ( sK77 @ X1 @ X2 ) @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_174 ),
inference(trivial_inequality_removal,[],[f1641]) ).
thf(f1643,plain,
( ! [X2: $i,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ sK83 @ X1 ) ) )
| ~ spl85_176 ),
inference(forward_demodulation,[],[f1620,f46]) ).
thf(f1644,plain,
( ! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ sK83 @ X1 ) ) )
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1643]) ).
thf(f1645,plain,
( ! [X2: $i,X3: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( $true = $false ) )
| ~ spl85_176 ),
inference(forward_demodulation,[],[f1644,f46]) ).
thf(f1646,plain,
( ! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( f @ X2 @ sK84 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1645]) ).
thf(f1657,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true = $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false ) )
| ~ spl85_171 ),
inference(forward_demodulation,[],[f1599,f46]) ).
thf(f1658,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X3 @ X5 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false ) )
| ~ spl85_171 ),
inference(trivial_inequality_removal,[],[f1657]) ).
thf(f1659,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true = $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_171 ),
inference(forward_demodulation,[],[f1658,f46]) ).
thf(f1660,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false ) )
| ~ spl85_171 ),
inference(trivial_inequality_removal,[],[f1659]) ).
thf(f1661,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true = $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false ) )
| ~ spl85_171 ),
inference(forward_demodulation,[],[f1660,f46]) ).
thf(f1662,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false ) )
| ~ spl85_171 ),
inference(trivial_inequality_removal,[],[f1661]) ).
thf(f1663,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true = $false ) )
| ~ spl85_171 ),
inference(forward_demodulation,[],[f1662,f46]) ).
thf(f1664,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ ( sK80 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( ( f @ X4 @ X4 @ ( sK82 @ X4 @ X6 ) )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) )
| ~ spl85_171 ),
inference(trivial_inequality_removal,[],[f1663]) ).
thf(f1667,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true = $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) ) )
| ~ spl85_167 ),
inference(forward_demodulation,[],[f1583,f46]) ).
thf(f1668,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) ) )
| ~ spl85_167 ),
inference(trivial_inequality_removal,[],[f1667]) ).
thf(f1669,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) )
| ~ spl85_167 ),
inference(forward_demodulation,[],[f1668,f46]) ).
thf(f1670,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( mrel @ X5 @ X6 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( mrel @ X1 @ X3 )
= $false ) )
| ~ spl85_167 ),
inference(trivial_inequality_removal,[],[f1669]) ).
thf(f1671,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ X1 @ X3 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) )
| ~ spl85_167 ),
inference(forward_demodulation,[],[f1670,f46]) ).
thf(f1672,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( mrel @ X1 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) ) )
| ~ spl85_167 ),
inference(trivial_inequality_removal,[],[f1671]) ).
thf(f1673,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $true = $false )
| ( ( mrel @ sK76 @ X1 )
= $false ) )
| ~ spl85_167 ),
inference(forward_demodulation,[],[f1672,f46]) ).
thf(f1674,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( mrel @ sK76 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) )
| ~ spl85_167 ),
inference(trivial_inequality_removal,[],[f1673]) ).
thf(f1675,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) ) )
| ~ spl85_167 ),
inference(forward_demodulation,[],[f1674,f46]) ).
thf(f1676,plain,
( ! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ X2 @ ( sK78 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK77 @ X1 @ X2 ) @ X6 ) )
| ( ( eiw_di @ X4 @ X3 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) )
| ~ spl85_167 ),
inference(trivial_inequality_removal,[],[f1675]) ).
thf(f1677,plain,
( ! [X2: mworld,X3: mworld,X0: $i,X6: mworld,X4: mworld,X5: mworld] :
( ( ( eiw_di @ sK84 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X6 ) )
| ( ( eiw_di @ X0 @ X4 )
= $false )
| ( $true = $false )
| ( ( f @ X0 @ ( sK77 @ X2 @ sK84 ) @ X3 )
= $true )
| ( ( f @ X0 @ X0 @ X5 )
= $true ) )
| ~ spl85_167
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1676,f1646]) ).
thf(f1681,plain,
( ! [X2: mworld,X3: mworld,X0: $i,X6: mworld,X4: mworld,X5: mworld] :
( ( ( f @ X0 @ ( sK77 @ X2 @ sK84 ) @ X3 )
= $true )
| ( ( f @ X0 @ X0 @ X5 )
= $true )
| ( ( eiw_di @ X0 @ X4 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X6 ) )
| ( ( eiw_di @ sK84 @ X2 )
= $false ) )
| ~ spl85_167
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1677]) ).
thf(f1690,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld] :
( ( $true != $true )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( $true
= ( f @ ( sK77 @ X0 @ sK84 ) @ ( sK77 @ X0 @ sK84 ) @ X1 ) ) )
| ~ spl85_167
| ~ spl85_176 ),
inference(equality_factoring,[],[f1681]) ).
thf(f1695,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld] :
( ( $true
= ( f @ ( sK77 @ X0 @ sK84 ) @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) )
| ~ spl85_167
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1706,definition,
( spl85_179
<=> ! [X1: mworld] :
( $false
= ( eiw_di @ sK84 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl85_179])],[avatar_definition]) ).
thf(f1707,plain,
( ! [X1: mworld] :
( $false
= ( eiw_di @ sK84 @ X1 ) )
| ~ spl85_179 ),
inference(avatar_component_clause,[],[f1706]) ).
thf(f1725,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X4: mworld,X5: mworld] :
( ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $true = $false )
| ( $false
= ( f @ ( sK77 @ X0 @ sK84 ) @ ( sK77 @ X0 @ sK84 ) @ ( sK82 @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1664,f1695]) ).
thf(f1734,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X4: mworld,X5: mworld] :
( ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $true = $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $false
= ( f @ ( sK77 @ X0 @ sK84 ) @ ( sK77 @ X0 @ sK84 ) @ ( sK82 @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(duplicate_literal_removal,[],[f1725]) ).
thf(f1735,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( f @ ( sK77 @ X0 @ sK84 ) @ ( sK77 @ X0 @ sK84 ) @ ( sK82 @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1734]) ).
thf(f1741,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X6 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1735,f1695]) ).
thf(f1746,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X6 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( $true = $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(duplicate_literal_removal,[],[f1741]) ).
thf(f1747,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X6 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X5 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1746]) ).
thf(f1758,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( $false != $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(equality_factoring,[],[f1747]) ).
thf(f1762,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X4 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1758]) ).
thf(f1773,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $true = $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1642,f1762]) ).
thf(f1777,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld] :
( ( $true = $false )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(duplicate_literal_removal,[],[f1773]) ).
thf(f1778,plain,
( ! [X2: mworld,X3: mworld,X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X3 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1777]) ).
thf(f1788,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( $false != $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(equality_factoring,[],[f1778]) ).
thf(f1790,plain,
( ! [X2: mworld,X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X2 ) )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1788]) ).
thf(f1799,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1642,f1790]) ).
thf(f1801,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( $true = $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(duplicate_literal_removal,[],[f1799]) ).
thf(f1802,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ ( sK77 @ X0 @ sK84 ) @ X1 ) )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1801]) ).
thf(f1809,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(constrained_superposition,[],[f1642,f1802]) ).
thf(f1810,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( ( eiw_di @ sK84 @ X0 )
= $false ) )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(duplicate_literal_removal,[],[f1809]) ).
thf(f1811,plain,
( ! [X0: mworld] :
( ( eiw_di @ sK84 @ X0 )
= $false )
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(trivial_inequality_removal,[],[f1810]) ).
thf(f1815,plain,
( spl85_179
| ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176 ),
inference(avatar_split_clause,[],[f1811,f1619,f1610,f1598,f1582,f1706]) ).
thf(f1818,plain,
( ( $true = $false )
| ~ spl85_177
| ~ spl85_179 ),
inference(constrained_superposition,[],[f1625,f1707]) ).
thf(f1821,plain,
( $false
| ~ spl85_177
| ~ spl85_179 ),
inference(trivial_inequality_removal,[],[f1818]) ).
thf(f1822,plain,
( ~ spl85_177
| ~ spl85_179 ),
inference(avatar_contradiction_clause,[],[f1821]) ).
cnf(s165,plain,
( spl85_162
| spl85_167 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s169,plain,
( spl85_162
| spl85_171 ),
inference(sat_conversion,[],[f1600]) ).
cnf(s172,plain,
( spl85_162
| spl85_174 ),
inference(sat_conversion,[],[f1612]) ).
cnf(s174,plain,
( spl85_162
| spl85_176 ),
inference(sat_conversion,[],[f1621]) ).
cnf(s175,plain,
( spl85_162
| spl85_177 ),
inference(sat_conversion,[],[f1626]) ).
cnf(s176,plain,
~ spl85_162,
inference(sat_conversion,[],[f1627]) ).
cnf(s180,plain,
( ~ spl85_167
| ~ spl85_171
| ~ spl85_174
| ~ spl85_176
| spl85_179 ),
inference(sat_conversion,[],[f1815]) ).
cnf(s183,plain,
( ~ spl85_177
| ~ spl85_179 ),
inference(sat_conversion,[],[f1822]) ).
cnf(s185,plain,
spl85_177,
inference(rat,[],[s175,s176]) ).
cnf(s186,plain,
~ spl85_179,
inference(rat,[],[s183,s185]) ).
cnf(s187,plain,
spl85_176,
inference(rat,[],[s174,s176]) ).
cnf(s189,plain,
spl85_174,
inference(rat,[],[s172,s176]) ).
cnf(s192,plain,
spl85_171,
inference(rat,[],[s169,s176]) ).
cnf(s193,plain,
~ spl85_167,
inference(rat,[],[s180,s186,s187,s189,s192]) ).
cnf(s197,plain,
$false,
inference(rat,[],[s165,s193,s176]) ).
thf(f1824,plain,
$false,
inference(avatar_sat_refutation,[],[s197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL960^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 10:57:01 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.32 % (4125284)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.56/0.32 % (4125291)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3446517517:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.56/0.32 % (4125291)Instruction limit reached!
% 0.56/0.32 % (4125291)------------------------------
% 0.56/0.32 % (4125291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125291)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125291)Termination reason: Instruction limit
% 0.56/0.32 % (4125291)Termination phase: Saturation
% 0.56/0.32 % (4125291)Time elapsed: 0.001 s
% 0.56/0.32 % (4125291)Peak memory usage: 11 MB
% 0.56/0.32 % (4125291)Instructions burned: 5 (million)
% 0.56/0.32 % (4125295)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.56/0.32 % (4125295)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
% 0.56/0.32 % (4125289)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3060605283:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.56/0.32 % (4125293)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3428482254:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.56/0.32 % (4125292)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=2954542647: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)
% 0.56/0.32 % (4125295)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=3284076449:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.56/0.32 % (4125294)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4005755216:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.56/0.32 % (4125297)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3731122314:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.56/0.32 % (4125297)Instruction limit reached!
% 0.56/0.32 % (4125297)------------------------------
% 0.56/0.32 % (4125297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125297)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125297)Termination reason: Instruction limit
% 0.56/0.32 % (4125297)Termination phase: Saturation
% 0.56/0.32 % (4125297)Time elapsed: 0.002 s
% 0.56/0.32 % (4125297)Peak memory usage: 11 MB
% 0.56/0.32 % (4125297)Instructions burned: 8 (million)
% 0.56/0.32 % (4125290)lrs+10_16_si=on:nwc=1.5:random_seed=653584422:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.56/0.32 % (4125293)Instruction limit reached!
% 0.56/0.32 % (4125293)------------------------------
% 0.56/0.32 % (4125293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125293)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125293)Termination reason: Instruction limit
% 0.56/0.32 % (4125293)Termination phase: Saturation
% 0.56/0.32 % (4125293)Time elapsed: 0.014 s
% 0.56/0.32 % (4125293)Peak memory usage: 12 MB
% 0.56/0.32 % (4125293)Instructions burned: 25 (million)
% 0.56/0.32 % (4125304)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1896885114:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.56/0.32 % (4125304)Instruction limit reached!
% 0.56/0.32 % (4125304)------------------------------
% 0.56/0.32 % (4125304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125304)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125304)Termination reason: Instruction limit
% 0.56/0.32 % (4125304)Termination phase: Saturation
% 0.56/0.32 % (4125304)Time elapsed: 0.001 s
% 0.56/0.32 % (4125304)Peak memory usage: 11 MB
% 0.56/0.32 % (4125304)Instructions burned: 6 (million)
% 0.56/0.32 % (4125308)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4285669635:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.56/0.32 % (4125306)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.32 % (4125308)Instruction limit reached!
% 0.56/0.32 % (4125308)------------------------------
% 0.56/0.32 % (4125308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125308)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125308)Termination reason: Instruction limit
% 0.56/0.32 % (4125308)Termination phase: Saturation
% 0.56/0.32 % (4125308)Time elapsed: 0.004 s
% 0.56/0.32 % (4125308)Peak memory usage: 12 MB
% 0.56/0.32 % (4125308)Instructions burned: 16 (million)
% 0.56/0.32 % (4125306)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2966577032:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.56/0.32 % (4125290)Instruction limit reached!
% 0.56/0.32 % (4125290)------------------------------
% 0.56/0.32 % (4125290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125290)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125290)Termination reason: Instruction limit
% 0.56/0.32 % (4125290)Termination phase: Saturation
% 0.56/0.32 % (4125290)Time elapsed: 0.023 s
% 0.56/0.32 % (4125290)Peak memory usage: 12 MB
% 0.56/0.32 % (4125290)Instructions burned: 18 (million)
% 0.56/0.32 % (4125289)Instruction limit reached!
% 0.56/0.32 % (4125289)------------------------------
% 0.56/0.32 % (4125289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125289)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125289)Termination reason: Instruction limit
% 0.56/0.32 % (4125289)Termination phase: Saturation
% 0.56/0.32 % (4125289)Time elapsed: 0.040 s
% 0.56/0.32 % (4125289)Peak memory usage: 12 MB
% 0.56/0.32 % (4125289)Instructions burned: 89 (million)
% 0.56/0.32 % (4125310)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
% 0.56/0.32 % (4125310)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.32 % (4125306)Instruction limit reached!
% 0.56/0.32 % (4125306)------------------------------
% 0.56/0.32 % (4125306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125306)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125306)Termination reason: Instruction limit
% 0.56/0.32 % (4125306)Termination phase: Saturation
% 0.56/0.32 % (4125306)Time elapsed: 0.007 s
% 0.56/0.32 % (4125306)Peak memory usage: 11 MB
% 0.56/0.32 % (4125306)Instructions burned: 8 (million)
% 0.56/0.32 % (4125310)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=374887298:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.56/0.32 % (4125295) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4125284-4125295"...
% 0.56/0.32 % (4125294)Instruction limit reached!
% 0.56/0.32 % (4125294)------------------------------
% 0.56/0.32 % (4125294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125294)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125294)Termination reason: Instruction limit
% 0.56/0.32 % (4125294)Termination phase: Saturation
% 0.56/0.32 % (4125294)Time elapsed: 0.045 s
% 0.56/0.32 % (4125294)Peak memory usage: 12 MB
% 0.56/0.32 % (4125294)Instructions burned: 76 (million)
% 0.56/0.32 % (4125310)Instruction limit reached!
% 0.56/0.32 % (4125310)------------------------------
% 0.56/0.32 % (4125310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125310)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125310)Termination reason: Instruction limit
% 0.56/0.32 % (4125310)Termination phase: Saturation
% 0.56/0.32 % (4125310)Time elapsed: 0.007 s
% 0.56/0.32 % (4125310)Peak memory usage: 12 MB
% 0.56/0.32 % (4125310)Instructions burned: 32 (million)
% 0.56/0.32 % (4125295)...printing done.
% 0.56/0.32 % (4125295)Refutation found. Thanks to Tanya!
% 0.56/0.32 % SZS status Theorem for theBenchmark
% 0.56/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.32 % (4125295)------------------------------
% 0.56/0.32 % (4125295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (4125295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (4125295)CaDiCaL version: 2.1.3
% 0.56/0.32 % (4125295)Termination reason: Refutation
% 0.56/0.32 % (4125295)Time elapsed: 0.059 s
% 0.56/0.32 % (4125295)Peak memory usage: 14 MB
% 0.56/0.32 % (4125295)Instructions burned: 132 (million)
% 0.56/0.32 % (4125284)Success in time 0.093 s
% 0.56/0.32 % Vampire exiting
%------------------------------------------------------------------------------