%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO905^6 : 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 : n020.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 08:50:36 AM UTC 2026
% Result : ContradictoryAxioms 2.24s 0.60s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 142
% Number of leaves : 35
% Syntax : Number of formulae : 1444 ( 122 unt; 0 typ; 19 def)
% Number of atoms : 65216 (14429 equ; 0 cnn)
% Maximal formula atoms : 159 ( 45 avg)
% Number of connectives : 99443 (1636 ~;14110 |;4191 &;64402 @)
% ( 19 <=>;6657 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 19 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 416 ( 416 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 109 usr; 25 con; 0-4 aty)
% (6295 !!;2133 ??; 0 @@+; 0 @@-)
% Number of variables : 21977 ( 80 sgn12521 !; 2 ?;21977 :)
% 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,
v1: mworld > $o ).
thf(func_def_12,type,
v2: mworld > $o ).
thf(func_def_13,type,
v3: mworld > $o ).
thf(func_def_14,type,
v4: mworld > $o ).
thf(func_def_15,type,
v5: mworld > $o ).
thf(func_def_16,type,
v6: mworld > $o ).
thf(func_def_17,type,
v7: mworld > $o ).
thf(func_def_18,type,
v8: mworld > $o ).
thf(func_def_19,type,
v9: mworld > $o ).
thf(func_def_20,type,
v10: mworld > $o ).
thf(func_def_21,type,
v12: mworld > $o ).
thf(func_def_22,type,
v11: mworld > $o ).
thf(func_def_23,type,
v14: mworld > $o ).
thf(func_def_24,type,
v13: mworld > $o ).
thf(func_def_25,type,
v16: mworld > $o ).
thf(func_def_26,type,
v15: mworld > $o ).
thf(func_def_27,type,
v18: mworld > $o ).
thf(func_def_28,type,
v17: mworld > $o ).
thf(func_def_29,type,
v19: mworld > $o ).
thf(func_def_30,type,
v21: mworld > $o ).
thf(func_def_31,type,
v20: mworld > $o ).
thf(func_def_32,type,
v23: mworld > $o ).
thf(func_def_33,type,
v22: mworld > $o ).
thf(func_def_34,type,
v25: mworld > $o ).
thf(func_def_35,type,
v24: mworld > $o ).
thf(func_def_36,type,
v27: mworld > $o ).
thf(func_def_37,type,
v26: mworld > $o ).
thf(func_def_38,type,
v28: mworld > $o ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vIFF: $o > $o > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
sK0: mworld > mworld ).
thf(func_def_53,type,
sK1: mworld > mworld ).
thf(func_def_54,type,
sK2: mworld > mworld ).
thf(func_def_55,type,
sK3: mworld > mworld ).
thf(func_def_56,type,
sK4: mworld > mworld ).
thf(func_def_57,type,
sK5: mworld > mworld ).
thf(func_def_58,type,
sK6: mworld > mworld ).
thf(func_def_59,type,
sK7: mworld > mworld ).
thf(func_def_60,type,
sK8: mworld > mworld ).
thf(func_def_61,type,
sK9: mworld > mworld ).
thf(func_def_62,type,
sK10: mworld > mworld ).
thf(func_def_63,type,
sK11: mworld > mworld ).
thf(func_def_64,type,
sK12: mworld > mworld ).
thf(func_def_65,type,
sK13: mworld > mworld ).
thf(func_def_66,type,
sK14: mworld > mworld ).
thf(func_def_67,type,
sK15: mworld > mworld ).
thf(func_def_68,type,
sK16: mworld > mworld ).
thf(func_def_69,type,
sK17: mworld > mworld ).
thf(func_def_70,type,
sK18: mworld > mworld ).
thf(func_def_71,type,
sK19: mworld > mworld ).
thf(func_def_72,type,
sK20: mworld > mworld ).
thf(func_def_73,type,
sK21: mworld > mworld ).
thf(func_def_74,type,
sK22: mworld > mworld ).
thf(func_def_75,type,
sK23: mworld > mworld ).
thf(func_def_76,type,
sK24: mworld > mworld ).
thf(func_def_77,type,
sK25: mworld > mworld ).
thf(func_def_78,type,
sK26: mworld > mworld ).
thf(func_def_79,type,
sK27: mworld > mworld ).
thf(func_def_80,type,
sK28: mworld > mworld ).
thf(func_def_81,type,
sK29: mworld > mworld ).
thf(func_def_82,type,
sK30: mworld > mworld ).
thf(func_def_83,type,
sK31: mworld > mworld ).
thf(func_def_84,type,
sK32: mworld > mworld ).
thf(func_def_85,type,
sK33: mworld > mworld ).
thf(func_def_86,type,
sK34: mworld > mworld ).
thf(func_def_87,type,
sK35: mworld > mworld ).
thf(func_def_88,type,
sK36: mworld > mworld ).
thf(func_def_89,type,
sK37: mworld > mworld ).
thf(func_def_90,type,
sK38: mworld > mworld ).
thf(func_def_91,type,
sK39: 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(f4,axiom,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_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(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f28,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod19) ).
thf(f31,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod22) ).
thf(f33,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod24) ).
thf(f40,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod31) ).
thf(f43,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod34) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod36) ).
thf(f46,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod37) ).
thf(f47,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod38) ).
thf(f60,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X0: mworld] : $true ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alt1) ).
thf(f63,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f64,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f65,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f67,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f69,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f74,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f75,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f76,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f77,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f79,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f116,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f117,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f116]) ).
thf(f122,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f123,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f122]) ).
thf(f126,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f127,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f126]) ).
thf(f140,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f141,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f140]) ).
thf(f146,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f147,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f146]) ).
thf(f150,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f151,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f150]) ).
thf(f152,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f153,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f152]) ).
thf(f154,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f155,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f154]) ).
thf(f180,plain,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X0: mworld] : $true ) )
@ ( mdia
@ ^ [X1: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X3: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X4: mworld] : $true ) ) )
@ ( mdia
@ ^ [X5: mworld] : $true ) ) )
@ ( mdia
@ ^ [X6: mworld] : $true ) ) )
@ ( mdia
@ ^ [X7: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X8: mworld] : $true ) ) )
@ ( mdia
@ ^ [X9: mworld] : $true ) ) )
@ ( mdia
@ ^ [X10: mworld] : $true ) ) )
@ ( mdia
@ ^ [X11: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X12: mworld] : $true ) ) )
@ ( mdia
@ ^ [X13: mworld] : $true ) ) )
@ ( mdia
@ ^ [X14: mworld] : $true ) ) )
@ ( mdia
@ ^ [X15: mworld] : $true ) ) ),
inference(rectify,[],[f60]) ).
thf(f181,plain,
( $true
= ( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [Y0: mworld] : $true ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) ) ),
inference(fool_elimination,[],[f180]) ).
thf(f185,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f186,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f187,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f188,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f191,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f192,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f193,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f79]) ).
thf(f212,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f117]) ).
thf(f215,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f123]) ).
thf(f217,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f127]) ).
thf(f224,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f141]) ).
thf(f227,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f147]) ).
thf(f229,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f151]) ).
thf(f230,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f153]) ).
thf(f231,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f155]) ).
thf(f244,plain,
( $true
= ( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [Y0: mworld] : $true ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) ) ),
inference(cnf_transformation,[],[f181]) ).
thf(f266,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v25
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v13
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f212,f185,f191,f191,f191,f191,f188,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f191,f186]) ).
thf(f269,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v25
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v20
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f215,f185,f191,f191,f191,f191,f188,f191,f191,f191,f191,f191,f188,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f186]) ).
thf(f271,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v25 )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v19
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f217,f185,f191,f191,f191,f191,f188,f186,f191,f188,f186,f191,f191,f191,f191,f191,f188,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f186]) ).
thf(f278,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v19 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v15
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f224,f185,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f188,f191,f191,f191,f191,f191,f186]) ).
thf(f281,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v23 )
@ ( ^ [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 ) )
@ v22
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v12 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f227,f185,f191,f191,f191,f191,f191,f191,f188,f186,f191,f188,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191]) ).
thf(f283,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v21
@ ( ^ [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 ) )
@ v20
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f229,f185,f191,f191,f191,f191,f191,f191,f191,f191,f188,f191,f188,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f186]) ).
thf(f284,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v21
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v20 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v15
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f230,f185,f191,f191,f191,f191,f191,f191,f191,f191,f188,f191,f188,f186,f191,f191,f191,f191,f191,f188,f191,f191,f191]) ).
thf(f285,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v19 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) )
@ v10
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f231,f185,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f191,f191]) ).
thf(f298,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [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 ) ) )
@ v5 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v5 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v6 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v8 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [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 ) ) )
@ v13 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v14 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [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 ) ) )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v23 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v23 ) ) ) ) )
@ ( ^ [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 ) ) )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) ) ),
inference(definition_unfolding,[],[f244,f185,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f187,f191,f192,f192,f192,f192,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f192,f192,f192,f192,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f192,f192,f192,f192,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f187,f192,f192,f186,f192,f192,f192,f192]) ).
thf(f301,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& $true ) ) ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f303,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f301]) ).
thf(f304,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& $true ) ) ) ) ),
inference(beta-eta_normalization,[],[f304]) ).
thf(f306,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f305]) ).
thf(f308,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f306]) ).
thf(f309,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f313,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f311]) ).
thf(f314,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f315]) ).
thf(f318,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f316]) ).
thf(f319,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f319]) ).
thf(f321,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f321]) ).
thf(f324,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f326]) ).
thf(f329,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f331,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f331]) ).
thf(f334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f336]) ).
thf(f339,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f340]) ).
thf(f343,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f341]) ).
thf(f344,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f346,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f345]) ).
thf(f348,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f346]) ).
thf(f349,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f351,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f350]) ).
thf(f353,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f351]) ).
thf(f354,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f354]) ).
thf(f356,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f358,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f356]) ).
thf(f359,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f360]) ).
thf(f363,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f361]) ).
thf(f364,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f364]) ).
thf(f366,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f366]) ).
thf(f369,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f371]) ).
thf(f374,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f376]) ).
thf(f379,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f380]) ).
thf(f383,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f381]) ).
thf(f384,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f385]) ).
thf(f388,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f386]) ).
thf(f389,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f388]) ).
thf(f390,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f389]) ).
thf(f391,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f390]) ).
thf(f393,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f391]) ).
thf(f394,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
& $true ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f396,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
& $true ) ) ) ) ),
inference(imp_proxy_clausification,[],[f395]) ).
thf(f398,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f396]) ).
thf(f399,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f399]) ).
thf(f401,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f401]) ).
thf(f486,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f402]) ).
thf(f487,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f402]) ).
thf(f488,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) )
@ ( sK10 @ X20 ) ) ) ),
inference(sigma_proxy_clausification,[],[f487]) ).
thf(f489,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( mrel @ X20 @ ( sK10 @ X20 ) )
& ( v8 @ ( sK10 @ X20 ) ) ) ) ),
inference(beta-eta_normalization,[],[f488]) ).
thf(f490,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(and_proxy_clausification,[],[f489]) ).
thf(f492,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) )
@ ( sK11 @ X20 ) ) ) ),
inference(sigma_proxy_clausification,[],[f486]) ).
thf(f493,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( mrel @ X20 @ ( sK11 @ X20 ) )
& ~ ( v8 @ ( sK11 @ X20 ) ) ) ) ),
inference(beta-eta_normalization,[],[f492]) ).
thf(f494,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ~ ( v8 @ ( sK11 @ X20 ) ) ) ) ),
inference(and_proxy_clausification,[],[f493]) ).
thf(f496,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(not_proxy_clausification,[],[f494]) ).
thf(f513,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f377]) ).
thf(f519,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) )
@ ( sK17 @ X15 ) ) ) ),
inference(sigma_proxy_clausification,[],[f513]) ).
thf(f520,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ ( sK17 @ X15 ) )
& ~ ( v13 @ ( sK17 @ X15 ) ) ) ) ),
inference(beta-eta_normalization,[],[f519]) ).
thf(f521,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ~ ( v13 @ ( sK17 @ X15 ) ) ) ) ),
inference(and_proxy_clausification,[],[f520]) ).
thf(f523,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(not_proxy_clausification,[],[f521]) ).
thf(f525,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f372]) ).
thf(f526,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) )
@ ( sK18 @ X14 ) ) ) ),
inference(sigma_proxy_clausification,[],[f525]) ).
thf(f527,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ ( sK18 @ X14 ) )
& ( v14 @ ( sK18 @ X14 ) ) ) ) ),
inference(beta-eta_normalization,[],[f526]) ).
thf(f528,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(and_proxy_clausification,[],[f527]) ).
thf(f535,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f367]) ).
thf(f536,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f367]) ).
thf(f537,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) )
@ ( sK20 @ X13 ) ) ) ),
inference(sigma_proxy_clausification,[],[f536]) ).
thf(f538,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ ( sK20 @ X13 ) )
& ( v15 @ ( sK20 @ X13 ) ) ) ) ),
inference(beta-eta_normalization,[],[f537]) ).
thf(f539,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(and_proxy_clausification,[],[f538]) ).
thf(f541,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) )
@ ( sK21 @ X13 ) ) ) ),
inference(sigma_proxy_clausification,[],[f535]) ).
thf(f542,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ ( sK21 @ X13 ) )
& ~ ( v15 @ ( sK21 @ X13 ) ) ) ) ),
inference(beta-eta_normalization,[],[f541]) ).
thf(f543,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ~ ( v15 @ ( sK21 @ X13 ) ) ) ) ),
inference(and_proxy_clausification,[],[f542]) ).
thf(f545,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(not_proxy_clausification,[],[f543]) ).
thf(f573,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f337]) ).
thf(f574,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f337]) ).
thf(f575,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) )
@ ( sK28 @ X7 ) ) ) ),
inference(sigma_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ ( sK28 @ X7 ) )
& ( v21 @ ( sK28 @ X7 ) ) ) ) ),
inference(beta-eta_normalization,[],[f575]) ).
thf(f577,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(and_proxy_clausification,[],[f576]) ).
thf(f579,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) )
@ ( sK29 @ X7 ) ) ) ),
inference(sigma_proxy_clausification,[],[f573]) ).
thf(f580,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ ( sK29 @ X7 ) )
& ~ ( v21 @ ( sK29 @ X7 ) ) ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f581,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ~ ( v21 @ ( sK29 @ X7 ) ) ) ) ),
inference(and_proxy_clausification,[],[f580]) ).
thf(f583,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(not_proxy_clausification,[],[f581]) ).
thf(f584,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f332]) ).
thf(f590,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) )
@ ( sK31 @ X6 ) ) ) ),
inference(sigma_proxy_clausification,[],[f584]) ).
thf(f591,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ ( sK31 @ X6 ) )
& ~ ( v22 @ ( sK31 @ X6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ~ ( v22 @ ( sK31 @ X6 ) ) ) ) ),
inference(and_proxy_clausification,[],[f591]) ).
thf(f594,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f592]) ).
thf(f596,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f327]) ).
thf(f597,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) )
@ ( sK32 @ X5 ) ) ) ),
inference(sigma_proxy_clausification,[],[f596]) ).
thf(f598,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ ( sK32 @ X5 ) )
& ( v23 @ ( sK32 @ X5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f597]) ).
thf(f599,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(and_proxy_clausification,[],[f598]) ).
thf(f607,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f322]) ).
thf(f608,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) )
@ ( sK34 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ ( sK34 @ X4 ) )
& ( v24 @ ( sK34 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f608]) ).
thf(f610,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(and_proxy_clausification,[],[f609]) ).
thf(f1654,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f1655,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1654]) ).
thf(f1656,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1655]) ).
thf(f1657,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1656]) ).
thf(f1658,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1657]) ).
thf(f1659,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1658]) ).
thf(f1660,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1659]) ).
thf(f1661,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1660]) ).
thf(f1662,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1661]) ).
thf(f1663,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1662]) ).
thf(f1664,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1663]) ).
thf(f1665,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1664]) ).
thf(f1666,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1665]) ).
thf(f1667,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1666]) ).
thf(f1668,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1667]) ).
thf(f1669,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1668]) ).
thf(f1670,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1669]) ).
thf(f1671,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1670]) ).
thf(f1672,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1671]) ).
thf(f1673,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1672]) ).
thf(f1674,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1673]) ).
thf(f1675,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1674]) ).
thf(f1676,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1675]) ).
thf(f1677,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ~ ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1676]) ).
thf(f1678,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ~ ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1677]) ).
thf(f1679,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v21 @ X8 ) ) ) ),
inference(or_proxy_clausification,[],[f1678]) ).
thf(f1680,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $true
= ( ~ ( v21 @ X8 ) ) ) ),
inference(pi_proxy_clausification,[],[f1679]) ).
thf(f1681,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f1680]) ).
thf(f1682,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1681]) ).
thf(f1683,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1682]) ).
thf(f1684,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1683]) ).
thf(f1685,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1684]) ).
thf(f1686,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1685]) ).
thf(f1687,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f1686]) ).
thf(f1688,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) ) ),
inference(pi_proxy_clausification,[],[f1687]) ).
thf(f1689,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f1688]) ).
thf(f1690,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f1689]) ).
thf(f1691,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1690]) ).
thf(f1692,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1691]) ).
thf(f1693,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1692]) ).
thf(f1694,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1693]) ).
thf(f1695,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f1694]) ).
thf(f1696,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1695]) ).
thf(f1697,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1696]) ).
thf(f1698,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1697]) ).
thf(f1699,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1698]) ).
thf(f1700,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1699]) ).
thf(f1701,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f1700]) ).
thf(f1702,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1701]) ).
thf(f1703,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1702]) ).
thf(f1704,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1703]) ).
thf(f1705,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1704]) ).
thf(f1706,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1705]) ).
thf(f1707,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1706]) ).
thf(f1708,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1707]) ).
thf(f1709,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1708]) ).
thf(f1710,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f1709]) ).
thf(f1711,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1710]) ).
thf(f1712,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1711]) ).
thf(f1713,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f1712]) ).
thf(f1714,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1713]) ).
thf(f1715,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1714]) ).
thf(f1716,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(or_proxy_clausification,[],[f1715]) ).
thf(f1717,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) )
@ X20 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(pi_proxy_clausification,[],[f1716]) ).
thf(f1718,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) ) ) ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(beta-eta_normalization,[],[f1717]) ).
thf(f1719,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1718]) ).
thf(f1720,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f1719]) ).
thf(f1721,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( v8 @ X21 ) ) ) ),
inference(beta-eta_normalization,[],[f1720]) ).
thf(f1722,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(imp_proxy_clausification,[],[f1721]) ).
thf(f1723,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f1724,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1723]) ).
thf(f1725,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1724]) ).
thf(f1726,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1725]) ).
thf(f1727,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1726]) ).
thf(f1728,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1727]) ).
thf(f1729,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1728]) ).
thf(f1730,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1729]) ).
thf(f1731,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1730]) ).
thf(f1732,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1731]) ).
thf(f1733,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1732]) ).
thf(f1734,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1733]) ).
thf(f1735,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1734]) ).
thf(f1736,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1735]) ).
thf(f1737,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1736]) ).
thf(f1738,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1737]) ).
thf(f1739,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1738]) ).
thf(f1740,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1739]) ).
thf(f1741,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1740]) ).
thf(f1742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1741]) ).
thf(f1743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1742]) ).
thf(f1744,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1743]) ).
thf(f1745,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1744]) ).
thf(f1746,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1745]) ).
thf(f1747,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1746]) ).
thf(f1748,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f1747]) ).
thf(f1749,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1748]) ).
thf(f1750,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ~ ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1749]) ).
thf(f1751,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ~ ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1750]) ).
thf(f1752,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v20 @ X9 ) ) ) ),
inference(or_proxy_clausification,[],[f1751]) ).
thf(f1753,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $true
= ( ~ ( v20 @ X9 ) ) ) ),
inference(pi_proxy_clausification,[],[f1752]) ).
thf(f1754,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( v20 @ X9 ) ) ),
inference(not_proxy_clausification,[],[f1753]) ).
thf(f1755,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v20 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f1754]) ).
thf(f1756,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1755]) ).
thf(f1757,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f1756]) ).
thf(f1758,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1757]) ).
thf(f1759,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1758]) ).
thf(f1760,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1759]) ).
thf(f1761,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1760]) ).
thf(f1762,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1761]) ).
thf(f1763,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f1762]) ).
thf(f1764,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1763]) ).
thf(f1765,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1764]) ).
thf(f1766,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1765]) ).
thf(f1767,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1766]) ).
thf(f1768,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1767]) ).
thf(f1769,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(or_proxy_clausification,[],[f1768]) ).
thf(f1770,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) )
@ X15 ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1769]) ).
thf(f1771,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f1770]) ).
thf(f1772,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1771]) ).
thf(f1773,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1772]) ).
thf(f1774,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1773]) ).
thf(f1775,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1774]) ).
thf(f1776,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1775]) ).
thf(f1777,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( v12 @ X17 ) ) ) ),
inference(beta-eta_normalization,[],[f1776]) ).
thf(f1778,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(imp_proxy_clausification,[],[f1777]) ).
thf(f1779,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f1780,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1779]) ).
thf(f1781,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1780]) ).
thf(f1782,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1781]) ).
thf(f1783,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1782]) ).
thf(f1784,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1783]) ).
thf(f1785,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1784]) ).
thf(f1786,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1785]) ).
thf(f1787,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1786]) ).
thf(f1788,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1787]) ).
thf(f1789,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1788]) ).
thf(f1790,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1789]) ).
thf(f1791,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1790]) ).
thf(f1792,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1791]) ).
thf(f1793,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1792]) ).
thf(f1794,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1793]) ).
thf(f1795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1794]) ).
thf(f1796,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1795]) ).
thf(f1797,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1796]) ).
thf(f1798,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1797]) ).
thf(f1799,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1798]) ).
thf(f1800,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1799]) ).
thf(f1801,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1800]) ).
thf(f1802,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1801]) ).
thf(f1803,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1802]) ).
thf(f1804,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f1803]) ).
thf(f1805,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1804]) ).
thf(f1806,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1805]) ).
thf(f1807,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1806]) ).
thf(f1808,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(or_proxy_clausification,[],[f1807]) ).
thf(f1809,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f1808]) ).
thf(f1810,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f1809]) ).
thf(f1811,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1810]) ).
thf(f1812,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f1811]) ).
thf(f1813,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1812]) ).
thf(f1814,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1813]) ).
thf(f1815,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1814]) ).
thf(f1816,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1815]) ).
thf(f1817,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1816]) ).
thf(f1818,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f1817]) ).
thf(f1819,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1818]) ).
thf(f1820,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1819]) ).
thf(f1821,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1820]) ).
thf(f1822,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ~ ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1821]) ).
thf(f1823,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ~ ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1822]) ).
thf(f1824,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v15 @ X14 ) ) ) ),
inference(or_proxy_clausification,[],[f1823]) ).
thf(f1825,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $true
= ( ~ ( v15 @ X14 ) ) ) ),
inference(pi_proxy_clausification,[],[f1824]) ).
thf(f1826,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $false
= ( v15 @ X14 ) ) ),
inference(not_proxy_clausification,[],[f1825]) ).
thf(f1827,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v15 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f1826]) ).
thf(f1828,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1827]) ).
thf(f1829,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1828]) ).
thf(f1830,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1829]) ).
thf(f1831,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1830]) ).
thf(f1832,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1831]) ).
thf(f1833,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1832]) ).
thf(f1834,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1833]) ).
thf(f1835,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f1834]) ).
thf(f1836,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1835]) ).
thf(f1837,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1836]) ).
thf(f1838,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f1837]) ).
thf(f1839,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ~ ( v10 @ X19 ) ) ) ),
inference(beta-eta_normalization,[],[f1838]) ).
thf(f1840,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ~ ( v10 @ X19 ) ) ) ),
inference(imp_proxy_clausification,[],[f1839]) ).
thf(f1841,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(not_proxy_clausification,[],[f1840]) ).
thf(f1928,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v23 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v22 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v12 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f1929,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v23 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v22 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v12 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1928]) ).
thf(f1930,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v23 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v22 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v12 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1929]) ).
thf(f1931,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v23 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v22 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v12 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1930]) ).
thf(f1932,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v23 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v22 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v12 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1931]) ).
thf(f1933,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v23 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v22 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v12 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1932]) ).
thf(f1934,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v23 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v22 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v12 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1933]) ).
thf(f1935,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v23 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v22 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v12 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1934]) ).
thf(f1936,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v23 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v22 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v12 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1935]) ).
thf(f1937,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v23 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v22 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v12 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1936]) ).
thf(f1938,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v23 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v22 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v12 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1937]) ).
thf(f1939,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v23 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v22 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v12 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1938]) ).
thf(f1940,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v23 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v22 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v12 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1939]) ).
thf(f1941,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v23 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v22 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v12 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1940]) ).
thf(f1942,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ~ ( v23 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v22 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v12 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1941]) ).
thf(f1943,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ~ ( v23 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v22 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v12 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1942]) ).
thf(f1944,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ~ ( v23 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v22 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v12 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1943]) ).
thf(f1945,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( ~ ( v23 @ X6 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( v22 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v12 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1944]) ).
thf(f1946,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ~ ( v23 @ X6 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( v22 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v12 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1945]) ).
thf(f1947,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( v22 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v12 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v23 @ X6 ) ) ) ),
inference(or_proxy_clausification,[],[f1946]) ).
thf(f1948,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( v22 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v12 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( $true
= ( ~ ( v23 @ X6 ) ) ) ),
inference(pi_proxy_clausification,[],[f1947]) ).
thf(f1949,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( v22 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v12 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( $false
= ( v23 @ X6 ) ) ),
inference(not_proxy_clausification,[],[f1948]) ).
thf(f1950,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( ( v22 @ X7 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v12 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v23 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f1949]) ).
thf(f1951,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( ( v22 @ X7 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v12 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1950]) ).
thf(f1952,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v12 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(or_proxy_clausification,[],[f1951]) ).
thf(f1953,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v12 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1952]) ).
thf(f1954,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v12 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f1953]) ).
thf(f1955,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v12 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1954]) ).
thf(f1956,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v12 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f1955]) ).
thf(f1957,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v12 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1956]) ).
thf(f1958,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v12 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1957]) ).
thf(f1959,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v12 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1958]) ).
thf(f1960,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v12 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1959]) ).
thf(f1961,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v12 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1960]) ).
thf(f1962,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v12 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f1961]) ).
thf(f1963,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v12 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1962]) ).
thf(f1964,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v12 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1963]) ).
thf(f1965,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v12 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1964]) ).
thf(f1966,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v12 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1965]) ).
thf(f1967,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v12 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1966]) ).
thf(f1968,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v12 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f1967]) ).
thf(f1969,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v12 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1968]) ).
thf(f1970,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v12 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1969]) ).
thf(f1971,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v12 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1970]) ).
thf(f1972,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v12 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1971]) ).
thf(f1973,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v12 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1972]) ).
thf(f1974,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v12 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f1973]) ).
thf(f1975,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v12 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1974]) ).
thf(f1976,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v12 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1975]) ).
thf(f1977,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v12 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1976]) ).
thf(f1978,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ~ ( v12 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1977]) ).
thf(f1979,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ~ ( v12 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1978]) ).
thf(f1980,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ~ ( v12 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v10 @ Y2 ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1979]) ).
thf(f1981,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( ~ ( v12 @ X17 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1980]) ).
thf(f1982,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ~ ( v12 @ X17 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1981]) ).
thf(f1983,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v12 @ X17 ) ) ) ),
inference(or_proxy_clausification,[],[f1982]) ).
thf(f1984,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) )
@ X18 ) )
| ( $true
= ( ~ ( v12 @ X17 ) ) ) ),
inference(pi_proxy_clausification,[],[f1983]) ).
thf(f1985,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v10 @ Y1 ) ) ) )
@ X18 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(not_proxy_clausification,[],[f1984]) ).
thf(f1986,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( v10 @ Y0 ) ) ) ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(beta-eta_normalization,[],[f1985]) ).
thf(f1987,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( v10 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1986]) ).
thf(f1988,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( v10 @ Y0 ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f1987]) ).
thf(f1989,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( v10 @ X19 ) ) ) ),
inference(beta-eta_normalization,[],[f1988]) ).
thf(f1990,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(imp_proxy_clausification,[],[f1989]) ).
thf(f2163,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f2164,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2163]) ).
thf(f2165,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2164]) ).
thf(f2166,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2165]) ).
thf(f2167,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2166]) ).
thf(f2168,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2167]) ).
thf(f2169,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2168]) ).
thf(f2170,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2169]) ).
thf(f2171,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2170]) ).
thf(f2172,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2171]) ).
thf(f2173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2172]) ).
thf(f2174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2173]) ).
thf(f2175,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2174]) ).
thf(f2176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2175]) ).
thf(f2177,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2176]) ).
thf(f2178,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2177]) ).
thf(f2179,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f2178]) ).
thf(f2180,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(pi_proxy_clausification,[],[f2179]) ).
thf(f2181,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f2180]) ).
thf(f2182,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2181]) ).
thf(f2183,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2182]) ).
thf(f2184,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f2183]) ).
thf(f2185,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2184]) ).
thf(f2186,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2185]) ).
thf(f2187,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2186]) ).
thf(f2188,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2187]) ).
thf(f2189,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2188]) ).
thf(f2190,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2189]) ).
thf(f2191,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2190]) ).
thf(f2192,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2191]) ).
thf(f2193,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2192]) ).
thf(f2194,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2193]) ).
thf(f2195,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2194]) ).
thf(f2196,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) ) ),
inference(or_proxy_clausification,[],[f2195]) ).
thf(f2197,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) ) ),
inference(pi_proxy_clausification,[],[f2196]) ).
thf(f2198,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f2197]) ).
thf(f2199,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f2198]) ).
thf(f2200,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2199]) ).
thf(f2201,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2200]) ).
thf(f2202,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2201]) ).
thf(f2203,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2202]) ).
thf(f2204,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2203]) ).
thf(f2205,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2204]) ).
thf(f2206,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2205]) ).
thf(f2207,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2206]) ).
thf(f2208,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2207]) ).
thf(f2209,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2208]) ).
thf(f2210,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(or_proxy_clausification,[],[f2209]) ).
thf(f2211,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2210]) ).
thf(f2212,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v15 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f2211]) ).
thf(f2213,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2212]) ).
thf(f2214,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2213]) ).
thf(f2215,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2214]) ).
thf(f2216,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2215]) ).
thf(f2217,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2216]) ).
thf(f2218,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2217]) ).
thf(f2219,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2218]) ).
thf(f2220,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2219]) ).
thf(f2221,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2220]) ).
thf(f2222,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2221]) ).
thf(f2223,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2222]) ).
thf(f2224,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ~ ( v10 @ X19 ) ) ) ),
inference(beta-eta_normalization,[],[f2223]) ).
thf(f2225,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ~ ( v10 @ X19 ) ) ) ),
inference(imp_proxy_clausification,[],[f2224]) ).
thf(f2226,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(not_proxy_clausification,[],[f2225]) ).
thf(f2712,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f2713,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2712]) ).
thf(f2714,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2713]) ).
thf(f2715,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2714]) ).
thf(f2716,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2715]) ).
thf(f2717,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2716]) ).
thf(f2718,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2717]) ).
thf(f2719,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2718]) ).
thf(f2720,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2719]) ).
thf(f2721,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2720]) ).
thf(f2722,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2721]) ).
thf(f2723,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( ~ ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2722]) ).
thf(f2724,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2723]) ).
thf(f2725,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f2724]) ).
thf(f2726,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(pi_proxy_clausification,[],[f2725]) ).
thf(f2727,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f2726]) ).
thf(f2728,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2727]) ).
thf(f2729,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2728]) ).
thf(f2730,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f2729]) ).
thf(f2731,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(pi_proxy_clausification,[],[f2730]) ).
thf(f2732,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f2731]) ).
thf(f2733,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2732]) ).
thf(f2734,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2733]) ).
thf(f2735,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f2734]) ).
thf(f2736,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2735]) ).
thf(f2737,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2736]) ).
thf(f2738,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2737]) ).
thf(f2739,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2738]) ).
thf(f2740,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2739]) ).
thf(f2741,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2740]) ).
thf(f2742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2741]) ).
thf(f2743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2742]) ).
thf(f2744,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2743]) ).
thf(f2745,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2744]) ).
thf(f2746,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2745]) ).
thf(f2747,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v19 @ X10 ) ) ),
inference(or_proxy_clausification,[],[f2746]) ).
thf(f2748,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $true
= ( v19 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2747]) ).
thf(f2749,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v19 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f2748]) ).
thf(f2750,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2749]) ).
thf(f2751,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2750]) ).
thf(f2752,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2751]) ).
thf(f2753,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2752]) ).
thf(f2754,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2753]) ).
thf(f2755,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2754]) ).
thf(f2756,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2755]) ).
thf(f2757,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2756]) ).
thf(f2758,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2757]) ).
thf(f2759,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2758]) ).
thf(f2760,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2759]) ).
thf(f2761,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2760]) ).
thf(f2762,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2761]) ).
thf(f2763,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2762]) ).
thf(f2764,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2763]) ).
thf(f2765,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2764]) ).
thf(f2766,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2765]) ).
thf(f2767,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2766]) ).
thf(f2768,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2767]) ).
thf(f2769,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2768]) ).
thf(f2770,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2769]) ).
thf(f2771,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2770]) ).
thf(f2772,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2771]) ).
thf(f2773,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2772]) ).
thf(f2774,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2773]) ).
thf(f2775,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f2774]) ).
thf(f2776,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2775]) ).
thf(f2777,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2776]) ).
thf(f2778,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f2777]) ).
thf(f2779,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ~ ( v8 @ X21 ) ) ) ),
inference(beta-eta_normalization,[],[f2778]) ).
thf(f2780,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ~ ( v8 @ X21 ) ) ) ),
inference(imp_proxy_clausification,[],[f2779]) ).
thf(f2781,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(not_proxy_clausification,[],[f2780]) ).
thf(f2849,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v14 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f269]) ).
thf(f2850,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v14 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2849]) ).
thf(f2851,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2850]) ).
thf(f2852,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2851]) ).
thf(f2853,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2852]) ).
thf(f2854,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2853]) ).
thf(f2855,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2854]) ).
thf(f2856,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2855]) ).
thf(f2857,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2856]) ).
thf(f2858,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2857]) ).
thf(f2859,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2858]) ).
thf(f2860,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2859]) ).
thf(f2861,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2860]) ).
thf(f2862,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f2861]) ).
thf(f2863,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2862]) ).
thf(f2864,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2863]) ).
thf(f2865,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2864]) ).
thf(f2866,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2865]) ).
thf(f2867,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2866]) ).
thf(f2868,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2867]) ).
thf(f2869,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f2868]) ).
thf(f2870,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2869]) ).
thf(f2871,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2870]) ).
thf(f2872,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2871]) ).
thf(f2873,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2872]) ).
thf(f2874,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2873]) ).
thf(f2875,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2874]) ).
thf(f2876,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2875]) ).
thf(f2877,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2876]) ).
thf(f2878,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(or_proxy_clausification,[],[f2877]) ).
thf(f2879,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2878]) ).
thf(f2880,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2879]) ).
thf(f2881,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2880]) ).
thf(f2882,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2881]) ).
thf(f2883,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2882]) ).
thf(f2884,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2883]) ).
thf(f2885,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2884]) ).
thf(f2886,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2885]) ).
thf(f2887,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2886]) ).
thf(f2888,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2887]) ).
thf(f2889,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2888]) ).
thf(f2890,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2889]) ).
thf(f2891,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2890]) ).
thf(f2892,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2891]) ).
thf(f2893,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2892]) ).
thf(f2894,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2893]) ).
thf(f2895,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( ~ ( v14 @ X15 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2894]) ).
thf(f2896,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ~ ( v14 @ X15 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2895]) ).
thf(f2897,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v14 @ X15 ) ) ) ),
inference(or_proxy_clausification,[],[f2896]) ).
thf(f2898,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) )
| ( $true
= ( ~ ( v14 @ X15 ) ) ) ),
inference(pi_proxy_clausification,[],[f2897]) ).
thf(f2899,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) )
| ( $false
= ( v14 @ X15 ) ) ),
inference(not_proxy_clausification,[],[f2898]) ).
thf(f2900,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f2899]) ).
thf(f2901,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2900]) ).
thf(f2902,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2901]) ).
thf(f2903,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2902]) ).
thf(f2904,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2903]) ).
thf(f2905,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2904]) ).
thf(f2906,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2905]) ).
thf(f2907,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2906]) ).
thf(f2908,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2907]) ).
thf(f2909,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2908]) ).
thf(f2910,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2909]) ).
thf(f2911,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f2910]) ).
thf(f2912,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2911]) ).
thf(f2913,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2912]) ).
thf(f2914,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f2913]) ).
thf(f2915,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ~ ( v8 @ X21 ) ) ) ),
inference(beta-eta_normalization,[],[f2914]) ).
thf(f2916,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ~ ( v8 @ X21 ) ) ) ),
inference(imp_proxy_clausification,[],[f2915]) ).
thf(f2917,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(not_proxy_clausification,[],[f2916]) ).
thf(f3081,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v13 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f3082,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v13 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f3081]) ).
thf(f3083,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3082]) ).
thf(f3084,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3083]) ).
thf(f3085,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f3084]) ).
thf(f3086,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3085]) ).
thf(f3087,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3086]) ).
thf(f3088,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3087]) ).
thf(f3089,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3088]) ).
thf(f3090,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3089]) ).
thf(f3091,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3090]) ).
thf(f3092,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3091]) ).
thf(f3093,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3092]) ).
thf(f3094,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f3093]) ).
thf(f3095,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3094]) ).
thf(f3096,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3095]) ).
thf(f3097,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3096]) ).
thf(f3098,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f3097]) ).
thf(f3099,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(pi_proxy_clausification,[],[f3098]) ).
thf(f3100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f3099]) ).
thf(f3101,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v13 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3100]) ).
thf(f3102,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v13 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3101]) ).
thf(f3103,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v13 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f3102]) ).
thf(f3104,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3103]) ).
thf(f3105,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3104]) ).
thf(f3106,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f3105]) ).
thf(f3107,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3106]) ).
thf(f3108,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3107]) ).
thf(f3109,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f3108]) ).
thf(f3110,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3109]) ).
thf(f3111,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3110]) ).
thf(f3112,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f3111]) ).
thf(f3113,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3112]) ).
thf(f3114,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3113]) ).
thf(f3115,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f3114]) ).
thf(f3116,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3115]) ).
thf(f3117,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3116]) ).
thf(f3118,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f3117]) ).
thf(f3119,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3118]) ).
thf(f3120,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3119]) ).
thf(f3121,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f3120]) ).
thf(f3122,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3121]) ).
thf(f3123,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3122]) ).
thf(f3124,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f3123]) ).
thf(f3125,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3124]) ).
thf(f3126,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3125]) ).
thf(f3127,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f3126]) ).
thf(f3128,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3127]) ).
thf(f3129,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3128]) ).
thf(f3130,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f3129]) ).
thf(f3131,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( ( v13 @ X16 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3130]) ).
thf(f3132,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( v13 @ X16 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3131]) ).
thf(f3133,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(or_proxy_clausification,[],[f3132]) ).
thf(f3134,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) )
@ X17 ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(pi_proxy_clausification,[],[f3133]) ).
thf(f3135,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ~ ( v12 @ X17 ) ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f3134]) ).
thf(f3136,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $true
= ( ~ ( v12 @ X17 ) ) ) ),
inference(imp_proxy_clausification,[],[f3135]) ).
thf(f3137,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(not_proxy_clausification,[],[f3136]) ).
thf(f4548,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f610,f193]) ).
thf(f4549,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f4548]) ).
thf(f4550,plain,
! [X2: mworld,X3: mworld,X4: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4549,f193]) ).
thf(f4551,plain,
! [X2: mworld,X3: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f4550]) ).
thf(f4552,plain,
! [X3: mworld,X4: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4551,f193]) ).
thf(f4553,plain,
! [X3: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f4552]) ).
thf(f4554,plain,
! [X4: mworld] :
( ( $true = $false )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4553,f193]) ).
thf(f4555,plain,
! [X4: mworld] :
( $true
= ( v24 @ ( sK34 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4554]) ).
thf(f4566,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f599,f193]) ).
thf(f4567,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4566]) ).
thf(f4568,plain,
! [X2: mworld,X3: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4567,f193]) ).
thf(f4569,plain,
! [X2: mworld,X3: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4568]) ).
thf(f4570,plain,
! [X3: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4569,f193]) ).
thf(f4571,plain,
! [X3: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4570]) ).
thf(f4572,plain,
! [X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4571,f193]) ).
thf(f4573,plain,
! [X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4572]) ).
thf(f4574,plain,
! [X5: mworld] :
( ( $true = $false )
| ( $true
= ( v23 @ ( sK32 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4573,f193]) ).
thf(f4575,plain,
! [X5: mworld] :
( $true
= ( v23 @ ( sK32 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4574]) ).
thf(f4600,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f594,f193]) ).
thf(f4601,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4600]) ).
thf(f4602,plain,
! [X2: mworld,X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4601,f193]) ).
thf(f4603,plain,
! [X2: mworld,X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4602]) ).
thf(f4604,plain,
! [X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4603,f193]) ).
thf(f4605,plain,
! [X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4604]) ).
thf(f4606,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4605,f193]) ).
thf(f4607,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4606]) ).
thf(f4608,plain,
! [X6: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4607,f193]) ).
thf(f4609,plain,
! [X6: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4608]) ).
thf(f4610,plain,
! [X6: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4609,f193]) ).
thf(f4611,plain,
! [X6: mworld] :
( $false
= ( v22 @ ( sK31 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4610]) ).
thf(f4614,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f577,f193]) ).
thf(f4615,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4614]) ).
thf(f4616,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4615,f193]) ).
thf(f4617,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4616]) ).
thf(f4618,plain,
! [X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4617,f193]) ).
thf(f4619,plain,
! [X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4618]) ).
thf(f4620,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4619,f193]) ).
thf(f4621,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4620]) ).
thf(f4622,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4621,f193]) ).
thf(f4623,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4622]) ).
thf(f4624,plain,
! [X6: mworld,X7: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4623,f193]) ).
thf(f4625,plain,
! [X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4624]) ).
thf(f4626,plain,
! [X7: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4625,f193]) ).
thf(f4627,plain,
! [X7: mworld] :
( $true
= ( v21 @ ( sK28 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4626]) ).
thf(f4628,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f583,f193]) ).
thf(f4629,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4628]) ).
thf(f4630,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4629,f193]) ).
thf(f4631,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4630]) ).
thf(f4632,plain,
! [X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4631,f193]) ).
thf(f4633,plain,
! [X3: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4632]) ).
thf(f4634,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4633,f193]) ).
thf(f4635,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4634]) ).
thf(f4636,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4635,f193]) ).
thf(f4637,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4636]) ).
thf(f4638,plain,
! [X6: mworld,X7: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4637,f193]) ).
thf(f4639,plain,
! [X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4638]) ).
thf(f4640,plain,
! [X7: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ ( sK29 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4639,f193]) ).
thf(f4641,plain,
! [X7: mworld] :
( $false
= ( v21 @ ( sK29 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4640]) ).
thf(f4694,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f539,f193]) ).
thf(f4695,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4694]) ).
thf(f4696,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4695,f193]) ).
thf(f4697,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4696]) ).
thf(f4698,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4697,f193]) ).
thf(f4699,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4698]) ).
thf(f4700,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4699,f193]) ).
thf(f4701,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4700]) ).
thf(f4702,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4701,f193]) ).
thf(f4703,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4702]) ).
thf(f4704,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4703,f193]) ).
thf(f4705,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4704]) ).
thf(f4706,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4705,f193]) ).
thf(f4707,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4706]) ).
thf(f4708,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4707,f193]) ).
thf(f4709,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4708]) ).
thf(f4710,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4709,f193]) ).
thf(f4711,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4710]) ).
thf(f4712,plain,
! [X10: mworld,X11: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4711,f193]) ).
thf(f4713,plain,
! [X10: mworld,X11: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4712]) ).
thf(f4714,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4713,f193]) ).
thf(f4715,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4714]) ).
thf(f4716,plain,
! [X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4715,f193]) ).
thf(f4717,plain,
! [X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4716]) ).
thf(f4718,plain,
! [X13: mworld] :
( ( $true = $false )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4717,f193]) ).
thf(f4719,plain,
! [X13: mworld] :
( $true
= ( v15 @ ( sK20 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4718]) ).
thf(f4720,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f545,f193]) ).
thf(f4721,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4720]) ).
thf(f4722,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4721,f193]) ).
thf(f4723,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4722]) ).
thf(f4724,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4723,f193]) ).
thf(f4725,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4724]) ).
thf(f4726,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4725,f193]) ).
thf(f4727,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4726]) ).
thf(f4728,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4727,f193]) ).
thf(f4729,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4728]) ).
thf(f4730,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4729,f193]) ).
thf(f4731,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4730]) ).
thf(f4732,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4731,f193]) ).
thf(f4733,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4732]) ).
thf(f4734,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4733,f193]) ).
thf(f4735,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4734]) ).
thf(f4736,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4735,f193]) ).
thf(f4737,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4736]) ).
thf(f4738,plain,
! [X10: mworld,X11: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4737,f193]) ).
thf(f4739,plain,
! [X10: mworld,X11: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4738]) ).
thf(f4740,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4739,f193]) ).
thf(f4741,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4740]) ).
thf(f4742,plain,
! [X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4741,f193]) ).
thf(f4743,plain,
! [X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4742]) ).
thf(f4744,plain,
! [X13: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ ( sK21 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4743,f193]) ).
thf(f4745,plain,
! [X13: mworld] :
( $false
= ( v15 @ ( sK21 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4744]) ).
thf(f4748,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f528,f193]) ).
thf(f4749,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4748]) ).
thf(f4750,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4749,f193]) ).
thf(f4751,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4750]) ).
thf(f4752,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4751,f193]) ).
thf(f4753,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4752]) ).
thf(f4754,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4753,f193]) ).
thf(f4755,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4754]) ).
thf(f4756,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4755,f193]) ).
thf(f4757,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4756]) ).
thf(f4758,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4757,f193]) ).
thf(f4759,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4758]) ).
thf(f4760,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4759,f193]) ).
thf(f4761,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4760]) ).
thf(f4762,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4761,f193]) ).
thf(f4763,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4762]) ).
thf(f4764,plain,
! [X10: mworld,X11: mworld,X9: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4763,f193]) ).
thf(f4765,plain,
! [X10: mworld,X11: mworld,X9: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4764]) ).
thf(f4766,plain,
! [X10: mworld,X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4765,f193]) ).
thf(f4767,plain,
! [X10: mworld,X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4766]) ).
thf(f4768,plain,
! [X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4767,f193]) ).
thf(f4769,plain,
! [X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4768]) ).
thf(f4770,plain,
! [X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4769,f193]) ).
thf(f4771,plain,
! [X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4770]) ).
thf(f4772,plain,
! [X14: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4771,f193]) ).
thf(f4773,plain,
! [X14: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4772]) ).
thf(f4774,plain,
! [X14: mworld] :
( ( $true = $false )
| ( $true
= ( v14 @ ( sK18 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4773,f193]) ).
thf(f4775,plain,
! [X14: mworld] :
( $true
= ( v14 @ ( sK18 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f4774]) ).
thf(f4836,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f523,f193]) ).
thf(f4837,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4836]) ).
thf(f4838,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4837,f193]) ).
thf(f4839,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4838]) ).
thf(f4840,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4839,f193]) ).
thf(f4841,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4840]) ).
thf(f4842,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4841,f193]) ).
thf(f4843,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4842]) ).
thf(f4844,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4843,f193]) ).
thf(f4845,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4844]) ).
thf(f4846,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4845,f193]) ).
thf(f4847,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4846]) ).
thf(f4848,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4847,f193]) ).
thf(f4849,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4848]) ).
thf(f4850,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4849,f193]) ).
thf(f4851,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4850]) ).
thf(f4852,plain,
! [X10: mworld,X11: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4851,f193]) ).
thf(f4853,plain,
! [X10: mworld,X11: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4852]) ).
thf(f4854,plain,
! [X10: mworld,X11: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4853,f193]) ).
thf(f4855,plain,
! [X10: mworld,X11: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4854]) ).
thf(f4856,plain,
! [X11: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4855,f193]) ).
thf(f4857,plain,
! [X11: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4856]) ).
thf(f4858,plain,
! [X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4857,f193]) ).
thf(f4859,plain,
! [X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4858]) ).
thf(f4860,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4859,f193]) ).
thf(f4861,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4860]) ).
thf(f4862,plain,
! [X14: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4861,f193]) ).
thf(f4863,plain,
! [X14: mworld,X15: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4862]) ).
thf(f4864,plain,
! [X15: mworld] :
( ( $true = $false )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4863,f193]) ).
thf(f4865,plain,
! [X15: mworld] :
( $false
= ( v13 @ ( sK17 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4864]) ).
thf(f4902,definition,
( spl40_4
<=> ! [X6: mworld] :
( $false
= ( v23 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_4])],[avatar_definition]) ).
thf(f4903,plain,
( ! [X6: mworld] :
( $false
= ( v23 @ X6 ) )
| ~ spl40_4 ),
inference(avatar_component_clause,[],[f4902]) ).
thf(f4918,plain,
( ( $true = $false )
| ~ spl40_4 ),
inference(constrained_superposition,[],[f4903,f4575]) ).
thf(f4922,plain,
( $false
| ~ spl40_4 ),
inference(trivial_inequality_removal,[],[f4918]) ).
thf(f4923,plain,
~ spl40_4,
inference(avatar_contradiction_clause,[],[f4922]) ).
thf(f4925,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f1778,f193]) ).
thf(f4926,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4925]) ).
thf(f4927,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4926,f193]) ).
thf(f4928,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4927]) ).
thf(f4929,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4928,f193]) ).
thf(f4930,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4929]) ).
thf(f4931,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4930,f193]) ).
thf(f4932,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4931]) ).
thf(f4933,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4932,f193]) ).
thf(f4934,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4933]) ).
thf(f4935,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4934,f193]) ).
thf(f4936,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4935]) ).
thf(f4937,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4936,f193]) ).
thf(f4938,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4937]) ).
thf(f4939,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4938,f193]) ).
thf(f4940,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4939]) ).
thf(f4941,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4940,f193]) ).
thf(f4942,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4941]) ).
thf(f4943,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4942,f193]) ).
thf(f4944,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4943]) ).
thf(f4945,plain,
! [X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4944,f193]) ).
thf(f4946,plain,
! [X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4945]) ).
thf(f4947,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4946,f193]) ).
thf(f4948,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4947]) ).
thf(f4949,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4948,f193]) ).
thf(f4950,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4949]) ).
thf(f4951,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4950,f193]) ).
thf(f4952,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4951]) ).
thf(f4953,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4952,f193]) ).
thf(f4954,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4953]) ).
thf(f4955,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4954,f193]) ).
thf(f4956,plain,
! [X8: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4955]) ).
thf(f4957,plain,
! [X8: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4956,f193]) ).
thf(f4958,plain,
! [X8: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $true
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4957]) ).
thf(f4960,definition,
( spl40_7
<=> ! [X17: mworld] :
( $true
= ( v12 @ X17 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_7])],[avatar_definition]) ).
thf(f4961,plain,
( ! [X17: mworld] :
( $true
= ( v12 @ X17 ) )
| ~ spl40_7 ),
inference(avatar_component_clause,[],[f4960]) ).
thf(f4963,definition,
( spl40_8
<=> ! [X14: mworld] :
( $true
= ( v15 @ X14 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_8])],[avatar_definition]) ).
thf(f4964,plain,
( ! [X14: mworld] :
( $true
= ( v15 @ X14 ) )
| ~ spl40_8 ),
inference(avatar_component_clause,[],[f4963]) ).
thf(f4966,definition,
( spl40_9
<=> ! [X9: mworld] :
( $false
= ( v20 @ X9 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_9])],[avatar_definition]) ).
thf(f4967,plain,
( ! [X9: mworld] :
( $false
= ( v20 @ X9 ) )
| ~ spl40_9 ),
inference(avatar_component_clause,[],[f4966]) ).
thf(f4969,definition,
( spl40_10
<=> ! [X8: mworld] :
( $true
= ( v21 @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_10])],[avatar_definition]) ).
thf(f4970,plain,
( ! [X8: mworld] :
( $true
= ( v21 @ X8 ) )
| ~ spl40_10 ),
inference(avatar_component_clause,[],[f4969]) ).
thf(f4971,plain,
( spl40_7
| spl40_8
| spl40_9
| spl40_10 ),
inference(avatar_split_clause,[],[f4958,f4969,f4966,f4963,f4960]) ).
thf(f4972,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f3137,f193]) ).
thf(f4973,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4972]) ).
thf(f4974,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4973,f193]) ).
thf(f4975,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4974]) ).
thf(f4976,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4975,f193]) ).
thf(f4977,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4976]) ).
thf(f4978,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4977,f193]) ).
thf(f4979,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4978]) ).
thf(f4980,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4979,f193]) ).
thf(f4981,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4980]) ).
thf(f4982,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4981,f193]) ).
thf(f4983,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4982]) ).
thf(f4984,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4983,f193]) ).
thf(f4985,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4984]) ).
thf(f4986,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4985,f193]) ).
thf(f4987,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4986]) ).
thf(f4988,plain,
! [X10: mworld,X11: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4987,f193]) ).
thf(f4989,plain,
! [X10: mworld,X11: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4988]) ).
thf(f4990,plain,
! [X10: mworld,X11: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4989,f193]) ).
thf(f4991,plain,
! [X10: mworld,X11: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4990]) ).
thf(f4992,plain,
! [X11: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4991,f193]) ).
thf(f4993,plain,
! [X11: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4992]) ).
thf(f4994,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4993,f193]) ).
thf(f4995,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4994]) ).
thf(f4996,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4995,f193]) ).
thf(f4997,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4996]) ).
thf(f4998,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4997,f193]) ).
thf(f4999,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4998]) ).
thf(f5000,plain,
! [X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4999,f193]) ).
thf(f5001,plain,
! [X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5000]) ).
thf(f5002,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f5001,f193]) ).
thf(f5003,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5002]) ).
thf(f5004,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f5003,f193]) ).
thf(f5005,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5004]) ).
thf(f5006,plain,
( ! [X16: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v13 @ X16 ) ) )
| ~ spl40_7 ),
inference(forward_demodulation,[],[f5005,f4961]) ).
thf(f5007,plain,
( ! [X16: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v13 @ X16 ) ) )
| ~ spl40_7 ),
inference(trivial_inequality_removal,[],[f5006]) ).
thf(f5009,definition,
( spl40_11
<=> ! [X16: mworld] :
( $true
= ( v13 @ X16 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_11])],[avatar_definition]) ).
thf(f5010,plain,
( ! [X16: mworld] :
( $true
= ( v13 @ X16 ) )
| ~ spl40_11 ),
inference(avatar_component_clause,[],[f5009]) ).
thf(f5012,definition,
( spl40_12
<=> ! [X5: mworld] :
( $false
= ( v24 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_12])],[avatar_definition]) ).
thf(f5013,plain,
( ! [X5: mworld] :
( $false
= ( v24 @ X5 ) )
| ~ spl40_12 ),
inference(avatar_component_clause,[],[f5012]) ).
thf(f5015,definition,
( spl40_13
<=> ! [X4: mworld] :
( $true
= ( v25 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_13])],[avatar_definition]) ).
thf(f5016,plain,
( ! [X4: mworld] :
( $true
= ( v25 @ X4 ) )
| ~ spl40_13 ),
inference(avatar_component_clause,[],[f5015]) ).
thf(f5017,plain,
( spl40_11
| spl40_12
| spl40_13
| ~ spl40_7 ),
inference(avatar_split_clause,[],[f5007,f4960,f5015,f5012,f5009]) ).
thf(f5018,plain,
( ( $true = $false )
| ~ spl40_11 ),
inference(constrained_superposition,[],[f5010,f4865]) ).
thf(f5022,plain,
( $false
| ~ spl40_11 ),
inference(trivial_inequality_removal,[],[f5018]) ).
thf(f5023,plain,
~ spl40_11,
inference(avatar_contradiction_clause,[],[f5022]) ).
thf(f5025,plain,
( ( $true = $false )
| ~ spl40_12 ),
inference(constrained_superposition,[],[f5013,f4555]) ).
thf(f5029,plain,
( $false
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5025]) ).
thf(f5030,plain,
~ spl40_12,
inference(avatar_contradiction_clause,[],[f5029]) ).
thf(f5032,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f490,f193]) ).
thf(f5033,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5032]) ).
thf(f5034,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5033,f193]) ).
thf(f5035,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5034]) ).
thf(f5036,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5035,f193]) ).
thf(f5037,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5036]) ).
thf(f5038,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5037,f193]) ).
thf(f5039,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5038]) ).
thf(f5040,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5039,f193]) ).
thf(f5041,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5040]) ).
thf(f5042,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5041,f193]) ).
thf(f5043,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5042]) ).
thf(f5044,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5043,f193]) ).
thf(f5045,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5044]) ).
thf(f5046,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5045,f193]) ).
thf(f5047,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5046]) ).
thf(f5048,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5047,f193]) ).
thf(f5049,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5048]) ).
thf(f5050,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5049,f193]) ).
thf(f5051,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5050]) ).
thf(f5052,plain,
! [X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5051,f193]) ).
thf(f5053,plain,
! [X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5052]) ).
thf(f5054,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5053,f193]) ).
thf(f5055,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5054]) ).
thf(f5056,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5055,f193]) ).
thf(f5057,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5056]) ).
thf(f5058,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5057,f193]) ).
thf(f5059,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5058]) ).
thf(f5060,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5059,f193]) ).
thf(f5061,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5060]) ).
thf(f5062,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5061,f193]) ).
thf(f5063,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5062]) ).
thf(f5064,plain,
! [X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5063,f193]) ).
thf(f5065,plain,
! [X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5064]) ).
thf(f5066,plain,
! [X18: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5065,f193]) ).
thf(f5067,plain,
! [X18: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5066]) ).
thf(f5068,plain,
! [X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5067,f193]) ).
thf(f5069,plain,
! [X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5068]) ).
thf(f5070,plain,
! [X20: mworld] :
( ( $true = $false )
| ( $true
= ( v8 @ ( sK10 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5069,f193]) ).
thf(f5071,plain,
! [X20: mworld] :
( $true
= ( v8 @ ( sK10 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5070]) ).
thf(f5072,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f496,f193]) ).
thf(f5073,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5072]) ).
thf(f5074,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5073,f193]) ).
thf(f5075,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5074]) ).
thf(f5076,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5075,f193]) ).
thf(f5077,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5076]) ).
thf(f5078,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5077,f193]) ).
thf(f5079,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5078]) ).
thf(f5080,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5079,f193]) ).
thf(f5081,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5080]) ).
thf(f5082,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5081,f193]) ).
thf(f5083,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5082]) ).
thf(f5084,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5083,f193]) ).
thf(f5085,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5084]) ).
thf(f5086,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5085,f193]) ).
thf(f5087,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5086]) ).
thf(f5088,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5087,f193]) ).
thf(f5089,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5088]) ).
thf(f5090,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5089,f193]) ).
thf(f5091,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5090]) ).
thf(f5092,plain,
! [X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5091,f193]) ).
thf(f5093,plain,
! [X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5092]) ).
thf(f5094,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5093,f193]) ).
thf(f5095,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5094]) ).
thf(f5096,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5095,f193]) ).
thf(f5097,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5096]) ).
thf(f5098,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5097,f193]) ).
thf(f5099,plain,
! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5098]) ).
thf(f5100,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5099,f193]) ).
thf(f5101,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5100]) ).
thf(f5102,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5101,f193]) ).
thf(f5103,plain,
! [X18: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5102]) ).
thf(f5104,plain,
! [X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5103,f193]) ).
thf(f5105,plain,
! [X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5104]) ).
thf(f5106,plain,
! [X18: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5105,f193]) ).
thf(f5107,plain,
! [X18: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5106]) ).
thf(f5108,plain,
! [X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5107,f193]) ).
thf(f5109,plain,
! [X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5108]) ).
thf(f5110,plain,
! [X20: mworld] :
( ( $true = $false )
| ( $false
= ( v8 @ ( sK11 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5109,f193]) ).
thf(f5111,plain,
! [X20: mworld] :
( $false
= ( v8 @ ( sK11 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5110]) ).
thf(f5114,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f1841,f193]) ).
thf(f5115,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5114]) ).
thf(f5116,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5115,f193]) ).
thf(f5117,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5116]) ).
thf(f5118,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5117,f193]) ).
thf(f5119,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5118]) ).
thf(f5120,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5119,f193]) ).
thf(f5121,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5120]) ).
thf(f5122,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5121,f193]) ).
thf(f5123,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5122]) ).
thf(f5124,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5123,f193]) ).
thf(f5125,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5124]) ).
thf(f5126,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5125,f193]) ).
thf(f5127,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5126]) ).
thf(f5128,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5127,f193]) ).
thf(f5129,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5128]) ).
thf(f5130,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5129,f193]) ).
thf(f5131,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5130]) ).
thf(f5132,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5131,f193]) ).
thf(f5133,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5132]) ).
thf(f5134,plain,
! [X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5133,f193]) ).
thf(f5135,plain,
! [X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5134]) ).
thf(f5136,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5135,f193]) ).
thf(f5137,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5136]) ).
thf(f5138,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5137,f193]) ).
thf(f5139,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5138]) ).
thf(f5140,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5139,f193]) ).
thf(f5141,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5140]) ).
thf(f5142,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5141,f193]) ).
thf(f5143,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5142]) ).
thf(f5144,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5143,f193]) ).
thf(f5145,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5144]) ).
thf(f5146,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5145,f193]) ).
thf(f5147,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5146]) ).
thf(f5148,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X14: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5147,f193]) ).
thf(f5149,plain,
! [X18: mworld,X8: mworld,X19: mworld,X9: mworld,X14: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5148]) ).
thf(f5150,plain,
! [X8: mworld,X19: mworld,X9: mworld,X14: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5149,f193]) ).
thf(f5151,plain,
! [X8: mworld,X19: mworld,X9: mworld,X14: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5150]) ).
thf(f5153,definition,
( spl40_14
<=> ! [X19: mworld] :
( $false
= ( v10 @ X19 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_14])],[avatar_definition]) ).
thf(f5154,plain,
( ! [X19: mworld] :
( $false
= ( v10 @ X19 ) )
| ~ spl40_14 ),
inference(avatar_component_clause,[],[f5153]) ).
thf(f5156,definition,
( spl40_15
<=> ! [X14: mworld] :
( $false
= ( v15 @ X14 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_15])],[avatar_definition]) ).
thf(f5157,plain,
( ! [X14: mworld] :
( $false
= ( v15 @ X14 ) )
| ~ spl40_15 ),
inference(avatar_component_clause,[],[f5156]) ).
thf(f5159,definition,
( spl40_16
<=> ! [X9: mworld] :
( $true
= ( v20 @ X9 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_16])],[avatar_definition]) ).
thf(f5160,plain,
( ! [X9: mworld] :
( $true
= ( v20 @ X9 ) )
| ~ spl40_16 ),
inference(avatar_component_clause,[],[f5159]) ).
thf(f5161,plain,
( spl40_14
| spl40_15
| spl40_16
| spl40_10 ),
inference(avatar_split_clause,[],[f5151,f4969,f5159,f5156,f5153]) ).
thf(f5162,plain,
( ( $true = $false )
| ~ spl40_10 ),
inference(constrained_superposition,[],[f4970,f4641]) ).
thf(f5166,plain,
( $false
| ~ spl40_10 ),
inference(trivial_inequality_removal,[],[f5162]) ).
thf(f5167,plain,
~ spl40_10,
inference(avatar_contradiction_clause,[],[f5166]) ).
thf(f5170,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f1990,f193]) ).
thf(f5171,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5170]) ).
thf(f5172,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5171,f193]) ).
thf(f5173,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5172]) ).
thf(f5174,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5173,f193]) ).
thf(f5175,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5174]) ).
thf(f5176,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5175,f193]) ).
thf(f5177,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5176]) ).
thf(f5178,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5177,f193]) ).
thf(f5179,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5178]) ).
thf(f5180,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5179,f193]) ).
thf(f5181,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5180]) ).
thf(f5182,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5181,f193]) ).
thf(f5183,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5182]) ).
thf(f5184,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5183,f193]) ).
thf(f5185,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5184]) ).
thf(f5186,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5185,f193]) ).
thf(f5187,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5186]) ).
thf(f5188,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5187,f193]) ).
thf(f5189,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5188]) ).
thf(f5190,plain,
! [X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5189,f193]) ).
thf(f5191,plain,
! [X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5190]) ).
thf(f5192,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5191,f193]) ).
thf(f5193,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5192]) ).
thf(f5194,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5193,f193]) ).
thf(f5195,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5194]) ).
thf(f5196,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5195,f193]) ).
thf(f5197,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5196]) ).
thf(f5198,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5197,f193]) ).
thf(f5199,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5198]) ).
thf(f5200,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5199,f193]) ).
thf(f5201,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5200]) ).
thf(f5202,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5201,f193]) ).
thf(f5203,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5202]) ).
thf(f5204,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5203,f193]) ).
thf(f5205,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5204]) ).
thf(f5213,definition,
( spl40_17
<=> ! [X7: mworld] :
( $true
= ( v22 @ X7 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_17])],[avatar_definition]) ).
thf(f5214,plain,
( ! [X7: mworld] :
( $true
= ( v22 @ X7 ) )
| ~ spl40_17 ),
inference(avatar_component_clause,[],[f5213]) ).
thf(f5216,plain,
( ( $true = $false )
| ~ spl40_17 ),
inference(constrained_superposition,[],[f5214,f4611]) ).
thf(f5220,plain,
( $false
| ~ spl40_17 ),
inference(trivial_inequality_removal,[],[f5216]) ).
thf(f5221,plain,
~ spl40_17,
inference(avatar_contradiction_clause,[],[f5220]) ).
thf(f5222,plain,
! [X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5205,f193]) ).
thf(f5223,plain,
! [X6: mworld,X19: mworld,X7: mworld,X17: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5222]) ).
thf(f5369,definition,
( spl40_21
<=> ! [X8: mworld] :
( $false
= ( v21 @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_21])],[avatar_definition]) ).
thf(f5370,plain,
( ! [X8: mworld] :
( $false
= ( v21 @ X8 ) )
| ~ spl40_21 ),
inference(avatar_component_clause,[],[f5369]) ).
thf(f5464,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f1722,f193]) ).
thf(f5465,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5464]) ).
thf(f5466,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5465,f193]) ).
thf(f5467,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5466]) ).
thf(f5468,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5467,f193]) ).
thf(f5469,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5468]) ).
thf(f5470,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5469,f193]) ).
thf(f5471,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5470]) ).
thf(f5472,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5471,f193]) ).
thf(f5473,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5472]) ).
thf(f5474,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5473,f193]) ).
thf(f5475,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5474]) ).
thf(f5476,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5475,f193]) ).
thf(f5477,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5476]) ).
thf(f5478,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5477,f193]) ).
thf(f5479,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5478]) ).
thf(f5480,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5479,f193]) ).
thf(f5481,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5480]) ).
thf(f5482,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5481,f193]) ).
thf(f5483,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5482]) ).
thf(f5484,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5483,f193]) ).
thf(f5485,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5484]) ).
thf(f5486,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5485,f193]) ).
thf(f5487,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5486]) ).
thf(f5488,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5487,f193]) ).
thf(f5489,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5488]) ).
thf(f5490,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5489,f193]) ).
thf(f5491,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5490]) ).
thf(f5492,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5491,f193]) ).
thf(f5493,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5492]) ).
thf(f5494,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5493,f193]) ).
thf(f5495,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5494]) ).
thf(f5496,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5495,f193]) ).
thf(f5497,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5496]) ).
thf(f5498,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5497,f193]) ).
thf(f5499,plain,
! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5498]) ).
thf(f5500,plain,
! [X21: mworld,X10: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5499,f193]) ).
thf(f5501,plain,
! [X21: mworld,X10: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5500]) ).
thf(f5502,plain,
! [X21: mworld,X10: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5501,f193]) ).
thf(f5503,plain,
! [X21: mworld,X10: mworld,X8: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5502]) ).
thf(f5504,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) )
| ~ spl40_14 ),
inference(forward_demodulation,[],[f5503,f5154]) ).
thf(f5505,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v8 @ X21 ) ) )
| ~ spl40_14 ),
inference(trivial_inequality_removal,[],[f5504]) ).
thf(f5506,plain,
( ! [X21: mworld,X10: mworld,X8: mworld] :
( ( $true = $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v8 @ X21 ) ) )
| ~ spl40_14 ),
inference(forward_demodulation,[],[f5505,f193]) ).
thf(f5507,plain,
( ! [X21: mworld,X10: mworld,X8: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v8 @ X21 ) ) )
| ~ spl40_14 ),
inference(trivial_inequality_removal,[],[f5506]) ).
thf(f5509,definition,
( spl40_22
<=> ! [X21: mworld] :
( $true
= ( v8 @ X21 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_22])],[avatar_definition]) ).
thf(f5510,plain,
( ! [X21: mworld] :
( $true
= ( v8 @ X21 ) )
| ~ spl40_22 ),
inference(avatar_component_clause,[],[f5509]) ).
thf(f5512,definition,
( spl40_23
<=> ! [X10: mworld] :
( $false
= ( v19 @ X10 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_23])],[avatar_definition]) ).
thf(f5513,plain,
( ! [X10: mworld] :
( $false
= ( v19 @ X10 ) )
| ~ spl40_23 ),
inference(avatar_component_clause,[],[f5512]) ).
thf(f5514,plain,
( spl40_22
| spl40_23
| spl40_21
| ~ spl40_14 ),
inference(avatar_split_clause,[],[f5507,f5153,f5369,f5512,f5509]) ).
thf(f5516,plain,
( ( $true = $false )
| ~ spl40_21 ),
inference(constrained_superposition,[],[f5370,f4627]) ).
thf(f5520,plain,
( $false
| ~ spl40_21 ),
inference(trivial_inequality_removal,[],[f5516]) ).
thf(f5521,plain,
~ spl40_21,
inference(avatar_contradiction_clause,[],[f5520]) ).
thf(f5523,plain,
( ( $true = $false )
| ~ spl40_22 ),
inference(constrained_superposition,[],[f5510,f5111]) ).
thf(f5527,plain,
( $false
| ~ spl40_22 ),
inference(trivial_inequality_removal,[],[f5523]) ).
thf(f5528,plain,
~ spl40_22,
inference(avatar_contradiction_clause,[],[f5527]) ).
thf(f5531,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f2781,f193]) ).
thf(f5532,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5531]) ).
thf(f5533,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5532,f193]) ).
thf(f5534,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5533]) ).
thf(f5535,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5534,f193]) ).
thf(f5536,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5535]) ).
thf(f5537,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5536,f193]) ).
thf(f5538,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5537]) ).
thf(f5539,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5538,f193]) ).
thf(f5540,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5539]) ).
thf(f5541,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5540,f5016]) ).
thf(f5542,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5541]) ).
thf(f5543,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5542,f193]) ).
thf(f5544,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5543]) ).
thf(f5545,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5544,f193]) ).
thf(f5546,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5545]) ).
thf(f5547,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5546,f193]) ).
thf(f5548,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5547]) ).
thf(f5549,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5548,f193]) ).
thf(f5550,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5549]) ).
thf(f5551,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5550,f193]) ).
thf(f5552,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5551]) ).
thf(f5553,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5552,f193]) ).
thf(f5554,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5553]) ).
thf(f5555,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5554,f5513]) ).
thf(f5556,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5555]) ).
thf(f5557,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5556,f193]) ).
thf(f5558,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5557]) ).
thf(f5559,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5558,f193]) ).
thf(f5560,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5559]) ).
thf(f5561,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5560,f193]) ).
thf(f5562,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5561]) ).
thf(f5563,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5562,f193]) ).
thf(f5564,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5563]) ).
thf(f5565,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5564,f193]) ).
thf(f5566,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5565]) ).
thf(f5567,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5566,f193]) ).
thf(f5568,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5567]) ).
thf(f5569,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5568,f193]) ).
thf(f5570,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5569]) ).
thf(f5571,plain,
( ! [X21: mworld,X19: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5570,f193]) ).
thf(f5572,plain,
( ! [X21: mworld,X19: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5571]) ).
thf(f5573,plain,
( ! [X21: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5572,f193]) ).
thf(f5574,plain,
( ! [X21: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5573]) ).
thf(f5575,plain,
( ! [X21: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5574,f193]) ).
thf(f5576,plain,
( ! [X21: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_13
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5575]) ).
thf(f5578,definition,
( spl40_24
<=> ! [X21: mworld] :
( $false
= ( v8 @ X21 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_24])],[avatar_definition]) ).
thf(f5579,plain,
( ! [X21: mworld] :
( $false
= ( v8 @ X21 ) )
| ~ spl40_24 ),
inference(avatar_component_clause,[],[f5578]) ).
thf(f5580,plain,
( spl40_24
| spl40_12
| ~ spl40_13
| ~ spl40_23 ),
inference(avatar_split_clause,[],[f5576,f5512,f5015,f5012,f5578]) ).
thf(f5582,plain,
( ( $true = $false )
| ~ spl40_24 ),
inference(constrained_superposition,[],[f5579,f5071]) ).
thf(f5586,plain,
( $false
| ~ spl40_24 ),
inference(trivial_inequality_removal,[],[f5582]) ).
thf(f5587,plain,
~ spl40_24,
inference(avatar_contradiction_clause,[],[f5586]) ).
thf(f5591,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5540,f193]) ).
thf(f5592,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5591]) ).
thf(f5595,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5592,f193]) ).
thf(f5596,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5595]) ).
thf(f5599,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5596,f193]) ).
thf(f5600,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5599]) ).
thf(f5603,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5600,f193]) ).
thf(f5604,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5603]) ).
thf(f5607,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5604,f193]) ).
thf(f5608,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5607]) ).
thf(f5611,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5608,f193]) ).
thf(f5612,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5611]) ).
thf(f5615,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5612,f5513]) ).
thf(f5616,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5615]) ).
thf(f5619,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5616,f193]) ).
thf(f5620,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5619]) ).
thf(f5623,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5620,f193]) ).
thf(f5624,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5623]) ).
thf(f5627,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5624,f193]) ).
thf(f5628,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5627]) ).
thf(f5631,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5628,f193]) ).
thf(f5632,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5631]) ).
thf(f5635,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X4: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5632,f193]) ).
thf(f5636,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X4: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5635]) ).
thf(f5639,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X4: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5636,f193]) ).
thf(f5640,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X4: mworld,X17: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5639]) ).
thf(f5643,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5640,f193]) ).
thf(f5644,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5643]) ).
thf(f5647,plain,
( ! [X21: mworld,X19: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5644,f193]) ).
thf(f5648,plain,
( ! [X21: mworld,X19: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5647]) ).
thf(f5651,plain,
( ! [X21: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5648,f193]) ).
thf(f5652,plain,
( ! [X21: mworld,X4: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5651]) ).
thf(f5655,plain,
( ! [X21: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(forward_demodulation,[],[f5652,f193]) ).
thf(f5656,plain,
( ! [X21: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5655]) ).
thf(f5660,definition,
( spl40_25
<=> ! [X4: mworld] :
( $false
= ( v25 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_25])],[avatar_definition]) ).
thf(f5661,plain,
( ! [X4: mworld] :
( $false
= ( v25 @ X4 ) )
| ~ spl40_25 ),
inference(avatar_component_clause,[],[f5660]) ).
thf(f5662,plain,
( spl40_24
| spl40_12
| spl40_25
| ~ spl40_23 ),
inference(avatar_split_clause,[],[f5656,f5512,f5660,f5012,f5578]) ).
thf(f5725,plain,
( ( $true = $false )
| ~ spl40_8 ),
inference(constrained_superposition,[],[f4964,f4745]) ).
thf(f5729,plain,
( $false
| ~ spl40_8 ),
inference(trivial_inequality_removal,[],[f5725]) ).
thf(f5730,plain,
~ spl40_8,
inference(avatar_contradiction_clause,[],[f5729]) ).
thf(f5731,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f2917,f193]) ).
thf(f5732,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5731]) ).
thf(f5733,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5732,f193]) ).
thf(f5734,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5733]) ).
thf(f5735,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5734,f193]) ).
thf(f5736,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5735]) ).
thf(f5737,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5736,f193]) ).
thf(f5738,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5737]) ).
thf(f5739,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5738,f193]) ).
thf(f5740,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5739]) ).
thf(f5741,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5740,f5661]) ).
thf(f5742,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5741]) ).
thf(f5743,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5742,f193]) ).
thf(f5744,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5743]) ).
thf(f5745,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5744,f193]) ).
thf(f5746,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5745]) ).
thf(f5747,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5746,f193]) ).
thf(f5748,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5747]) ).
thf(f5749,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5748,f193]) ).
thf(f5750,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5749]) ).
thf(f5751,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5750,f193]) ).
thf(f5752,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5751]) ).
thf(f5753,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5752,f4967]) ).
thf(f5754,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5753]) ).
thf(f5755,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5754,f193]) ).
thf(f5756,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5755]) ).
thf(f5757,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5756,f193]) ).
thf(f5758,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5757]) ).
thf(f5759,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5758,f193]) ).
thf(f5760,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5759]) ).
thf(f5761,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5760,f193]) ).
thf(f5762,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5761]) ).
thf(f5763,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5762,f193]) ).
thf(f5764,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5763]) ).
thf(f5765,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5764,f193]) ).
thf(f5766,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5765]) ).
thf(f5767,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5766,f193]) ).
thf(f5768,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5767]) ).
thf(f5769,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5768,f193]) ).
thf(f5770,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5769]) ).
thf(f5771,plain,
( ! [X21: mworld,X19: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5770,f193]) ).
thf(f5772,plain,
( ! [X21: mworld,X19: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5771]) ).
thf(f5773,plain,
( ! [X21: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5772,f193]) ).
thf(f5774,plain,
( ! [X21: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5773]) ).
thf(f5775,plain,
( ! [X21: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5774,f193]) ).
thf(f5776,plain,
( ! [X21: mworld,X15: mworld] :
( ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl40_9
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5775]) ).
thf(f5778,definition,
( spl40_28
<=> ! [X15: mworld] :
( $false
= ( v14 @ X15 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_28])],[avatar_definition]) ).
thf(f5779,plain,
( ! [X15: mworld] :
( $false
= ( v14 @ X15 ) )
| ~ spl40_28 ),
inference(avatar_component_clause,[],[f5778]) ).
thf(f5780,plain,
( spl40_24
| spl40_28
| ~ spl40_9
| ~ spl40_25 ),
inference(avatar_split_clause,[],[f5776,f5660,f4966,f5778,f5578]) ).
thf(f5782,plain,
( ( $true = $false )
| ~ spl40_28 ),
inference(constrained_superposition,[],[f5779,f4775]) ).
thf(f5786,plain,
( $false
| ~ spl40_28 ),
inference(trivial_inequality_removal,[],[f5782]) ).
thf(f5787,plain,
~ spl40_28,
inference(avatar_contradiction_clause,[],[f5786]) ).
thf(f5795,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f2226,f193]) ).
thf(f5796,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5795]) ).
thf(f5803,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5796,f193]) ).
thf(f5804,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5803]) ).
thf(f5809,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5804,f193]) ).
thf(f5810,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5809]) ).
thf(f5815,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5810,f193]) ).
thf(f5816,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5815]) ).
thf(f5821,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5816,f193]) ).
thf(f5822,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5821]) ).
thf(f5827,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5822,f193]) ).
thf(f5828,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5827]) ).
thf(f5833,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5828,f193]) ).
thf(f5834,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5833]) ).
thf(f5839,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5834,f193]) ).
thf(f5840,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5839]) ).
thf(f5845,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5840,f193]) ).
thf(f5846,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5845]) ).
thf(f5851,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5846,f193]) ).
thf(f5852,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5851]) ).
thf(f5857,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5852,f193]) ).
thf(f5858,plain,
! [X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5857]) ).
thf(f5863,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5858,f193]) ).
thf(f5864,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5863]) ).
thf(f5867,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5864,f193]) ).
thf(f5868,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5867]) ).
thf(f5871,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5868,f193]) ).
thf(f5872,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5871]) ).
thf(f5875,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5872,f193]) ).
thf(f5876,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5875]) ).
thf(f5879,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5876,f193]) ).
thf(f5880,plain,
! [X10: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5879]) ).
thf(f5883,plain,
! [X10: mworld,X18: mworld,X19: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5880,f193]) ).
thf(f5884,plain,
! [X10: mworld,X18: mworld,X19: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5883]) ).
thf(f5887,plain,
! [X10: mworld,X18: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5884,f193]) ).
thf(f5888,plain,
! [X10: mworld,X18: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5887]) ).
thf(f5891,plain,
! [X10: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[],[f5888,f193]) ).
thf(f5892,plain,
! [X10: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5891]) ).
thf(f5955,plain,
( ( $true = $false )
| ~ spl40_15 ),
inference(constrained_superposition,[],[f5157,f4719]) ).
thf(f5959,plain,
( $false
| ~ spl40_15 ),
inference(trivial_inequality_removal,[],[f5955]) ).
thf(f5960,plain,
~ spl40_15,
inference(avatar_contradiction_clause,[],[f5959]) ).
thf(f6002,plain,
( ! [X6: mworld,X19: mworld,X7: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( v10 @ X19 ) ) )
| ~ spl40_7 ),
inference(forward_demodulation,[],[f5223,f4961]) ).
thf(f6003,plain,
( ! [X6: mworld,X19: mworld,X7: mworld] :
( ( $false
= ( v23 @ X6 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( v10 @ X19 ) ) )
| ~ spl40_7 ),
inference(trivial_inequality_removal,[],[f6002]) ).
thf(f6005,definition,
( spl40_29
<=> ! [X19: mworld] :
( $true
= ( v10 @ X19 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_29])],[avatar_definition]) ).
thf(f6006,plain,
( ! [X19: mworld] :
( $true
= ( v10 @ X19 ) )
| ~ spl40_29 ),
inference(avatar_component_clause,[],[f6005]) ).
thf(f6007,plain,
( spl40_29
| spl40_17
| spl40_4
| ~ spl40_7 ),
inference(avatar_split_clause,[],[f6003,f4960,f4902,f5213,f6005]) ).
thf(f6008,plain,
( ! [X10: mworld,X14: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) ) )
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5892,f6006]) ).
thf(f6009,plain,
( ! [X10: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $true
= ( v15 @ X14 ) ) )
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f6008]) ).
thf(f6010,plain,
( spl40_8
| spl40_23
| spl40_12
| ~ spl40_29 ),
inference(avatar_split_clause,[],[f6009,f6005,f5012,f5512,f4963]) ).
thf(f6016,plain,
( ( $true = $false )
| ~ spl40_9
| ~ spl40_16 ),
inference(constrained_superposition,[],[f4967,f5160]) ).
thf(f6020,plain,
( $false
| ~ spl40_9
| ~ spl40_16 ),
inference(trivial_inequality_removal,[],[f6016]) ).
thf(f6021,plain,
( ~ spl40_9
| ~ spl40_16 ),
inference(avatar_contradiction_clause,[],[f6020]) ).
cnf(s172,plain,
~ spl40_4,
inference(sat_conversion,[],[f4923]) ).
cnf(s177,plain,
( spl40_7
| spl40_8
| spl40_9
| spl40_10 ),
inference(sat_conversion,[],[f4971]) ).
cnf(s182,plain,
( ~ spl40_7
| spl40_11
| spl40_12
| spl40_13 ),
inference(sat_conversion,[],[f5017]) ).
cnf(s186,plain,
~ spl40_11,
inference(sat_conversion,[],[f5023]) ).
cnf(s190,plain,
~ spl40_12,
inference(sat_conversion,[],[f5030]) ).
cnf(s199,plain,
( spl40_10
| spl40_14
| spl40_15
| spl40_16 ),
inference(sat_conversion,[],[f5161]) ).
cnf(s203,plain,
~ spl40_10,
inference(sat_conversion,[],[f5167]) ).
cnf(s212,plain,
~ spl40_17,
inference(sat_conversion,[],[f5221]) ).
cnf(s235,plain,
( ~ spl40_14
| spl40_21
| spl40_22
| spl40_23 ),
inference(sat_conversion,[],[f5514]) ).
cnf(s239,plain,
~ spl40_21,
inference(sat_conversion,[],[f5521]) ).
cnf(s243,plain,
~ spl40_22,
inference(sat_conversion,[],[f5528]) ).
cnf(s248,plain,
( spl40_12
| ~ spl40_13
| ~ spl40_23
| spl40_24 ),
inference(sat_conversion,[],[f5580]) ).
cnf(s252,plain,
~ spl40_24,
inference(sat_conversion,[],[f5587]) ).
cnf(s256,plain,
( spl40_12
| ~ spl40_23
| spl40_24
| spl40_25 ),
inference(sat_conversion,[],[f5662]) ).
cnf(s274,plain,
~ spl40_8,
inference(sat_conversion,[],[f5730]) ).
cnf(s279,plain,
( ~ spl40_9
| spl40_24
| ~ spl40_25
| spl40_28 ),
inference(sat_conversion,[],[f5780]) ).
cnf(s283,plain,
~ spl40_28,
inference(sat_conversion,[],[f5787]) ).
cnf(s307,plain,
~ spl40_15,
inference(sat_conversion,[],[f5960]) ).
cnf(s314,plain,
( spl40_4
| ~ spl40_7
| spl40_17
| spl40_29 ),
inference(sat_conversion,[],[f6007]) ).
cnf(s319,plain,
( spl40_8
| spl40_12
| spl40_23
| ~ spl40_29 ),
inference(sat_conversion,[],[f6010]) ).
cnf(s327,plain,
( ~ spl40_9
| ~ spl40_16 ),
inference(sat_conversion,[],[f6021]) ).
cnf(s328,plain,
( ~ spl40_9
| spl40_24
| ~ spl40_25 ),
inference(rat,[],[s279,s283]) ).
cnf(s331,plain,
( spl40_12
| ~ spl40_13
| ~ spl40_23 ),
inference(rat,[],[s248,s252]) ).
cnf(s332,plain,
( ~ spl40_14
| spl40_23 ),
inference(rat,[],[s235,s243,s239]) ).
cnf(s335,plain,
( spl40_14
| spl40_16 ),
inference(rat,[],[s199,s307,s203]) ).
cnf(s336,plain,
( ~ spl40_7
| spl40_13 ),
inference(rat,[],[s182,s190,s186]) ).
cnf(s337,plain,
( spl40_7
| spl40_9 ),
inference(rat,[],[s177,s203,s274]) ).
cnf(s339,plain,
~ spl40_9,
inference(rat,[],[s332,s256,s335,s328,s327,s252,s190]) ).
cnf(s340,plain,
spl40_7,
inference(rat,[],[s337,s339]) ).
cnf(s341,plain,
spl40_29,
inference(rat,[],[s314,s172,s212,s340]) ).
cnf(s344,plain,
spl40_13,
inference(rat,[],[s336,s340]) ).
cnf(s345,plain,
spl40_23,
inference(rat,[],[s319,s190,s274,s341]) ).
cnf(s348,plain,
$false,
inference(rat,[],[s331,s190,s345,s344]) ).
thf(f6023,plain,
$false,
inference(avatar_sat_refutation,[],[s348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO905^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n020.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 17:27:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 2.24/0.60 % (1356272)Will run a generic schedule for satisfiability detection.
% 2.24/0.60 % (1356279)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1459854382:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.24/0.60 % (1356278)% WARNING: option uhcvi not known.
% 2.24/0.60 % (1356278)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3322951867:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.24/0.60 % (1356280)dis+10_1_sil=32000:sp=arity:random_seed=217732175:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.24/0.60 % (1356281)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3788476715:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.24/0.60 % (1356277)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3233206082_2999 on theBenchmark for (2999ds/0Mi)
% 2.24/0.60 % (1356282)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3833265217:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.24/0.60 % (1356283)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=835987394:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.24/0.60 % (1356278)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.24/0.60 % (1356281)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.24/0.60 % (1356280)Instruction limit reached!
% 2.24/0.60 % (1356280)------------------------------
% 2.24/0.60 % (1356280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356280)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356280)Termination reason: Instruction limit
% 2.24/0.60 % (1356280)Termination phase: Property scanning
% 2.24/0.60 % (1356280)Time elapsed: 0.036 s
% 2.24/0.60 % (1356280)Peak memory usage: 10 MB
% 2.24/0.60 % (1356280)Instructions burned: 103 (million)
% 2.24/0.60 % (1356281)Instruction limit reached!
% 2.24/0.60 % (1356281)------------------------------
% 2.24/0.60 % (1356281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356281)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356281)Termination reason: Instruction limit
% 2.24/0.60 % (1356281)Termination phase: Property scanning
% 2.24/0.60 % (1356281)Time elapsed: 0.041 s
% 2.24/0.60 % (1356281)Peak memory usage: 10 MB
% 2.24/0.60 % (1356281)Instructions burned: 118 (million)
% 2.24/0.60 % (1356282)Instruction limit reached!
% 2.24/0.60 % (1356282)------------------------------
% 2.24/0.60 % (1356282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356282)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356282)Termination reason: Instruction limit
% 2.24/0.60 % (1356282)Termination phase: Property scanning
% 2.24/0.60 % (1356282)Time elapsed: 0.047 s
% 2.24/0.60 % (1356282)Peak memory usage: 10 MB
% 2.24/0.60 % (1356282)Instructions burned: 131 (million)
% 2.24/0.60 % (1356291)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3543451866:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.24/0.60 % Exception at run slice level
% 2.24/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.24/0.60 % (1356278)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.24/0.60 % (1356283)Instruction limit reached!
% 2.24/0.60 % (1356283)------------------------------
% 2.24/0.60 % (1356283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356283)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356283)Termination reason: Instruction limit
% 2.24/0.60 % (1356283)Termination phase: Saturation
% 2.24/0.60 % (1356283)Time elapsed: 0.058 s
% 2.24/0.60 % (1356283)Peak memory usage: 12 MB
% 2.24/0.60 % (1356283)Instructions burned: 160 (million)
% 2.24/0.60 % (1356292)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2900552808:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.24/0.60 % (1356295)ott-21_1_sil=16000:fs=off:random_seed=787225007:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.24/0.60 % (1356293)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=1374509304:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.24/0.60 % (1356297)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3642974892:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.24/0.60 % (1356292)Instruction limit reached!
% 2.24/0.60 % (1356292)------------------------------
% 2.24/0.60 % (1356292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356292)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356292)Termination reason: Instruction limit
% 2.24/0.60 % (1356292)Termination phase: Property scanning
% 2.24/0.60 % (1356292)Time elapsed: 0.047 s
% 2.24/0.60 % (1356292)Peak memory usage: 10 MB
% 2.24/0.60 % (1356292)Instructions burned: 134 (million)
% 2.24/0.60 % Exception at run slice level
% 2.24/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.24/0.60 % (1356293)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.24/0.60 % (1356301)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3342927159:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.24/0.60 % (1356302)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=55477446:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.24/0.60 % (1356295)Instruction limit reached!
% 2.24/0.60 % (1356295)------------------------------
% 2.24/0.60 % (1356295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356295)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356295)Termination reason: Instruction limit
% 2.24/0.60 % (1356295)Termination phase: Saturation
% 2.24/0.60 % (1356295)Time elapsed: 0.066 s
% 2.24/0.60 % (1356295)Peak memory usage: 12 MB
% 2.24/0.60 % (1356295)Instructions burned: 182 (million)
% 2.24/0.60 % (1356305)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1294971533:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.24/0.60 % Exception at run slice level
% 2.24/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.24/0.60 % (1356293)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.24/0.60 % (1356307)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=2094054280:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.24/0.60 % (1356279) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1356272-1356279"...
% 2.24/0.60 % Exception at run slice level
% 2.24/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.24/0.60 % (1356307)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.24/0.60 % (1356309)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=323894574:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.24/0.60 % (1356309)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.24/0.60 % (1356297)Instruction limit reached!
% 2.24/0.60 % (1356297)------------------------------
% 2.24/0.60 % (1356297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (1356297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (1356297)CaDiCaL version: 2.1.3
% 2.24/0.60 % (1356297)Termination reason: Instruction limit
% 2.24/0.60 % (1356297)Termination phase: Saturation
% 2.24/0.60 % (1356297)Time elapsed: 0.179 s
% 2.24/0.60 % (1356297)Peak memory usage: 13 MB
% 2.24/0.60 % (1356297)Instructions burned: 480 (million)
% 2.24/0.60 % (1356311)fmb+10_1_sil=64000:random_seed=3997830978:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.24/0.60 % (1356311)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.24/0.60 % (1356279)...printing done.
% 2.24/0.60 % (1356279)Refutation found. Thanks to Tanya!
% 2.24/0.60 % SZS status ContradictoryAxioms for theBenchmark
% 2.24/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/0.63 % (1356279)------------------------------
% 2.62/0.63 % (1356279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.63 % (1356279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.63 % (1356279)CaDiCaL version: 2.1.3
% 2.62/0.63 % (1356279)Termination reason: Refutation
% 2.62/0.63 % (1356279)Time elapsed: 0.323 s
% 2.62/0.63 % (1356279)Peak memory usage: 17 MB
% 2.62/0.63 % (1356279)Instructions burned: 1578 (million)
% 2.62/0.63 % (1356272)Success in time 0.394 s
% 2.62/0.63 % Vampire exiting
%------------------------------------------------------------------------------