%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:15:29 AM UTC 2026
% Result : Theorem 2.39s 0.58s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 9
% Syntax : Number of formulae : 155 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 2961 ( 559 equ; 0 cnn)
% Maximal formula atoms : 38 ( 19 avg)
% Number of connectives : 5701 ( 86 ~; 410 |; 108 &;4193 @)
% ( 0 <=>; 497 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 40 usr; 8 con; 0-4 aty)
% ( 383 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 1034 ( 595 ^; 437 !; 2 ?;1034 :)
% 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,
vNOT: $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: mworld > $i ).
thf(func_def_29,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK1: mworld ).
thf(func_def_34,type,
sK2: mworld > $i > $i ).
thf(func_def_35,type,
sK3: $i > mworld > mworld > $i > mworld ).
thf(func_def_36,type,
sK4: $i > mworld > mworld ).
thf(func_def_37,type,
sK5: $i > mworld > mworld ).
thf(func_def_38,type,
sK6: mworld > $i > mworld ).
thf(func_def_39,type,
sK7: $i > mworld > $i > mworld ).
thf(func_def_40,type,
sK8: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
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,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f17,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f19,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f23,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f27,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f31,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f35,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f37,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,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(f39,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,[],[f38]) ).
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,[],[f39]) ).
thf(f42,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f43,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f48,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f50,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f52,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f53,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f54,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(f57,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] :
( ( eiw_di @ Y3 @ Y2 )
& ( Y1 @ 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] :
( ( Y3 @ Y5 )
& ( Y4 @ 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] :
( ( Y3 @ Y5 )
& ( Y4 @ 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] :
( ( Y3 @ Y5 )
& ( Y4 @ 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] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ 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,[],[f54,f42,f48,f46,f48,f52,f53,f48,f52,f44,f48,f46,f48,f44,f48,f48,f43,f48,f48,f46,f44,f48,f48,f43,f48,f48,f48,f43,f53,f48,f52,f48]) ).
thf(f58,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y1 )
& ( !! @ 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 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ 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 @ Y3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( f @ Y4 @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y1 )
& ( !! @ 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 )
=> ( f @ Y5 @ Y3 @ Y7 ) ) )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( f @ Y5 @ Y5 @ Y8 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y4 @ Y6 )
=> ( ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y5 @ Y2 @ 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 @ Y3 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( f @ Y4 @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ 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 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ 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 @ Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ 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 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ 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 @ Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f63,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f64,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ 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 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ 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 @ Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f65,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ 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 )
=> ( f @ Y4 @ Y2 @ Y6 ) ) )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( f @ Y4 @ Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y3 @ Y5 )
=> ( ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y4 @ Y1 @ 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 @ Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK1 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ 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 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ 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 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ 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 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ 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 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ 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 )
=> ( f @ Y3 @ Y1 @ Y5 ) ) )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( f @ Y3 @ Y3 @ Y6 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y3 @ Y0 @ 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 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ 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 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ 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 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ 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 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ 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 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ 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 )
=> ( f @ Y2 @ Y0 @ Y4 ) ) )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( f @ Y2 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y2 @ X2 @ 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 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ( eiw_di @ ( sK2 @ X1 @ X2 ) @ X1 )
& ( !! @ 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 )
=> ( f @ Y1 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $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 )
=> ( f @ Y1 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( eiw_di @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f75,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ X2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( f @ Y1 @ Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y3 ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f76,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ 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 )
=> ( f @ Y0 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ X2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X3 @ Y1 )
=> ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y2 ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ( eiw_di @ X4 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ X4 @ X4 @ Y2 ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f96,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f97,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ( mrel @ X5 @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f106,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f107,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ ( sK5 @ X4 @ X6 ) ) ) ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( ( mrel @ X6 @ ( sK5 @ X4 @ X6 ) )
=> ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f112,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y1 ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f113,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X5 )
=> ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ 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 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X3: mworld,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ ( sK6 @ X5 @ X4 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ ( sK6 @ X5 @ X4 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X4 @ X4 @ Y1 ) ) ) )
@ ( sK6 @ X5 @ X4 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
@ X6 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( f @ X4 @ X2 @ Y0 ) )
@ ( sK7 @ X2 @ X5 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ( mrel @ X5 @ ( sK6 @ X5 @ X4 ) )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) )
| ( $false
= ( ( mrel @ X5 @ ( sK7 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) )
| ( $false
= ( ( mrel @ X5 @ ( sK7 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f126,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) )
| ( $false
= ( ( mrel @ X5 @ ( sK7 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) ) ) ),
inference(not_proxy_clausification,[],[f121]) ).
thf(f127,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ X7 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) )
| ( $false
= ( ( mrel @ X5 @ ( sK7 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( ( mrel @ X5 @ ( sK7 @ X2 @ X5 @ X4 ) )
=> ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK6 @ X5 @ X4 ) @ Y0 )
=> ( f @ X4 @ X4 @ Y0 ) )
@ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f133,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $true
= ( ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 )
=> ( f @ X4 @ X4 @ X7 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f134,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK8 ) ),
inference(sigma_proxy_clausification,[],[f63]) ).
thf(f136,plain,
( $false
= ( ( mrel @ sK1 @ sK8 )
=> ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK8 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK8 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK8 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK8 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK8 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK8 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f137]) ).
thf(f140,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK8 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK8 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y0 @ Y3 ) ) ) ) ) ) ) )
@ sK9 ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( $true
= ( ( eiw_di @ sK9 @ sK8 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK9 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK9 @ Y2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $true
= ( eiw_di @ sK9 @ sK8 ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f144,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ sK9 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK8 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK9 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK9 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( f @ Y0 @ sK9 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK9 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK9 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( f @ X2 @ sK9 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ sK9 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK8 @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( f @ X2 @ sK9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f230,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( $true = $false )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ X0 @ X2 ) )
| ( $true
= ( f @ X1 @ sK9 @ X2 ) ) ),
inference(constrained_superposition,[],[f152,f50]) ).
thf(f240,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ X0 @ X2 ) )
| ( $true
= ( f @ X1 @ sK9 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f250,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( $true = $false )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $true
= ( f @ X1 @ sK9 @ X2 ) ) ),
inference(forward_demodulation,[],[f240,f50]) ).
thf(f251,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $true
= ( f @ X1 @ sK9 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f859,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f110,f50]) ).
thf(f860,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f859]) ).
thf(f861,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f860,f50]) ).
thf(f862,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f861]) ).
thf(f863,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f862,f50]) ).
thf(f864,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f863]) ).
thf(f865,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f864,f50]) ).
thf(f866,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ ( sK3 @ X2 @ X1 @ X5 @ X4 ) ) )
| ( $false
= ( f @ X4 @ X4 @ ( sK5 @ X4 @ X6 ) ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f865]) ).
thf(f1392,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(forward_demodulation,[],[f134,f50]) ).
thf(f1393,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f1392]) ).
thf(f1394,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(forward_demodulation,[],[f1393,f50]) ).
thf(f1395,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X5 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f1394]) ).
thf(f1396,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(forward_demodulation,[],[f1395,f50]) ).
thf(f1397,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ ( sK6 @ X5 @ X4 ) @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f1396]) ).
thf(f1398,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(forward_demodulation,[],[f1397,f50]) ).
thf(f1399,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1400,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $true = $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) ) ),
inference(forward_demodulation,[],[f1399,f50]) ).
thf(f1401,plain,
! [X2: $i,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: $i,X5: mworld] :
( ( $false
= ( f @ X4 @ X2 @ ( sK7 @ X2 @ X5 @ X4 ) ) )
| ( $true
= ( f @ X4 @ ( sK2 @ X1 @ X2 ) @ X6 ) )
| ( $true
= ( f @ X4 @ X4 @ X7 ) )
| ( $false
= ( eiw_di @ X4 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1400]) ).
thf(f1472,plain,
! [X2: mworld,X3: mworld,X0: $i,X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $true
= ( f @ X0 @ ( sK2 @ X3 @ sK9 ) @ X4 ) )
| ( $true
= ( f @ X0 @ X0 @ X5 ) )
| ( $false
= ( eiw_di @ X0 @ X6 ) )
| ( $false
= ( eiw_di @ sK9 @ X3 ) ) ),
inference(constrained_superposition,[],[f251,f1401]) ).
thf(f1581,plain,
! [X2: mworld,X3: mworld,X0: $i,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( f @ X0 @ ( sK2 @ X3 @ sK9 ) @ X4 ) )
| ( $true
= ( f @ X0 @ X0 @ X5 ) )
| ( $false
= ( eiw_di @ X0 @ X6 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ sK9 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f1472]) ).
thf(f2136,plain,
! [X2: mworld,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $false != $false )
| ( $true
= ( f @ X0 @ ( sK2 @ X2 @ sK9 ) @ X3 ) )
| ( $true
= ( f @ X0 @ X0 @ X4 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( eiw_di @ sK9 @ X2 ) ) ),
inference(equality_factoring,[],[f1581]) ).
thf(f2139,plain,
! [X2: mworld,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $true
= ( f @ X0 @ ( sK2 @ X2 @ sK9 ) @ X3 ) )
| ( $true
= ( f @ X0 @ X0 @ X4 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( eiw_di @ sK9 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f2136]) ).
thf(f2326,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true != $true )
| ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X2 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(equality_factoring,[],[f2139]) ).
thf(f2329,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X2 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2326]) ).
thf(f2454,plain,
! [X0: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(constrained_superposition,[],[f74,f2329]) ).
thf(f2455,plain,
! [X0: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f2454]) ).
thf(f2456,plain,
! [X0: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f2455]) ).
thf(f2482,plain,
! [X0: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) ) ),
inference(forward_demodulation,[],[f2456,f50]) ).
thf(f2483,plain,
! [X0: mworld,X1: mworld] :
( ( $true
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ X1 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2482]) ).
thf(f2499,plain,
! [X2: mworld,X3: mworld,X0: mworld] :
( ( $true = $false )
| ( $false
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ ( sK5 @ ( sK2 @ X0 @ sK9 ) @ X2 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X3 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(constrained_superposition,[],[f866,f2483]) ).
thf(f2506,plain,
! [X2: mworld,X3: mworld,X0: mworld] :
( ( $true = $false )
| ( $false
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ ( sK5 @ ( sK2 @ X0 @ sK9 ) @ X2 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X3 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f2499]) ).
thf(f2507,plain,
! [X2: mworld,X3: mworld,X0: mworld] :
( ( $false
= ( f @ ( sK2 @ X0 @ sK9 ) @ ( sK2 @ X0 @ sK9 ) @ ( sK5 @ ( sK2 @ X0 @ sK9 ) @ X2 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X3 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2506]) ).
thf(f3125,plain,
! [X2: mworld,X0: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X2 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(constrained_superposition,[],[f2483,f2507]) ).
thf(f3141,plain,
! [X2: mworld,X0: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f3125]) ).
thf(f3142,plain,
! [X2: mworld,X0: mworld] :
( ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK9 ) @ X2 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f3141]) ).
thf(f3193,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(constrained_superposition,[],[f74,f3142]) ).
thf(f3194,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f3193]) ).
thf(f3195,plain,
! [X0: mworld] :
( ( $false
= ( eiw_di @ sK9 @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f3194]) ).
thf(f3199,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ X0 ) ) ),
inference(forward_demodulation,[],[f3195,f50]) ).
thf(f3200,plain,
! [X0: mworld] :
( $false
= ( eiw_di @ sK9 @ X0 ) ),
inference(trivial_inequality_removal,[],[f3199]) ).
thf(f3205,plain,
$true = $false,
inference(constrained_superposition,[],[f143,f3200]) ).
thf(f3206,plain,
$false,
inference(trivial_inequality_removal,[],[f3205]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 10:56:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.39/0.58 % (1519301)Will run a generic schedule for satisfiability detection.
% 2.39/0.58 % (1519310)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1253764526:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.39/0.58 % (1519310)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % (1519307)% WARNING: option uhcvi not known.
% 2.39/0.58 % (1519306)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3954588125_2999 on theBenchmark for (2999ds/0Mi)
% 2.39/0.58 % (1519307)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=278759380:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.39/0.58 % (1519309)dis+10_1_sil=32000:sp=arity:random_seed=2175275796:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.39/0.58 % (1519307)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519307)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.39/0.58 % (1519308)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3600747142:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.39/0.58 % (1519311)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=584760222:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.39/0.58 % (1519312)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1339096657:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.39/0.58 % (1519310)Instruction limit reached!
% 2.39/0.58 % (1519310)------------------------------
% 2.39/0.58 % (1519310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519310)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519310)Termination reason: Instruction limit
% 2.39/0.58 % (1519310)Termination phase: Saturation
% 2.39/0.58 % (1519310)Time elapsed: 0.029 s
% 2.39/0.58 % (1519310)Peak memory usage: 12 MB
% 2.39/0.58 % (1519310)Instructions burned: 120 (million)
% 2.39/0.58 % (1519317)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1464139677:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519321)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2001585158:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.39/0.58 % (1519323)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3635451825:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.39/0.58 % (1519323)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % (1519309)Instruction limit reached!
% 2.39/0.58 % (1519309)------------------------------
% 2.39/0.58 % (1519309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519309)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519309)Termination reason: Instruction limit
% 2.39/0.58 % (1519309)Termination phase: Saturation
% 2.39/0.58 % (1519309)Time elapsed: 0.049 s
% 2.39/0.58 % (1519309)Peak memory usage: 12 MB
% 2.39/0.58 % (1519309)Instructions burned: 104 (million)
% 2.39/0.58 % (1519323)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.39/0.58 % (1519326)ott-21_1_sil=16000:fs=off:random_seed=2798637740:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.39/0.58 % (1519321)Instruction limit reached!
% 2.39/0.58 % (1519321)------------------------------
% 2.39/0.58 % (1519321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519321)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519321)Termination reason: Instruction limit
% 2.39/0.58 % (1519321)Termination phase: Saturation
% 2.39/0.58 % (1519321)Time elapsed: 0.035 s
% 2.39/0.58 % (1519321)Peak memory usage: 13 MB
% 2.39/0.58 % (1519321)Instructions burned: 135 (million)
% 2.39/0.58 % (1519328)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2637183513:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 2.39/0.58 % (1519311)Instruction limit reached!
% 2.39/0.58 % (1519311)------------------------------
% 2.39/0.58 % (1519311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519311)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519311)Termination reason: Instruction limit
% 2.39/0.58 % (1519311)Termination phase: Saturation
% 2.39/0.58 % (1519311)Time elapsed: 0.105 s
% 2.39/0.58 % (1519311)Peak memory usage: 12 MB
% 2.39/0.58 % (1519311)Instructions burned: 131 (million)
% 2.39/0.58 % (1519330)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1352938746:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.39/0.58 % (1519312)Instruction limit reached!
% 2.39/0.58 % (1519312)------------------------------
% 2.39/0.58 % (1519312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519312)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519312)Termination reason: Instruction limit
% 2.39/0.58 % (1519312)Termination phase: Saturation
% 2.39/0.58 % (1519312)Time elapsed: 0.130 s
% 2.39/0.58 % (1519312)Peak memory usage: 12 MB
% 2.39/0.58 % (1519312)Instructions burned: 160 (million)
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519332)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3046309851:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.39/0.58 % (1519333)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4241562710:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519326)Instruction limit reached!
% 2.39/0.58 % (1519326)------------------------------
% 2.39/0.58 % (1519326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519326)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519326)Termination reason: Instruction limit
% 2.39/0.58 % (1519326)Termination phase: Saturation
% 2.39/0.58 % (1519326)Time elapsed: 0.103 s
% 2.39/0.58 % (1519326)Peak memory usage: 13 MB
% 2.39/0.58 % (1519326)Instructions burned: 180 (million)
% 2.39/0.58 % (1519337)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=157681419:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.39/0.58 % (1519337)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % (1519336)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1753415641:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.39/0.58 % (1519328)Instruction limit reached!
% 2.39/0.58 % (1519328)------------------------------
% 2.39/0.58 % (1519328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.58 % (1519328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.58 % (1519328)CaDiCaL version: 2.1.3
% 2.39/0.58 % (1519328)Termination reason: Instruction limit
% 2.39/0.58 % (1519328)Termination phase: Saturation
% 2.39/0.58 % (1519328)Time elapsed: 0.126 s
% 2.39/0.58 % (1519328)Peak memory usage: 13 MB
% 2.39/0.58 % (1519328)Instructions burned: 481 (million)
% 2.39/0.58 % (1519336)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % (1519340)fmb+10_1_sil=64000:random_seed=3494804131:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.39/0.58 % (1519340)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519342)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2635709516:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519344)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=316070850:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 2.39/0.58 % Exception at run slice level
% 2.39/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.39/0.58 % (1519346)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4275861749:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 2.39/0.58 % (1519346)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.39/0.58 % (1519323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1519301-1519323"...
% 2.39/0.58 % (1519323)...printing done.
% 2.39/0.58 % (1519323)Refutation found. Thanks to Tanya!
% 2.39/0.58 % SZS status Theorem for theBenchmark
% 2.39/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.59 % (1519323)------------------------------
% 2.39/0.59 % (1519323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.59 % (1519323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.59 % (1519323)CaDiCaL version: 2.1.3
% 2.39/0.59 % (1519323)Termination reason: Refutation
% 2.39/0.59 % (1519323)Time elapsed: 0.280 s
% 2.39/0.59 % (1519323)Peak memory usage: 14 MB
% 2.39/0.59 % (1519323)Instructions burned: 433 (million)
% 2.39/0.59 % (1519301)Success in time 0.366 s
% 2.39/0.59 % Vampire exiting
%------------------------------------------------------------------------------