%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO904^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:50:35 AM UTC 2026
% Result : ContradictoryAxioms 3.69s 0.89s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 161
% Number of leaves : 36
% Syntax : Number of formulae : 1507 ( 128 unt; 0 typ; 20 def)
% Number of atoms : 69340 (15600 equ; 0 cnn)
% Maximal formula atoms : 159 ( 46 avg)
% Number of connectives : 104793 (1756 ~;15201 |;4386 &;67909 @)
% ( 20 <=>;6825 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 20 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 415 ( 415 >; 0 *; 0 +; 0 <<)
% Number of symbols : 115 ( 110 usr; 26 con; 0-4 aty)
% (6459 !!;2237 ??; 0 @@+; 0 @@-)
% Number of variables : 23380 ( 80 sgn13653 !; 2 ?;23380 :)
% 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(f11,axiom,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod2) ).
thf(f13,axiom,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod4) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod6) ).
thf(f17,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod8) ).
thf(f33,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod24) ).
thf(f34,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod25) ).
thf(f39,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod30) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod36) ).
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(f82,plain,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f83,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f82]) ).
thf(f86,plain,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f87,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f90,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f91,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f94,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f95,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f126,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f127,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f126]) ).
thf(f128,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f129,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f128]) ).
thf(f138,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f139,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f138]) ).
thf(f150,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f151,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f150]) ).
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(f195,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f83]) ).
thf(f197,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f87]) ).
thf(f199,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f201,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f217,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f127]) ).
thf(f218,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f129]) ).
thf(f223,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f139]) ).
thf(f229,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f151]) ).
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(f249,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v28
@ ( ^ [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 ) )
@ v26
@ ( ^ [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] :
( !! @ 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 ) ) )
@ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f195,f185,f191,f188,f191,f191,f188,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191]) ).
thf(f251,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v28
@ ( ^ [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] :
( !! @ 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 > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ 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 ) ) )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f197,f185,f191,f188,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f188,f191,f191,f191,f191,f191]) ).
thf(f253,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [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 ) )
@ v26
@ ( ^ [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 )
@ v16 )
@ ( ^ [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 )
@ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f199,f185,f191,f188,f186,f191,f191,f188,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f186]) ).
thf(f255,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [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 > $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 ) ) )
@ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f201,f185,f191,f188,f186,f191,f191,f191,f191,f188,f186,f191,f191,f188,f191,f191,f191,f191]) ).
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 > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v26 )
@ ( ^ [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 )
@ v18 )
@ ( ^ [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 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f217,f185,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f186]) ).
thf(f272,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 > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ 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 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ 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] :
( !! @ 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 )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f218,f185,f191,f191,f191,f191,f188,f191,f191,f188,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f186]) ).
thf(f277,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] :
( !! @ 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] :
( !! @ 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 ) ) )
@ ( ^ [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 )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f223,f185,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f191,f191,f191,f188,f191,f191,f191,f191,f186]) ).
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 > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ 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] :
( !! @ 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 )
@ v10 )
@ ( ^ [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 )
@ v9 )
@ ( ^ [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 ) ) )
@ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f229,f185,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f191,f188,f186,f191,f188,f186,f191,f191,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(f362,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 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f361]) ).
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(f403,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 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f401]) ).
thf(f404,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
= ( 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 )
=> ( ( !! @ 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 ) ) ) ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f403]) ).
thf(f405,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
= ( 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 @ X21 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ~ ( v7 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f404]) ).
thf(f406,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ~ ( v7 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f405]) ).
thf(f407,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ~ ( v7 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f406]) ).
thf(f408,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f406]) ).
thf(f409,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) )
@ X22 ) ) ),
inference(pi_proxy_clausification,[],[f408]) ).
thf(f410,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ( mrel @ X21 @ X22 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f409]) ).
thf(f411,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f410]) ).
thf(f412,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f411]) ).
thf(f413,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f411]) ).
thf(f414,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ 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 )
& $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 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) )
@ X23 ) ) ),
inference(pi_proxy_clausification,[],[f413]) ).
thf(f415,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( mrel @ X22 @ X23 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ 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 @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f414]) ).
thf(f416,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ 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 @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f415]) ).
thf(f417,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f416]) ).
thf(f453,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f417]) ).
thf(f459,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) )
@ ( sK5 @ X23 ) ) ) ),
inference(sigma_proxy_clausification,[],[f453]) ).
thf(f460,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ( mrel @ X23 @ ( sK5 @ X23 ) )
& ~ ( v5 @ ( sK5 @ X23 ) ) ) ) ),
inference(beta-eta_normalization,[],[f459]) ).
thf(f461,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ~ ( v5 @ ( sK5 @ X23 ) ) ) ) ),
inference(and_proxy_clausification,[],[f460]) ).
thf(f463,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(not_proxy_clausification,[],[f461]) ).
thf(f465,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f412]) ).
thf(f466,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) )
@ ( sK6 @ X22 ) ) ) ),
inference(sigma_proxy_clausification,[],[f465]) ).
thf(f467,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( mrel @ X22 @ ( sK6 @ X22 ) )
& ( v6 @ ( sK6 @ X22 ) ) ) ) ),
inference(beta-eta_normalization,[],[f466]) ).
thf(f468,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(and_proxy_clausification,[],[f467]) ).
thf(f476,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f407]) ).
thf(f477,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) )
@ ( sK8 @ X21 ) ) ) ),
inference(sigma_proxy_clausification,[],[f476]) ).
thf(f478,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ( mrel @ X21 @ ( sK8 @ X21 ) )
& ( v7 @ ( sK8 @ X21 ) ) ) ) ),
inference(beta-eta_normalization,[],[f477]) ).
thf(f479,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(and_proxy_clausification,[],[f478]) ).
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(f514,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(f515,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 ) )
@ ( sK16 @ X15 ) ) ) ),
inference(sigma_proxy_clausification,[],[f514]) ).
thf(f516,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 @ ( sK16 @ X15 ) )
& ( v13 @ ( sK16 @ X15 ) ) ) ) ),
inference(beta-eta_normalization,[],[f515]) ).
thf(f517,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 @ ( sK16 @ X15 ) ) ) ),
inference(and_proxy_clausification,[],[f516]) ).
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(f524,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(f530,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 ) )
@ ( sK19 @ X14 ) ) ) ),
inference(sigma_proxy_clausification,[],[f524]) ).
thf(f531,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 @ ( sK19 @ X14 ) )
& ~ ( v14 @ ( sK19 @ X14 ) ) ) ) ),
inference(beta-eta_normalization,[],[f530]) ).
thf(f532,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 @ ( sK19 @ X14 ) ) ) ) ),
inference(and_proxy_clausification,[],[f531]) ).
thf(f534,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(not_proxy_clausification,[],[f532]) ).
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(f547,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 )
& ( v16 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f362]) ).
thf(f548,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
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) )
@ ( sK22 @ X12 ) ) ) ),
inference(sigma_proxy_clausification,[],[f547]) ).
thf(f549,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
= ( ( mrel @ X12 @ ( sK22 @ X12 ) )
& ( v16 @ ( sK22 @ X12 ) ) ) ) ),
inference(beta-eta_normalization,[],[f548]) ).
thf(f550,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
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(and_proxy_clausification,[],[f549]) ).
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(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(f585,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(f586,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 ) )
@ ( sK30 @ X6 ) ) ) ),
inference(sigma_proxy_clausification,[],[f585]) ).
thf(f587,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 @ ( sK30 @ X6 ) )
& ( v22 @ ( sK30 @ X6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f586]) ).
thf(f588,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 @ ( sK30 @ X6 ) ) ) ),
inference(and_proxy_clausification,[],[f587]) ).
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(f595,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(f601,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 ) )
@ ( sK33 @ X5 ) ) ) ),
inference(sigma_proxy_clausification,[],[f595]) ).
thf(f602,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 @ ( sK33 @ X5 ) )
& ~ ( v23 @ ( sK33 @ X5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f601]) ).
thf(f603,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 @ ( sK33 @ X5 ) ) ) ) ),
inference(and_proxy_clausification,[],[f602]) ).
thf(f605,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
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f603]) ).
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(f1746,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ~ ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f1747,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ~ ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1746]) ).
thf(f1748,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1747]) ).
thf(f1749,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1748]) ).
thf(f1750,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1749]) ).
thf(f1751,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1750]) ).
thf(f1752,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1751]) ).
thf(f1753,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1752]) ).
thf(f1754,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1753]) ).
thf(f1755,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1754]) ).
thf(f1756,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1755]) ).
thf(f1757,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1756]) ).
thf(f1758,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1757]) ).
thf(f1759,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1758]) ).
thf(f1760,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1759]) ).
thf(f1761,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1760]) ).
thf(f1762,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1761]) ).
thf(f1763,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1762]) ).
thf(f1764,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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1763]) ).
thf(f1765,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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1764]) ).
thf(f1766,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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1765]) ).
thf(f1767,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
= ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1766]) ).
thf(f1768,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 )
=> ( ~ ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v22 @ X7 ) ) ) ),
inference(or_proxy_clausification,[],[f1767]) ).
thf(f1769,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 )
=> ( ~ ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $true
= ( ~ ( v22 @ X7 ) ) ) ),
inference(pi_proxy_clausification,[],[f1768]) ).
thf(f1770,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 )
=> ( ~ ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $false
= ( v22 @ X7 ) ) ),
inference(not_proxy_clausification,[],[f1769]) ).
thf(f1771,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 )
=> ( ~ ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v22 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f1770]) ).
thf(f1772,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 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1771]) ).
thf(f1773,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f1772]) ).
thf(f1774,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1773]) ).
thf(f1775,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1774]) ).
thf(f1776,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1775]) ).
thf(f1777,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1776]) ).
thf(f1778,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1777]) ).
thf(f1779,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f1778]) ).
thf(f1780,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1779]) ).
thf(f1781,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1780]) ).
thf(f1782,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1781]) ).
thf(f1783,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1782]) ).
thf(f1784,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1783]) ).
thf(f1785,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f1784]) ).
thf(f1786,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1785]) ).
thf(f1787,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1786]) ).
thf(f1788,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1787]) ).
thf(f1789,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1788]) ).
thf(f1790,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1789]) ).
thf(f1791,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f1790]) ).
thf(f1792,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1791]) ).
thf(f1793,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1792]) ).
thf(f1794,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1793]) ).
thf(f1795,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1794]) ).
thf(f1796,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1795]) ).
thf(f1797,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1796]) ).
thf(f1798,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v9 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1797]) ).
thf(f1799,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
= ( 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 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v9 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1798]) ).
thf(f1800,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
= ( 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 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v9 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f1799]) ).
thf(f1801,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
= ( 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 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v9 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1800]) ).
thf(f1802,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
= ( 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 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ~ ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v9 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1801]) ).
thf(f1803,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
= ( 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 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ~ ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v9 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f1802]) ).
thf(f1804,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
= ( 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 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( ~ ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ~ ( v9 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1803]) ).
thf(f1805,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ~ ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ~ ( v9 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1804]) ).
thf(f1806,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ~ ( v9 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v10 @ X19 ) ) ) ),
inference(or_proxy_clausification,[],[f1805]) ).
thf(f1807,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ~ ( v9 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X20 ) )
| ( $true
= ( ~ ( v10 @ X19 ) ) ) ),
inference(pi_proxy_clausification,[],[f1806]) ).
thf(f1808,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ~ ( v9 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X20 ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(not_proxy_clausification,[],[f1807]) ).
thf(f1809,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( ~ ( v9 @ 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 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v10 @ X19 ) ) ),
inference(beta-eta_normalization,[],[f1808]) ).
thf(f1810,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $true
= ( ~ ( v9 @ 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 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1809]) ).
thf(f1811,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $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 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v9 @ X20 ) ) ) ),
inference(or_proxy_clausification,[],[f1810]) ).
thf(f1812,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) )
@ X21 ) )
| ( $true
= ( ~ ( v9 @ X20 ) ) ) ),
inference(pi_proxy_clausification,[],[f1811]) ).
thf(f1813,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) )
@ X21 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(not_proxy_clausification,[],[f1812]) ).
thf(f1814,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(beta-eta_normalization,[],[f1813]) ).
thf(f1815,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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1814]) ).
thf(f1816,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,X22: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) )
@ X22 ) ) ),
inference(pi_proxy_clausification,[],[f1815]) ).
thf(f1817,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,X22: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $true
= ( ( mrel @ X21 @ X22 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1816]) ).
thf(f1818,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,X22: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1817]) ).
thf(f1819,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) )
@ X23 ) ) ),
inference(pi_proxy_clausification,[],[f1818]) ).
thf(f1820,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( mrel @ X22 @ X23 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1819]) ).
thf(f1821,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1820]) ).
thf(f1822,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) )
@ X24 ) ) ),
inference(pi_proxy_clausification,[],[f1821]) ).
thf(f1823,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ( mrel @ X23 @ X24 )
=> ( v5 @ X24 ) ) ) ),
inference(beta-eta_normalization,[],[f1822]) ).
thf(f1824,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(imp_proxy_clausification,[],[f1823]) ).
thf(f2207,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f2208,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2207]) ).
thf(f2209,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2208]) ).
thf(f2210,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2209]) ).
thf(f2211,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2210]) ).
thf(f2212,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2211]) ).
thf(f2213,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2212]) ).
thf(f2214,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2213]) ).
thf(f2215,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2214]) ).
thf(f2216,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2215]) ).
thf(f2217,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2216]) ).
thf(f2218,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2217]) ).
thf(f2219,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2218]) ).
thf(f2220,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 )
=> ( ( v13 @ 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f2219]) ).
thf(f2221,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 )
=> ( ( v13 @ 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(pi_proxy_clausification,[],[f2220]) ).
thf(f2222,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 )
=> ( ( v13 @ 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f2221]) ).
thf(f2223,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 )
=> ( ( v13 @ 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2222]) ).
thf(f2224,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2223]) ).
thf(f2225,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2224]) ).
thf(f2226,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 )
=> ( !! @ 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2225]) ).
thf(f2227,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 ) )
| ( $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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2226]) ).
thf(f2228,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 ) )
| ( $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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f2227]) ).
thf(f2229,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 ) )
| ( $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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2228]) ).
thf(f2230,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2229]) ).
thf(f2231,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2230]) ).
thf(f2232,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2231]) ).
thf(f2233,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2232]) ).
thf(f2234,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2233]) ).
thf(f2235,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2234]) ).
thf(f2236,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2235]) ).
thf(f2237,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2236]) ).
thf(f2238,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2237]) ).
thf(f2239,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2238]) ).
thf(f2240,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2239]) ).
thf(f2241,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2240]) ).
thf(f2242,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2241]) ).
thf(f2243,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2242]) ).
thf(f2244,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2243]) ).
thf(f2245,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2244]) ).
thf(f2246,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2245]) ).
thf(f2247,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2246]) ).
thf(f2248,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2247]) ).
thf(f2249,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2248]) ).
thf(f2250,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2249]) ).
thf(f2251,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2250]) ).
thf(f2252,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2251]) ).
thf(f2253,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2252]) ).
thf(f2254,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2253]) ).
thf(f2255,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2254]) ).
thf(f2256,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2255]) ).
thf(f2257,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
= ( 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 )
=> ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2256]) ).
thf(f2258,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
= ( 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 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(or_proxy_clausification,[],[f2257]) ).
thf(f2259,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
= ( 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 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2258]) ).
thf(f2260,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
= ( 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 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f2259]) ).
thf(f2261,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
= ( 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
= ( !! @ 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2260]) ).
thf(f2262,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
= ( 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
= ( ^ [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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2261]) ).
thf(f2263,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
= ( 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
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2262]) ).
thf(f2264,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2263]) ).
thf(f2265,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2264]) ).
thf(f2266,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( ( v10 @ 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 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2265]) ).
thf(f2267,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( v10 @ 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 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2266]) ).
thf(f2268,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
= ( 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
= ( 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 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(or_proxy_clausification,[],[f2267]) ).
thf(f2269,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
= ( 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
= ( 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 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) )
@ X20 ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2268]) ).
thf(f2270,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
= ( 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
= ( 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 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(beta-eta_normalization,[],[f2269]) ).
thf(f2271,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2270]) ).
thf(f2272,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f2271]) ).
thf(f2273,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2272]) ).
thf(f2274,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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2273]) ).
thf(f2275,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,X22: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) )
@ X22 ) ) ),
inference(pi_proxy_clausification,[],[f2274]) ).
thf(f2276,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,X22: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( ( mrel @ X21 @ X22 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2275]) ).
thf(f2277,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,X22: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2276]) ).
thf(f2278,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X23 ) ) ),
inference(pi_proxy_clausification,[],[f2277]) ).
thf(f2279,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( mrel @ X22 @ X23 )
=> ~ ( v6 @ X23 ) ) ) ),
inference(beta-eta_normalization,[],[f2278]) ).
thf(f2280,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( ~ ( v6 @ X23 ) ) ) ),
inference(imp_proxy_clausification,[],[f2279]) ).
thf(f2281,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(not_proxy_clausification,[],[f2280]) ).
thf(f2573,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f2574,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2573]) ).
thf(f2575,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2574]) ).
thf(f2576,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2575]) ).
thf(f2577,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2576]) ).
thf(f2578,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2577]) ).
thf(f2579,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2578]) ).
thf(f2580,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2579]) ).
thf(f2581,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2580]) ).
thf(f2582,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2581]) ).
thf(f2583,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2582]) ).
thf(f2584,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2583]) ).
thf(f2585,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2584]) ).
thf(f2586,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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f2585]) ).
thf(f2587,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 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2586]) ).
thf(f2588,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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2587]) ).
thf(f2589,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2588]) ).
thf(f2590,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2589]) ).
thf(f2591,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 )
=> ( ( 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2590]) ).
thf(f2592,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
= ( ( 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2591]) ).
thf(f2593,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v23 @ X6 ) ) ),
inference(or_proxy_clausification,[],[f2592]) ).
thf(f2594,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( $true
= ( v23 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2593]) ).
thf(f2595,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 )
=> ( ~ ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v23 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f2594]) ).
thf(f2596,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2595]) ).
thf(f2597,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v22 @ X7 ) ) ) ),
inference(or_proxy_clausification,[],[f2596]) ).
thf(f2598,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $true
= ( ~ ( v22 @ X7 ) ) ) ),
inference(pi_proxy_clausification,[],[f2597]) ).
thf(f2599,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $false
= ( v22 @ X7 ) ) ),
inference(not_proxy_clausification,[],[f2598]) ).
thf(f2600,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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v22 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f2599]) ).
thf(f2601,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
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2600]) ).
thf(f2602,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2601]) ).
thf(f2603,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2602]) ).
thf(f2604,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2603]) ).
thf(f2605,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2604]) ).
thf(f2606,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2605]) ).
thf(f2607,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2606]) ).
thf(f2608,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2607]) ).
thf(f2609,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2608]) ).
thf(f2610,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2609]) ).
thf(f2611,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2610]) ).
thf(f2612,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2611]) ).
thf(f2613,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2612]) ).
thf(f2614,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2613]) ).
thf(f2615,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2614]) ).
thf(f2616,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2615]) ).
thf(f2617,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2616]) ).
thf(f2618,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2617]) ).
thf(f2619,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2618]) ).
thf(f2620,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2619]) ).
thf(f2621,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2620]) ).
thf(f2622,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2621]) ).
thf(f2623,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2622]) ).
thf(f2624,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2623]) ).
thf(f2625,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2624]) ).
thf(f2626,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2625]) ).
thf(f2627,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2626]) ).
thf(f2628,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2627]) ).
thf(f2629,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2628]) ).
thf(f2630,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2629]) ).
thf(f2631,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2630]) ).
thf(f2632,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2631]) ).
thf(f2633,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2632]) ).
thf(f2634,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2633]) ).
thf(f2635,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f2634]) ).
thf(f2636,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ~ ( v9 @ X20 ) ) ) ),
inference(beta-eta_normalization,[],[f2635]) ).
thf(f2637,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ~ ( v9 @ X20 ) ) ) ),
inference(imp_proxy_clausification,[],[f2636]) ).
thf(f2638,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 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(not_proxy_clausification,[],[f2637]) ).
thf(f2639,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v26 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y21 )
| ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f2640,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v26 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y21 )
| ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2639]) ).
thf(f2641,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y20 )
| ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2640]) ).
thf(f2642,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y20 )
| ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2641]) ).
thf(f2643,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y20 )
| ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2642]) ).
thf(f2644,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ~ ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y19 )
| ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2643]) ).
thf(f2645,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ~ ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y19 )
| ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2644]) ).
thf(f2646,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ~ ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y19 )
| ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2645]) ).
thf(f2647,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ~ ( v26 @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2646]) ).
thf(f2648,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ~ ( v26 @ 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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2647]) ).
thf(f2649,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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v26 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f2648]) ).
thf(f2650,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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $true
= ( ~ ( v26 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f2649]) ).
thf(f2651,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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f2650]) ).
thf(f2652,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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2651]) ).
thf(f2653,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 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2652]) ).
thf(f2654,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2653]) ).
thf(f2655,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2654]) ).
thf(f2656,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2655]) ).
thf(f2657,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2656]) ).
thf(f2658,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2657]) ).
thf(f2659,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2658]) ).
thf(f2660,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f2659]) ).
thf(f2661,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2660]) ).
thf(f2662,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2661]) ).
thf(f2663,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2662]) ).
thf(f2664,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2663]) ).
thf(f2665,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2664]) ).
thf(f2666,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2665]) ).
thf(f2667,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2666]) ).
thf(f2668,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2667]) ).
thf(f2669,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2668]) ).
thf(f2670,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2669]) ).
thf(f2671,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2670]) ).
thf(f2672,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v7 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2671]) ).
thf(f2673,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2672]) ).
thf(f2674,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
= ( v26 @ X3 ) )
| ( $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
= ( ~ ( v18 @ 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 )
=> ( ~ ( v7 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2673]) ).
thf(f2675,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v7 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v18 @ X11 ) ) ) ),
inference(or_proxy_clausification,[],[f2674]) ).
thf(f2676,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v7 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $true
= ( ~ ( v18 @ X11 ) ) ) ),
inference(pi_proxy_clausification,[],[f2675]) ).
thf(f2677,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v7 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(not_proxy_clausification,[],[f2676]) ).
thf(f2678,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
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v7 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f2677]) ).
thf(f2679,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2678]) ).
thf(f2680,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2679]) ).
thf(f2681,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2680]) ).
thf(f2682,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2681]) ).
thf(f2683,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2682]) ).
thf(f2684,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2683]) ).
thf(f2685,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2684]) ).
thf(f2686,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2685]) ).
thf(f2687,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2686]) ).
thf(f2688,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2687]) ).
thf(f2689,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2688]) ).
thf(f2690,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2689]) ).
thf(f2691,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2690]) ).
thf(f2692,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2691]) ).
thf(f2693,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2692]) ).
thf(f2694,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2693]) ).
thf(f2695,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f2694]) ).
thf(f2696,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2695]) ).
thf(f2697,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2696]) ).
thf(f2698,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2697]) ).
thf(f2699,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2698]) ).
thf(f2700,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2699]) ).
thf(f2701,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f2700]) ).
thf(f2702,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2701]) ).
thf(f2703,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( ~ ( v7 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2702]) ).
thf(f2704,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v7 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) )
@ X21 ) ) ),
inference(pi_proxy_clausification,[],[f2703]) ).
thf(f2705,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ~ ( v7 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2704]) ).
thf(f2706,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
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ~ ( v7 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2705]) ).
thf(f2707,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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ~ ( v7 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) )
@ X22 ) ) ),
inference(pi_proxy_clausification,[],[f2706]) ).
thf(f2708,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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( ( mrel @ X21 @ X22 )
=> ( ~ ( v7 @ X22 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2707]) ).
thf(f2709,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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ~ ( v7 @ X22 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2708]) ).
thf(f2710,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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) )
| ( $true
= ( ~ ( v7 @ X22 ) ) ) ),
inference(or_proxy_clausification,[],[f2709]) ).
thf(f2711,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X23 ) )
| ( $true
= ( ~ ( v7 @ X22 ) ) ) ),
inference(pi_proxy_clausification,[],[f2710]) ).
thf(f2712,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X23 ) )
| ( $false
= ( v7 @ X22 ) ) ),
inference(not_proxy_clausification,[],[f2711]) ).
thf(f2713,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( ( mrel @ X22 @ X23 )
=> ~ ( v6 @ X23 ) ) )
| ( $false
= ( v7 @ X22 ) ) ),
inference(beta-eta_normalization,[],[f2712]) ).
thf(f2714,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $true
= ( ~ ( v6 @ X23 ) ) ) ),
inference(imp_proxy_clausification,[],[f2713]) ).
thf(f2715,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(not_proxy_clausification,[],[f2714]) ).
thf(f3874,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ~ ( v28 @ Y0 )
| ( !! @ 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 )
=> ( ( 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 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f3875,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ~ ( v28 @ Y0 )
| ( !! @ 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 )
=> ( ( 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 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f3874]) ).
thf(f3876,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ~ ( v28 @ 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 )
=> ( ( 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 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3875]) ).
thf(f3877,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( v28 @ 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 )
=> ( ( 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 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3876]) ).
thf(f3878,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 )
=> ( ( 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 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f3877]) ).
thf(f3879,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 )
=> ( ( 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 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f3878]) ).
thf(f3880,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 )
=> ( ( 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 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f3879]) ).
thf(f3881,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 )
=> ( ( 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 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3880]) ).
thf(f3882,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3881]) ).
thf(f3883,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3882]) ).
thf(f3884,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3883]) ).
thf(f3885,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3884]) ).
thf(f3886,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3885]) ).
thf(f3887,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3886]) ).
thf(f3888,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3887]) ).
thf(f3889,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3888]) ).
thf(f3890,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3889]) ).
thf(f3891,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3890]) ).
thf(f3892,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f3891]) ).
thf(f3893,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ 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 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) ) ),
inference(pi_proxy_clausification,[],[f3892]) ).
thf(f3894,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ 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 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f3893]) ).
thf(f3895,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X5 @ 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 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3894]) ).
thf(f3896,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3895]) ).
thf(f3897,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f3896]) ).
thf(f3898,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $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 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3897]) ).
thf(f3899,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $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 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3898]) ).
thf(f3900,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(or_proxy_clausification,[],[f3899]) ).
thf(f3901,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
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) )
@ X8 ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f3900]) ).
thf(f3902,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
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( v22 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f3901]) ).
thf(f3903,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3902]) ).
thf(f3904,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f3903]) ).
thf(f3905,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3904]) ).
thf(f3906,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3905]) ).
thf(f3907,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f3906]) ).
thf(f3908,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3907]) ).
thf(f3909,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3908]) ).
thf(f3910,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f3909]) ).
thf(f3911,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( v18 @ X11 ) ) ) ),
inference(beta-eta_normalization,[],[f3910]) ).
thf(f3912,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
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f3911]) ).
thf(f3991,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ~ ( v28 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v26 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f3992,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ~ ( v28 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v26 @ Y2 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f3991]) ).
thf(f3993,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ~ ( v28 @ X1 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3992]) ).
thf(f3994,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( v28 @ X1 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3993]) ).
thf(f3995,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f3994]) ).
thf(f3996,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f3995]) ).
thf(f3997,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f3996]) ).
thf(f3998,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3997]) ).
thf(f3999,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3998]) ).
thf(f4000,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v16 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3999]) ).
thf(f4001,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( v26 @ 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 )
=> ( ~ ( v16 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4000]) ).
thf(f4002,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( v26 @ 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 )
=> ( ~ ( v16 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4001]) ).
thf(f4003,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v16 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f4002]) ).
thf(f4004,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v16 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4003]) ).
thf(f4005,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v16 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4004]) ).
thf(f4006,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4005]) ).
thf(f4007,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4006]) ).
thf(f4008,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4007]) ).
thf(f4009,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4008]) ).
thf(f4010,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f4009]) ).
thf(f4011,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4010]) ).
thf(f4012,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4011]) ).
thf(f4013,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f4012]) ).
thf(f4014,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4013]) ).
thf(f4015,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4014]) ).
thf(f4016,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f4015]) ).
thf(f4017,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4016]) ).
thf(f4018,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4017]) ).
thf(f4019,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f4018]) ).
thf(f4020,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4019]) ).
thf(f4021,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4020]) ).
thf(f4022,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f4021]) ).
thf(f4023,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4022]) ).
thf(f4024,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4023]) ).
thf(f4025,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4024]) ).
thf(f4026,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4025]) ).
thf(f4027,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4026]) ).
thf(f4028,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f4027]) ).
thf(f4029,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4028]) ).
thf(f4030,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4029]) ).
thf(f4031,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f4030]) ).
thf(f4032,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( ~ ( v16 @ X13 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4031]) ).
thf(f4033,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( ~ ( v16 @ X13 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4032]) ).
thf(f4034,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v16 @ X13 ) ) ) ),
inference(or_proxy_clausification,[],[f4033]) ).
thf(f4035,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ~ ( v13 @ Y2 ) ) ) ) ) )
@ X14 ) )
| ( $true
= ( ~ ( v16 @ X13 ) ) ) ),
inference(pi_proxy_clausification,[],[f4034]) ).
thf(f4036,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ~ ( v13 @ Y2 ) ) ) ) ) )
@ X14 ) )
| ( $false
= ( v16 @ X13 ) ) ),
inference(not_proxy_clausification,[],[f4035]) ).
thf(f4037,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ~ ( v13 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( v16 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f4036]) ).
thf(f4038,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4037]) ).
thf(f4039,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f4038]) ).
thf(f4040,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4039]) ).
thf(f4041,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4040]) ).
thf(f4042,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) )
@ X16 ) ) ),
inference(pi_proxy_clausification,[],[f4041]) ).
thf(f4043,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ~ ( v13 @ X16 ) ) ) ),
inference(beta-eta_normalization,[],[f4042]) ).
thf(f4044,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ~ ( v13 @ X16 ) ) ) ),
inference(imp_proxy_clausification,[],[f4043]) ).
thf(f4045,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(not_proxy_clausification,[],[f4044]) ).
thf(f4126,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( v28 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f4127,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( v28 @ Y0 )
| ( !! @ 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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f4126]) ).
thf(f4128,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( v28 @ 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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4127]) ).
thf(f4129,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( v28 @ 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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4128]) ).
thf(f4130,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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f4129]) ).
thf(f4131,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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4130]) ).
thf(f4132,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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4131]) ).
thf(f4133,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4132]) ).
thf(f4134,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4133]) ).
thf(f4135,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4134]) ).
thf(f4136,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4135]) ).
thf(f4137,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4136]) ).
thf(f4138,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4137]) ).
thf(f4139,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4138]) ).
thf(f4140,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4139]) ).
thf(f4141,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4140]) ).
thf(f4142,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4141]) ).
thf(f4143,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f4142]) ).
thf(f4144,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4143]) ).
thf(f4145,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4144]) ).
thf(f4146,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f4145]) ).
thf(f4147,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4146]) ).
thf(f4148,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4147]) ).
thf(f4149,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f4148]) ).
thf(f4150,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4149]) ).
thf(f4151,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4150]) ).
thf(f4152,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f4151]) ).
thf(f4153,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4152]) ).
thf(f4154,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4153]) ).
thf(f4155,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f4154]) ).
thf(f4156,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4155]) ).
thf(f4157,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4156]) ).
thf(f4158,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4157]) ).
thf(f4159,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4158]) ).
thf(f4160,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4159]) ).
thf(f4161,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f4160]) ).
thf(f4162,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4161]) ).
thf(f4163,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4162]) ).
thf(f4164,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f4163]) ).
thf(f4165,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4164]) ).
thf(f4166,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
@ ^ [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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4165]) ).
thf(f4167,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
| ( !! @ 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 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f4166]) ).
thf(f4168,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ~ ( v15 @ 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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4167]) ).
thf(f4169,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( ~ ( v15 @ 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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4168]) ).
thf(f4170,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
@ ^ [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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v15 @ X14 ) ) ) ),
inference(or_proxy_clausification,[],[f4169]) ).
thf(f4171,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
| ( !! @ 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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $true
= ( ~ ( v15 @ X14 ) ) ) ),
inference(pi_proxy_clausification,[],[f4170]) ).
thf(f4172,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
| ( !! @ 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 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $false
= ( v15 @ X14 ) ) ),
inference(not_proxy_clausification,[],[f4171]) ).
thf(f4173,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( ( 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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v15 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f4172]) ).
thf(f4174,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $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 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4173]) ).
thf(f4175,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(or_proxy_clausification,[],[f4174]) ).
thf(f4176,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X16 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(pi_proxy_clausification,[],[f4175]) ).
thf(f4177,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f4176]) ).
thf(f4178,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( 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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4177]) ).
thf(f4179,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( 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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f4178]) ).
thf(f4180,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4179]) ).
thf(f4181,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( 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 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4180]) ).
thf(f4182,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f4181]) ).
thf(f4183,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4182]) ).
thf(f4184,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4183]) ).
thf(f4185,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) )
@ X19 ) ) ),
inference(pi_proxy_clausification,[],[f4184]) ).
thf(f4186,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4185]) ).
thf(f4187,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4186]) ).
thf(f4188,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) )
@ X20 ) ) ),
inference(pi_proxy_clausification,[],[f4187]) ).
thf(f4189,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( v9 @ X20 ) ) ) ),
inference(beta-eta_normalization,[],[f4188]) ).
thf(f4190,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) ),
inference(imp_proxy_clausification,[],[f4189]) ).
thf(f4247,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( v28 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v26 @ Y2 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f4248,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( v28 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v26 @ Y2 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f4247]) ).
thf(f4249,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( v28 @ X1 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4248]) ).
thf(f4250,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( v28 @ X1 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4249]) ).
thf(f4251,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f4250]) ).
thf(f4252,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v26 @ Y1 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4251]) ).
thf(f4253,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4252]) ).
thf(f4254,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4253]) ).
thf(f4255,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( v26 @ Y0 )
| ( !! @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4254]) ).
thf(f4256,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( v26 @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4255]) ).
thf(f4257,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( v26 @ 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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4256]) ).
thf(f4258,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f4257]) ).
thf(f4259,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4258]) ).
thf(f4260,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4259]) ).
thf(f4261,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4260]) ).
thf(f4262,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4261]) ).
thf(f4263,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4262]) ).
thf(f4264,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4263]) ).
thf(f4265,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f4264]) ).
thf(f4266,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4265]) ).
thf(f4267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4266]) ).
thf(f4268,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ) ),
inference(pi_proxy_clausification,[],[f4267]) ).
thf(f4269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4268]) ).
thf(f4270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4269]) ).
thf(f4271,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f4270]) ).
thf(f4272,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4271]) ).
thf(f4273,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4272]) ).
thf(f4274,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( v21 @ X8 ) ) ) ),
inference(or_proxy_clausification,[],[f4273]) ).
thf(f4275,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $true
= ( ~ ( v21 @ X8 ) ) ) ),
inference(pi_proxy_clausification,[],[f4274]) ).
thf(f4276,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f4275]) ).
thf(f4277,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f4276]) ).
thf(f4278,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4277]) ).
thf(f4279,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) ) ),
inference(pi_proxy_clausification,[],[f4278]) ).
thf(f4280,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4279]) ).
thf(f4281,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4280]) ).
thf(f4282,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4281]) ).
thf(f4283,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 )
=> ( v14 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4282]) ).
thf(f4284,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 ) )
| ( $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 ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4283]) ).
thf(f4285,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 ) )
| ( $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 ) ) ) ) ) ) ) )
@ X12 ) ) ),
inference(pi_proxy_clausification,[],[f4284]) ).
thf(f4286,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4285]) ).
thf(f4287,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4286]) ).
thf(f4288,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) )
@ X13 ) ) ),
inference(pi_proxy_clausification,[],[f4287]) ).
thf(f4289,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4288]) ).
thf(f4290,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4289]) ).
thf(f4291,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) )
@ X14 ) ) ),
inference(pi_proxy_clausification,[],[f4290]) ).
thf(f4292,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( v14 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4291]) ).
thf(f4293,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( v14 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4292]) ).
thf(f4294,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( v14 @ Y0 ) )
@ X15 ) ) ),
inference(pi_proxy_clausification,[],[f4293]) ).
thf(f4295,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( v14 @ X15 ) ) ) ),
inference(beta-eta_normalization,[],[f4294]) ).
thf(f4296,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f4295]) ).
thf(f4402,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(f4403,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,[],[f4402]) ).
thf(f4404,plain,
! [X2: mworld,X3: mworld,X4: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4403,f193]) ).
thf(f4405,plain,
! [X2: mworld,X3: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f4404]) ).
thf(f4406,plain,
! [X3: mworld,X4: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4405,f193]) ).
thf(f4407,plain,
! [X3: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f4406]) ).
thf(f4408,plain,
! [X4: mworld] :
( ( $true = $false )
| ( $true
= ( v24 @ ( sK34 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4407,f193]) ).
thf(f4409,plain,
! [X4: mworld] :
( $true
= ( v24 @ ( sK34 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4408]) ).
thf(f4430,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 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f605,f193]) ).
thf(f4431,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 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4430]) ).
thf(f4432,plain,
! [X2: mworld,X3: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4431,f193]) ).
thf(f4433,plain,
! [X2: mworld,X3: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4432]) ).
thf(f4434,plain,
! [X3: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4433,f193]) ).
thf(f4435,plain,
! [X3: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4434]) ).
thf(f4436,plain,
! [X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4435,f193]) ).
thf(f4437,plain,
! [X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4436]) ).
thf(f4438,plain,
! [X5: mworld] :
( ( $true = $false )
| ( $false
= ( v23 @ ( sK33 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4437,f193]) ).
thf(f4439,plain,
! [X5: mworld] :
( $false
= ( v23 @ ( sK33 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4438]) ).
thf(f4442,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 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f588,f193]) ).
thf(f4443,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 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4442]) ).
thf(f4444,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 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4443,f193]) ).
thf(f4445,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 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4444]) ).
thf(f4446,plain,
! [X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4445,f193]) ).
thf(f4447,plain,
! [X3: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4446]) ).
thf(f4448,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4447,f193]) ).
thf(f4449,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4448]) ).
thf(f4450,plain,
! [X6: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4449,f193]) ).
thf(f4451,plain,
! [X6: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4450]) ).
thf(f4452,plain,
! [X6: mworld] :
( ( $true = $false )
| ( $true
= ( v22 @ ( sK30 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4451,f193]) ).
thf(f4453,plain,
! [X6: mworld] :
( $true
= ( v22 @ ( sK30 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4452]) ).
thf(f4454,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(f4455,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,[],[f4454]) ).
thf(f4456,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,[],[f4455,f193]) ).
thf(f4457,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,[],[f4456]) ).
thf(f4458,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,[],[f4457,f193]) ).
thf(f4459,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,[],[f4458]) ).
thf(f4460,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4459,f193]) ).
thf(f4461,plain,
! [X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4460]) ).
thf(f4462,plain,
! [X6: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4461,f193]) ).
thf(f4463,plain,
! [X6: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4462]) ).
thf(f4464,plain,
! [X6: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4463,f193]) ).
thf(f4465,plain,
! [X6: mworld] :
( $false
= ( v22 @ ( sK31 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4464]) ).
thf(f4468,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(f4469,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,[],[f4468]) ).
thf(f4470,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,[],[f4469,f193]) ).
thf(f4471,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,[],[f4470]) ).
thf(f4472,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,[],[f4471,f193]) ).
thf(f4473,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,[],[f4472]) ).
thf(f4474,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,[],[f4473,f193]) ).
thf(f4475,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,[],[f4474]) ).
thf(f4476,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4475,f193]) ).
thf(f4477,plain,
! [X6: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4476]) ).
thf(f4478,plain,
! [X6: mworld,X7: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4477,f193]) ).
thf(f4479,plain,
! [X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4478]) ).
thf(f4480,plain,
! [X7: mworld] :
( ( $true = $false )
| ( $true
= ( v21 @ ( sK28 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4479,f193]) ).
thf(f4481,plain,
! [X7: mworld] :
( $true
= ( v21 @ ( sK28 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4480]) ).
thf(f4498,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] :
( ( $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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f550,f193]) ).
thf(f4499,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] :
( ( ( mrel @ 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
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4498]) ).
thf(f4500,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4499,f193]) ).
thf(f4501,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4500]) ).
thf(f4502,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4501,f193]) ).
thf(f4503,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4502]) ).
thf(f4504,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4503,f193]) ).
thf(f4505,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4504]) ).
thf(f4506,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4505,f193]) ).
thf(f4507,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4506]) ).
thf(f4508,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4507,f193]) ).
thf(f4509,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X12: 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 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4508]) ).
thf(f4510,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4509,f193]) ).
thf(f4511,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X12: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4510]) ).
thf(f4512,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4511,f193]) ).
thf(f4513,plain,
! [X10: mworld,X11: mworld,X8: mworld,X9: mworld,X12: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4512]) ).
thf(f4514,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4513,f193]) ).
thf(f4515,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4514]) ).
thf(f4516,plain,
! [X10: mworld,X11: mworld,X12: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4515,f193]) ).
thf(f4517,plain,
! [X10: mworld,X11: mworld,X12: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4516]) ).
thf(f4518,plain,
! [X11: mworld,X12: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4517,f193]) ).
thf(f4519,plain,
! [X11: mworld,X12: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(trivial_inequality_removal,[],[f4518]) ).
thf(f4520,plain,
! [X12: mworld] :
( ( $true = $false )
| ( $true
= ( v16 @ ( sK22 @ X12 ) ) ) ),
inference(forward_demodulation,[],[f4519,f193]) ).
thf(f4521,plain,
! [X12: mworld] :
( $true
= ( v16 @ ( sK22 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4520]) ).
thf(f4548,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f3912,f193]) ).
thf(f4549,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4548]) ).
thf(f4550,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4549,f193]) ).
thf(f4551,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $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
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4550]) ).
thf(f4552,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4551,f193]) ).
thf(f4553,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4552]) ).
thf(f4554,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4553,f193]) ).
thf(f4555,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4554]) ).
thf(f4556,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4555,f193]) ).
thf(f4557,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4556]) ).
thf(f4558,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4557,f193]) ).
thf(f4559,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4558]) ).
thf(f4560,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4559,f193]) ).
thf(f4561,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4560]) ).
thf(f4562,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4561,f193]) ).
thf(f4563,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4562]) ).
thf(f4564,plain,
! [X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4563,f193]) ).
thf(f4565,plain,
! [X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4564]) ).
thf(f4566,plain,
! [X10: mworld,X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4565,f193]) ).
thf(f4567,plain,
! [X10: mworld,X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4566]) ).
thf(f4568,plain,
! [X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(forward_demodulation,[],[f4567,f193]) ).
thf(f4569,plain,
! [X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v22 @ X7 ) )
| ( $true
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4568]) ).
thf(f4571,definition,
( spl40_3
<=> ! [X11: mworld] :
( $true
= ( v18 @ X11 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_3])],[avatar_definition]) ).
thf(f4572,plain,
( ! [X11: mworld] :
( $true
= ( v18 @ X11 ) )
| ~ spl40_3 ),
inference(avatar_component_clause,[],[f4571]) ).
thf(f4574,definition,
( spl40_4
<=> ! [X7: mworld] :
( $true
= ( v22 @ X7 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_4])],[avatar_definition]) ).
thf(f4575,plain,
( ! [X7: mworld] :
( $true
= ( v22 @ X7 ) )
| ~ spl40_4 ),
inference(avatar_component_clause,[],[f4574]) ).
thf(f4577,definition,
( spl40_5
<=> ! [X5: mworld] :
( $false
= ( v24 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_5])],[avatar_definition]) ).
thf(f4578,plain,
( ! [X5: mworld] :
( $false
= ( v24 @ X5 ) )
| ~ spl40_5 ),
inference(avatar_component_clause,[],[f4577]) ).
thf(f4580,definition,
( spl40_6
<=> ! [X1: mworld] :
( $false
= ( v28 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_6])],[avatar_definition]) ).
thf(f4581,plain,
( ! [X1: mworld] :
( $false
= ( v28 @ X1 ) )
| ~ spl40_6 ),
inference(avatar_component_clause,[],[f4580]) ).
thf(f4582,plain,
( spl40_3
| spl40_4
| spl40_5
| spl40_6 ),
inference(avatar_split_clause,[],[f4569,f4580,f4577,f4574,f4571]) ).
thf(f4583,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(f4584,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,[],[f4583]) ).
thf(f4585,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,[],[f4584,f193]) ).
thf(f4586,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,[],[f4585]) ).
thf(f4587,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,[],[f4586,f193]) ).
thf(f4588,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,[],[f4587]) ).
thf(f4589,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,[],[f4588,f193]) ).
thf(f4590,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,[],[f4589]) ).
thf(f4591,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,[],[f4590,f193]) ).
thf(f4592,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,[],[f4591]) ).
thf(f4593,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,[],[f4592,f193]) ).
thf(f4594,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,[],[f4593]) ).
thf(f4595,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,[],[f4594,f193]) ).
thf(f4596,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,[],[f4595]) ).
thf(f4597,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,[],[f4596,f193]) ).
thf(f4598,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,[],[f4597]) ).
thf(f4599,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,[],[f4598,f193]) ).
thf(f4600,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,[],[f4599]) ).
thf(f4601,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,[],[f4600,f193]) ).
thf(f4602,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,[],[f4601]) ).
thf(f4603,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4602,f193]) ).
thf(f4604,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4603]) ).
thf(f4605,plain,
! [X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4604,f193]) ).
thf(f4606,plain,
! [X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4605]) ).
thf(f4607,plain,
! [X13: mworld] :
( ( $true = $false )
| ( $true
= ( v15 @ ( sK20 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4606,f193]) ).
thf(f4608,plain,
! [X13: mworld] :
( $true
= ( v15 @ ( sK20 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4607]) ).
thf(f4665,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f534,f193]) ).
thf(f4666,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4665]) ).
thf(f4667,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4666,f193]) ).
thf(f4668,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4667]) ).
thf(f4669,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4668,f193]) ).
thf(f4670,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4669]) ).
thf(f4671,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4670,f193]) ).
thf(f4672,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4671]) ).
thf(f4673,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4672,f193]) ).
thf(f4674,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4673]) ).
thf(f4675,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4674,f193]) ).
thf(f4676,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4675]) ).
thf(f4677,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4676,f193]) ).
thf(f4678,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4677]) ).
thf(f4679,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4678,f193]) ).
thf(f4680,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4679]) ).
thf(f4681,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4680,f193]) ).
thf(f4682,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4681]) ).
thf(f4683,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4682,f193]) ).
thf(f4684,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 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4683]) ).
thf(f4685,plain,
! [X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4684,f193]) ).
thf(f4686,plain,
! [X11: mworld,X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4685]) ).
thf(f4687,plain,
! [X14: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4686,f193]) ).
thf(f4688,plain,
! [X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4687]) ).
thf(f4689,plain,
! [X14: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4688,f193]) ).
thf(f4690,plain,
! [X14: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(trivial_inequality_removal,[],[f4689]) ).
thf(f4691,plain,
! [X14: mworld] :
( ( $true = $false )
| ( $false
= ( v14 @ ( sK19 @ X14 ) ) ) ),
inference(forward_demodulation,[],[f4690,f193]) ).
thf(f4692,plain,
! [X14: mworld] :
( $false
= ( v14 @ ( sK19 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f4691]) ).
thf(f4728,definition,
( spl40_9
<=> ! [X8: mworld] :
( $false
= ( v21 @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_9])],[avatar_definition]) ).
thf(f4729,plain,
( ! [X8: mworld] :
( $false
= ( v21 @ X8 ) )
| ~ spl40_9 ),
inference(avatar_component_clause,[],[f4728]) ).
thf(f4740,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f517,f193]) ).
thf(f4741,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4740]) ).
thf(f4742,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4741,f193]) ).
thf(f4743,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4742]) ).
thf(f4744,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4743,f193]) ).
thf(f4745,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4744]) ).
thf(f4746,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4745,f193]) ).
thf(f4747,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4746]) ).
thf(f4748,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4747,f193]) ).
thf(f4749,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4748]) ).
thf(f4750,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4749,f193]) ).
thf(f4751,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4750]) ).
thf(f4752,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4751,f193]) ).
thf(f4753,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4752]) ).
thf(f4754,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4753,f193]) ).
thf(f4755,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4754]) ).
thf(f4756,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4755,f193]) ).
thf(f4757,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4756]) ).
thf(f4758,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4757,f193]) ).
thf(f4759,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4758]) ).
thf(f4760,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4759,f193]) ).
thf(f4761,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 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4760]) ).
thf(f4762,plain,
! [X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4761,f193]) ).
thf(f4763,plain,
! [X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4762]) ).
thf(f4764,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4763,f193]) ).
thf(f4765,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4764]) ).
thf(f4766,plain,
! [X14: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4765,f193]) ).
thf(f4767,plain,
! [X14: mworld,X15: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4766]) ).
thf(f4768,plain,
! [X15: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ ( sK16 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4767,f193]) ).
thf(f4769,plain,
! [X15: mworld] :
( $true
= ( v13 @ ( sK16 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4768]) ).
thf(f4770,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(f4771,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,[],[f4770]) ).
thf(f4772,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,[],[f4771,f193]) ).
thf(f4773,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,[],[f4772]) ).
thf(f4774,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,[],[f4773,f193]) ).
thf(f4775,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,[],[f4774]) ).
thf(f4776,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,[],[f4775,f193]) ).
thf(f4777,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,[],[f4776]) ).
thf(f4778,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,[],[f4777,f193]) ).
thf(f4779,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,[],[f4778]) ).
thf(f4780,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,[],[f4779,f193]) ).
thf(f4781,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,[],[f4780]) ).
thf(f4782,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,[],[f4781,f193]) ).
thf(f4783,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,[],[f4782]) ).
thf(f4784,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,[],[f4783,f193]) ).
thf(f4785,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,[],[f4784]) ).
thf(f4786,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,[],[f4785,f193]) ).
thf(f4787,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,[],[f4786]) ).
thf(f4788,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,[],[f4787,f193]) ).
thf(f4789,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,[],[f4788]) ).
thf(f4790,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,[],[f4789,f193]) ).
thf(f4791,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,[],[f4790]) ).
thf(f4792,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,[],[f4791,f193]) ).
thf(f4793,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,[],[f4792]) ).
thf(f4794,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4793,f193]) ).
thf(f4795,plain,
! [X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4794]) ).
thf(f4796,plain,
! [X14: mworld,X15: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4795,f193]) ).
thf(f4797,plain,
! [X14: mworld,X15: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f4796]) ).
thf(f4798,plain,
! [X15: mworld] :
( ( $true = $false )
| ( $false
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f4797,f193]) ).
thf(f4799,plain,
! [X15: mworld] :
( $false
= ( v13 @ ( sK17 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4798]) ).
thf(f4802,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4296,f193]) ).
thf(f4803,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4802]) ).
thf(f4804,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4803,f193]) ).
thf(f4805,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4804]) ).
thf(f4806,plain,
! [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 )
| ( $true
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4805,f193]) ).
thf(f4807,plain,
! [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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4806]) ).
thf(f4808,plain,
! [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 )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4807,f193]) ).
thf(f4809,plain,
! [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
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4808]) ).
thf(f4810,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4809,f193]) ).
thf(f4811,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4810]) ).
thf(f4812,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4811,f193]) ).
thf(f4813,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4812]) ).
thf(f4814,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4813,f193]) ).
thf(f4815,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4814]) ).
thf(f4816,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4815,f193]) ).
thf(f4817,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4816]) ).
thf(f4818,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4817,f193]) ).
thf(f4819,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $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
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4818]) ).
thf(f4820,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4819,f193]) ).
thf(f4821,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4820]) ).
thf(f4822,plain,
! [X3: mworld,X11: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4821,f193]) ).
thf(f4823,plain,
! [X3: mworld,X11: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4822]) ).
thf(f4824,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4823,f193]) ).
thf(f4825,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4824]) ).
thf(f4826,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4825,f193]) ).
thf(f4827,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4826]) ).
thf(f4828,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4827,f193]) ).
thf(f4829,plain,
! [X3: mworld,X1: mworld,X8: mworld,X14: mworld,X15: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4828]) ).
thf(f4830,plain,
! [X3: mworld,X1: mworld,X8: mworld,X15: mworld] :
( ( $true = $false )
| ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4829,f193]) ).
thf(f4831,plain,
! [X3: mworld,X1: mworld,X8: mworld,X15: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4830]) ).
thf(f4833,definition,
( spl40_11
<=> ! [X15: mworld] :
( $true
= ( v14 @ X15 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_11])],[avatar_definition]) ).
thf(f4834,plain,
( ! [X15: mworld] :
( $true
= ( v14 @ X15 ) )
| ~ spl40_11 ),
inference(avatar_component_clause,[],[f4833]) ).
thf(f4836,definition,
( spl40_12
<=> ! [X3: mworld] :
( $true
= ( v26 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_12])],[avatar_definition]) ).
thf(f4837,plain,
( ! [X3: mworld] :
( $true
= ( v26 @ X3 ) )
| ~ spl40_12 ),
inference(avatar_component_clause,[],[f4836]) ).
thf(f4839,definition,
( spl40_13
<=> ! [X1: mworld] :
( $true
= ( v28 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_13])],[avatar_definition]) ).
thf(f4840,plain,
( ! [X1: mworld] :
( $true
= ( v28 @ X1 ) )
| ~ spl40_13 ),
inference(avatar_component_clause,[],[f4839]) ).
thf(f4841,plain,
( spl40_11
| spl40_9
| spl40_12
| spl40_13 ),
inference(avatar_split_clause,[],[f4831,f4839,f4836,f4728,f4833]) ).
thf(f4843,plain,
( ( $true = $false )
| ~ spl40_9 ),
inference(constrained_superposition,[],[f4729,f4481]) ).
thf(f4847,plain,
( $false
| ~ spl40_9 ),
inference(trivial_inequality_removal,[],[f4843]) ).
thf(f4848,plain,
~ spl40_9,
inference(avatar_contradiction_clause,[],[f4847]) ).
thf(f4850,plain,
( ( $true = $false )
| ~ spl40_11 ),
inference(constrained_superposition,[],[f4834,f4692]) ).
thf(f4854,plain,
( $false
| ~ spl40_11 ),
inference(trivial_inequality_removal,[],[f4850]) ).
thf(f4855,plain,
~ spl40_11,
inference(avatar_contradiction_clause,[],[f4854]) ).
thf(f4889,definition,
( spl40_14
<=> ! [X16: mworld] :
( $false
= ( v13 @ X16 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_14])],[avatar_definition]) ).
thf(f4890,plain,
( ! [X16: mworld] :
( $false
= ( v13 @ X16 ) )
| ~ spl40_14 ),
inference(avatar_component_clause,[],[f4889]) ).
thf(f4899,plain,
( ( $true = $false )
| ~ spl40_14 ),
inference(constrained_superposition,[],[f4890,f4769]) ).
thf(f4903,plain,
( $false
| ~ spl40_14 ),
inference(trivial_inequality_removal,[],[f4899]) ).
thf(f4904,plain,
~ spl40_14,
inference(avatar_contradiction_clause,[],[f4903]) ).
thf(f4944,definition,
( spl40_18
<=> ! [X16: mworld] :
( $true
= ( v13 @ X16 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_18])],[avatar_definition]) ).
thf(f4945,plain,
( ! [X16: mworld] :
( $true
= ( v13 @ X16 ) )
| ~ spl40_18 ),
inference(avatar_component_clause,[],[f4944]) ).
thf(f4948,plain,
( ( $true = $false )
| ~ spl40_5 ),
inference(constrained_superposition,[],[f4578,f4409]) ).
thf(f4952,plain,
( $false
| ~ spl40_5 ),
inference(trivial_inequality_removal,[],[f4948]) ).
thf(f4953,plain,
~ spl40_5,
inference(avatar_contradiction_clause,[],[f4952]) ).
thf(f5077,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f479,f193]) ).
thf(f5078,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5077]) ).
thf(f5079,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5078,f193]) ).
thf(f5080,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5079]) ).
thf(f5081,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5080,f193]) ).
thf(f5082,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5081]) ).
thf(f5083,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5082,f193]) ).
thf(f5084,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
= ( 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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5083]) ).
thf(f5085,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5084,f193]) ).
thf(f5086,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5085]) ).
thf(f5087,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5086,f193]) ).
thf(f5088,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5087]) ).
thf(f5089,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5088,f193]) ).
thf(f5090,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5089]) ).
thf(f5091,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5090,f193]) ).
thf(f5092,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5091]) ).
thf(f5093,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5092,f193]) ).
thf(f5094,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 ) )
| ( $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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5093]) ).
thf(f5095,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5094,f193]) ).
thf(f5096,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5095]) ).
thf(f5097,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5096,f193]) ).
thf(f5098,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5097]) ).
thf(f5099,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5098,f193]) ).
thf(f5100,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5099]) ).
thf(f5101,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5100,f193]) ).
thf(f5102,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5101]) ).
thf(f5103,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5102,f193]) ).
thf(f5104,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
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5103]) ).
thf(f5105,plain,
! [X21: mworld,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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5104,f193]) ).
thf(f5106,plain,
! [X21: mworld,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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5105]) ).
thf(f5107,plain,
! [X21: mworld,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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5106,f193]) ).
thf(f5108,plain,
! [X21: mworld,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
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5107]) ).
thf(f5109,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5108,f193]) ).
thf(f5110,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5109]) ).
thf(f5111,plain,
! [X21: mworld,X18: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5110,f193]) ).
thf(f5112,plain,
! [X21: mworld,X18: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5111]) ).
thf(f5113,plain,
! [X21: mworld,X19: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5112,f193]) ).
thf(f5114,plain,
! [X21: mworld,X19: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5113]) ).
thf(f5115,plain,
! [X21: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5114,f193]) ).
thf(f5116,plain,
! [X21: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(trivial_inequality_removal,[],[f5115]) ).
thf(f5117,plain,
! [X21: mworld] :
( ( $true = $false )
| ( $true
= ( v7 @ ( sK8 @ X21 ) ) ) ),
inference(forward_demodulation,[],[f5116,f193]) ).
thf(f5118,plain,
! [X21: mworld] :
( $true
= ( v7 @ ( sK8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5117]) ).
thf(f5204,definition,
( spl40_20
<=> ! [X20: mworld] :
( $true
= ( v9 @ X20 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_20])],[avatar_definition]) ).
thf(f5205,plain,
( ! [X20: mworld] :
( $true
= ( v9 @ X20 ) )
| ~ spl40_20 ),
inference(avatar_component_clause,[],[f5204]) ).
thf(f5210,definition,
( spl40_22
<=> ! [X14: mworld] :
( $false
= ( v15 @ X14 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_22])],[avatar_definition]) ).
thf(f5211,plain,
( ! [X14: mworld] :
( $false
= ( v15 @ X14 ) )
| ~ spl40_22 ),
inference(avatar_component_clause,[],[f5210]) ).
thf(f5213,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f2638,f193]) ).
thf(f5214,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5213]) ).
thf(f5215,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5214,f193]) ).
thf(f5216,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5215]) ).
thf(f5217,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5216,f193]) ).
thf(f5218,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5217]) ).
thf(f5219,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5218,f193]) ).
thf(f5220,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 ) )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5219]) ).
thf(f5221,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 )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5220,f193]) ).
thf(f5222,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
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5221]) ).
thf(f5223,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5222,f193]) ).
thf(f5224,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5223]) ).
thf(f5225,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5224,f193]) ).
thf(f5226,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5225]) ).
thf(f5227,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5226,f193]) ).
thf(f5228,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,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5227]) ).
thf(f5229,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5228,f193]) ).
thf(f5230,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5229]) ).
thf(f5231,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5230,f193]) ).
thf(f5232,plain,
! [X10: mworld,X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5231]) ).
thf(f5233,plain,
! [X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5232,f193]) ).
thf(f5234,plain,
! [X11: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5233]) ).
thf(f5235,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5234,f193]) ).
thf(f5236,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5235]) ).
thf(f5237,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5236,f193]) ).
thf(f5238,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5237]) ).
thf(f5239,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5238,f193]) ).
thf(f5240,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5239]) ).
thf(f5241,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5240,f193]) ).
thf(f5242,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5241]) ).
thf(f5243,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5242,f193]) ).
thf(f5244,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5243]) ).
thf(f5245,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5244,f193]) ).
thf(f5246,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5245]) ).
thf(f5247,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5246,f193]) ).
thf(f5248,plain,
! [X18: mworld,X6: mworld,X19: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5247]) ).
thf(f5249,plain,
! [X6: mworld,X19: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5248,f193]) ).
thf(f5250,plain,
! [X6: mworld,X19: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5249]) ).
thf(f5251,plain,
! [X6: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5250,f193]) ).
thf(f5252,plain,
! [X6: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5251]) ).
thf(f5253,plain,
( ! [X6: mworld,X7: mworld,X4: mworld] :
( ( $true = $false )
| ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) ) )
| ~ spl40_20 ),
inference(forward_demodulation,[],[f5252,f5205]) ).
thf(f5254,plain,
( ! [X6: mworld,X7: mworld,X4: mworld] :
( ( $true
= ( v25 @ X4 ) )
| ( $true
= ( v23 @ X6 ) )
| ( $false
= ( v22 @ X7 ) ) )
| ~ spl40_20 ),
inference(trivial_inequality_removal,[],[f5253]) ).
thf(f5256,definition,
( spl40_23
<=> ! [X7: mworld] :
( $false
= ( v22 @ X7 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_23])],[avatar_definition]) ).
thf(f5257,plain,
( ! [X7: mworld] :
( $false
= ( v22 @ X7 ) )
| ~ spl40_23 ),
inference(avatar_component_clause,[],[f5256]) ).
thf(f5259,definition,
( spl40_24
<=> ! [X6: mworld] :
( $true
= ( v23 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_24])],[avatar_definition]) ).
thf(f5260,plain,
( ! [X6: mworld] :
( $true
= ( v23 @ X6 ) )
| ~ spl40_24 ),
inference(avatar_component_clause,[],[f5259]) ).
thf(f5262,definition,
( spl40_25
<=> ! [X4: mworld] :
( $true
= ( v25 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_25])],[avatar_definition]) ).
thf(f5263,plain,
( ! [X4: mworld] :
( $true
= ( v25 @ X4 ) )
| ~ spl40_25 ),
inference(avatar_component_clause,[],[f5262]) ).
thf(f5264,plain,
( spl40_23
| spl40_24
| spl40_25
| ~ spl40_20 ),
inference(avatar_split_clause,[],[f5254,f5204,f5262,f5259,f5256]) ).
thf(f5266,plain,
( ( $true = $false )
| ~ spl40_23 ),
inference(constrained_superposition,[],[f5257,f4453]) ).
thf(f5270,plain,
( $false
| ~ spl40_23 ),
inference(trivial_inequality_removal,[],[f5266]) ).
thf(f5271,plain,
~ spl40_23,
inference(avatar_contradiction_clause,[],[f5270]) ).
thf(f5273,plain,
( ( $true = $false )
| ~ spl40_24 ),
inference(constrained_superposition,[],[f5260,f4439]) ).
thf(f5277,plain,
( $false
| ~ spl40_24 ),
inference(trivial_inequality_removal,[],[f5273]) ).
thf(f5278,plain,
~ spl40_24,
inference(avatar_contradiction_clause,[],[f5277]) ).
thf(f5279,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f468,f193]) ).
thf(f5280,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5279]) ).
thf(f5281,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5280,f193]) ).
thf(f5282,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5281]) ).
thf(f5283,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5282,f193]) ).
thf(f5284,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5283]) ).
thf(f5285,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5284,f193]) ).
thf(f5286,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5285]) ).
thf(f5287,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5286,f193]) ).
thf(f5288,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5287]) ).
thf(f5289,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5288,f193]) ).
thf(f5290,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5289]) ).
thf(f5291,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5290,f193]) ).
thf(f5292,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,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5291]) ).
thf(f5293,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5292,f193]) ).
thf(f5294,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5293]) ).
thf(f5295,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5294,f193]) ).
thf(f5296,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5295]) ).
thf(f5297,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5296,f193]) ).
thf(f5298,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5297]) ).
thf(f5299,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5298,f193]) ).
thf(f5300,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5299]) ).
thf(f5301,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5300,f193]) ).
thf(f5302,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5301]) ).
thf(f5303,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5302,f193]) ).
thf(f5304,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5303]) ).
thf(f5305,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5304,f193]) ).
thf(f5306,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5305]) ).
thf(f5307,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5306,f193]) ).
thf(f5308,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X20: mworld] :
( ( $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
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5307]) ).
thf(f5309,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5308,f193]) ).
thf(f5310,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5309]) ).
thf(f5311,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5310,f193]) ).
thf(f5312,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5311]) ).
thf(f5313,plain,
! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5312,f193]) ).
thf(f5314,plain,
! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5313]) ).
thf(f5315,plain,
! [X21: mworld,X19: mworld,X22: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5314,f193]) ).
thf(f5316,plain,
! [X21: mworld,X19: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5315]) ).
thf(f5317,plain,
! [X21: mworld,X22: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5316,f193]) ).
thf(f5318,plain,
! [X21: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5317]) ).
thf(f5319,plain,
! [X21: mworld,X22: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5318,f193]) ).
thf(f5320,plain,
! [X21: mworld,X22: mworld] :
( ( $false
= ( mrel @ X21 @ X22 ) )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(trivial_inequality_removal,[],[f5319]) ).
thf(f5321,plain,
! [X22: mworld] :
( ( $true = $false )
| ( $true
= ( v6 @ ( sK6 @ X22 ) ) ) ),
inference(forward_demodulation,[],[f5320,f193]) ).
thf(f5322,plain,
! [X22: mworld] :
( $true
= ( v6 @ ( sK6 @ X22 ) ) ),
inference(trivial_inequality_removal,[],[f5321]) ).
thf(f5420,plain,
( ( $true = $false )
| ~ spl40_18 ),
inference(constrained_superposition,[],[f4945,f4799]) ).
thf(f5424,plain,
( $false
| ~ spl40_18 ),
inference(trivial_inequality_removal,[],[f5420]) ).
thf(f5425,plain,
~ spl40_18,
inference(avatar_contradiction_clause,[],[f5424]) ).
thf(f5482,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f463,f193]) ).
thf(f5483,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5482]) ).
thf(f5484,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5483,f193]) ).
thf(f5485,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5484]) ).
thf(f5486,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5485,f193]) ).
thf(f5487,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5486]) ).
thf(f5488,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5487,f193]) ).
thf(f5489,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5488]) ).
thf(f5490,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5489,f193]) ).
thf(f5491,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5490]) ).
thf(f5492,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,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5491,f193]) ).
thf(f5493,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,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5492]) ).
thf(f5494,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,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5493,f193]) ).
thf(f5495,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,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5494]) ).
thf(f5496,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5495,f193]) ).
thf(f5497,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5496]) ).
thf(f5498,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5497,f193]) ).
thf(f5499,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5498]) ).
thf(f5500,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5499,f193]) ).
thf(f5501,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5500]) ).
thf(f5502,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5501,f193]) ).
thf(f5503,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5502]) ).
thf(f5504,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5503,f193]) ).
thf(f5505,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5504]) ).
thf(f5506,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5505,f193]) ).
thf(f5507,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5506]) ).
thf(f5508,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5507,f193]) ).
thf(f5509,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5508]) ).
thf(f5510,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5509,f193]) ).
thf(f5511,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5510]) ).
thf(f5512,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5511,f193]) ).
thf(f5513,plain,
! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5512]) ).
thf(f5514,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5513,f193]) ).
thf(f5515,plain,
! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5514]) ).
thf(f5516,plain,
! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5515,f193]) ).
thf(f5517,plain,
! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5516]) ).
thf(f5518,plain,
! [X21: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5517,f193]) ).
thf(f5519,plain,
! [X21: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5518]) ).
thf(f5520,plain,
! [X21: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5519,f193]) ).
thf(f5521,plain,
! [X21: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5520]) ).
thf(f5522,plain,
! [X21: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5521,f193]) ).
thf(f5523,plain,
! [X21: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5522]) ).
thf(f5524,plain,
! [X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5523,f193]) ).
thf(f5525,plain,
! [X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5524]) ).
thf(f5526,plain,
! [X23: mworld] :
( ( $true = $false )
| ( $false
= ( v5 @ ( sK5 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5525,f193]) ).
thf(f5527,plain,
! [X23: mworld] :
( $false
= ( v5 @ ( sK5 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5526]) ).
thf(f5530,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f2281,f193]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5530]) ).
thf(f5532,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5531,f193]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5532]) ).
thf(f5534,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5533,f193]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5534]) ).
thf(f5536,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5535,f193]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5536]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5537,f193]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5538]) ).
thf(f5540,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,X22: mworld,X13: mworld,X20: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5539,f5263]) ).
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,X22: mworld,X13: mworld,X20: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5540]) ).
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,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5541,f193]) ).
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,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5542]) ).
thf(f5544,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,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5543,f193]) ).
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,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5544]) ).
thf(f5546,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5545,f193]) ).
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,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5546]) ).
thf(f5548,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5547,f193]) ).
thf(f5549,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5548]) ).
thf(f5550,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5549,f193]) ).
thf(f5551,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5550]) ).
thf(f5552,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5551,f193]) ).
thf(f5553,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5552]) ).
thf(f5554,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5553,f193]) ).
thf(f5555,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5554]) ).
thf(f5556,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5555,f193]) ).
thf(f5557,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5556]) ).
thf(f5558,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5557,f193]) ).
thf(f5559,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5558]) ).
thf(f5560,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5559,f193]) ).
thf(f5561,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5560]) ).
thf(f5562,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5561,f193]) ).
thf(f5563,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5562]) ).
thf(f5564,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5563,f193]) ).
thf(f5565,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5564]) ).
thf(f5566,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5565,f193]) ).
thf(f5567,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5566]) ).
thf(f5568,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5567,f193]) ).
thf(f5569,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5568]) ).
thf(f5570,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5569,f193]) ).
thf(f5571,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5570]) ).
thf(f5572,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5571,f193]) ).
thf(f5573,plain,
( ! [X21: mworld,X19: mworld,X16: mworld,X22: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5572]) ).
thf(f5574,plain,
( ! [X19: mworld,X16: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5573,f193]) ).
thf(f5575,plain,
( ! [X19: mworld,X16: mworld,X22: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5574]) ).
thf(f5576,plain,
( ! [X19: mworld,X16: mworld,X23: mworld] :
( ( $true = $false )
| ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(forward_demodulation,[],[f5575,f193]) ).
thf(f5577,plain,
( ! [X19: mworld,X16: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $true
= ( v10 @ X19 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_25 ),
inference(trivial_inequality_removal,[],[f5576]) ).
thf(f5579,definition,
( spl40_28
<=> ! [X23: mworld] :
( $false
= ( v6 @ X23 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_28])],[avatar_definition]) ).
thf(f5580,plain,
( ! [X23: mworld] :
( $false
= ( v6 @ X23 ) )
| ~ spl40_28 ),
inference(avatar_component_clause,[],[f5579]) ).
thf(f5582,definition,
( spl40_29
<=> ! [X19: mworld] :
( $true
= ( v10 @ X19 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_29])],[avatar_definition]) ).
thf(f5583,plain,
( ! [X19: mworld] :
( $true
= ( v10 @ X19 ) )
| ~ spl40_29 ),
inference(avatar_component_clause,[],[f5582]) ).
thf(f5584,plain,
( spl40_28
| spl40_29
| spl40_18
| ~ spl40_25 ),
inference(avatar_split_clause,[],[f5577,f5262,f4944,f5582,f5579]) ).
thf(f5586,plain,
( ( $true = $false )
| ~ spl40_28 ),
inference(constrained_superposition,[],[f5580,f5322]) ).
thf(f5590,plain,
( $false
| ~ spl40_28 ),
inference(trivial_inequality_removal,[],[f5586]) ).
thf(f5591,plain,
~ spl40_28,
inference(avatar_contradiction_clause,[],[f5590]) ).
thf(f5593,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f2715,f193]) ).
thf(f5594,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5593]) ).
thf(f5595,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5594,f193]) ).
thf(f5596,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5595]) ).
thf(f5597,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5596,f193]) ).
thf(f5598,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5597]) ).
thf(f5599,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(forward_demodulation,[],[f5598,f193]) ).
thf(f5600,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( v26 @ X3 ) )
| ( $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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5599]) ).
thf(f5601,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5600,f4837]) ).
thf(f5602,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5601]) ).
thf(f5603,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5602,f193]) ).
thf(f5604,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5603]) ).
thf(f5605,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,X22: mworld,X12: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5604,f193]) ).
thf(f5606,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,X22: mworld,X12: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5605]) ).
thf(f5607,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,X22: mworld,X12: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5606,f193]) ).
thf(f5608,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,X22: mworld,X12: mworld,X23: 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
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5607]) ).
thf(f5609,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5608,f193]) ).
thf(f5610,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5609]) ).
thf(f5611,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5610,f193]) ).
thf(f5612,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5611]) ).
thf(f5613,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5612,f193]) ).
thf(f5614,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5613]) ).
thf(f5615,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5614,f193]) ).
thf(f5616,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5615]) ).
thf(f5617,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5616,f193]) ).
thf(f5618,plain,
( ! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v18 @ X11 ) )
| ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5617]) ).
thf(f5619,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5618,f4572]) ).
thf(f5620,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5619]) ).
thf(f5621,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5620,f193]) ).
thf(f5622,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5621]) ).
thf(f5623,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5622,f193]) ).
thf(f5624,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5623]) ).
thf(f5625,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: 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
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5624,f193]) ).
thf(f5626,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $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
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5625]) ).
thf(f5627,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5626,f193]) ).
thf(f5628,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5627]) ).
thf(f5629,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5628,f193]) ).
thf(f5630,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X17: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5629]) ).
thf(f5631,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5630,f193]) ).
thf(f5632,plain,
( ! [X21: mworld,X18: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5631]) ).
thf(f5633,plain,
( ! [X21: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5632,f193]) ).
thf(f5634,plain,
( ! [X21: mworld,X19: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5633]) ).
thf(f5635,plain,
( ! [X21: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5634,f193]) ).
thf(f5636,plain,
( ! [X21: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5635]) ).
thf(f5637,plain,
( ! [X21: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5636,f193]) ).
thf(f5638,plain,
( ! [X21: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5637]) ).
thf(f5639,plain,
( ! [X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5638,f193]) ).
thf(f5640,plain,
( ! [X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5639]) ).
thf(f5641,plain,
( ! [X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(forward_demodulation,[],[f5640,f193]) ).
thf(f5642,plain,
( ! [X22: mworld,X23: mworld] :
( ( $false
= ( v7 @ X22 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl40_3
| ~ spl40_12 ),
inference(trivial_inequality_removal,[],[f5641]) ).
thf(f5644,definition,
( spl40_30
<=> ! [X22: mworld] :
( $false
= ( v7 @ X22 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_30])],[avatar_definition]) ).
thf(f5645,plain,
( ! [X22: mworld] :
( $false
= ( v7 @ X22 ) )
| ~ spl40_30 ),
inference(avatar_component_clause,[],[f5644]) ).
thf(f5646,plain,
( spl40_28
| spl40_30
| ~ spl40_3
| ~ spl40_12 ),
inference(avatar_split_clause,[],[f5642,f4836,f4571,f5644,f5579]) ).
thf(f5648,plain,
( ( $true = $false )
| ~ spl40_30 ),
inference(constrained_superposition,[],[f5645,f5118]) ).
thf(f5652,plain,
( $false
| ~ spl40_30 ),
inference(trivial_inequality_removal,[],[f5648]) ).
thf(f5653,plain,
~ spl40_30,
inference(avatar_contradiction_clause,[],[f5652]) ).
thf(f5655,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] :
( ( $true = $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(forward_demodulation,[],[f4045,f193]) ).
thf(f5656,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] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5655]) ).
thf(f5659,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] :
( ( $true = $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(forward_demodulation,[],[f5656,f193]) ).
thf(f5660,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5659]) ).
thf(f5663,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5660,f4840]) ).
thf(f5664,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X11: 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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5663]) ).
thf(f5667,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5664,f193]) ).
thf(f5668,plain,
( ! [X3: mworld,X10: mworld,X11: 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 @ X3 @ X4 ) )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5667]) ).
thf(f5671,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5668,f193]) ).
thf(f5672,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5671]) ).
thf(f5675,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5672,f193]) ).
thf(f5676,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5675]) ).
thf(f5679,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5676,f193]) ).
thf(f5680,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5679]) ).
thf(f5683,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5680,f193]) ).
thf(f5684,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5683]) ).
thf(f5687,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5684,f193]) ).
thf(f5688,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $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
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5687]) ).
thf(f5691,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5688,f193]) ).
thf(f5692,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5691]) ).
thf(f5695,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5692,f193]) ).
thf(f5696,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5695]) ).
thf(f5699,plain,
( ! [X3: mworld,X11: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5696,f193]) ).
thf(f5700,plain,
( ! [X3: mworld,X11: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5699]) ).
thf(f5703,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5700,f193]) ).
thf(f5704,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5703]) ).
thf(f5707,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5704,f193]) ).
thf(f5708,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5707]) ).
thf(f5711,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5708,f193]) ).
thf(f5712,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5711]) ).
thf(f5715,plain,
( ! [X3: mworld,X16: mworld,X15: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5712,f193]) ).
thf(f5716,plain,
( ! [X3: mworld,X16: mworld,X15: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5715]) ).
thf(f5719,plain,
( ! [X3: mworld,X16: mworld,X13: mworld] :
( ( $true = $false )
| ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(forward_demodulation,[],[f5716,f193]) ).
thf(f5720,plain,
( ! [X3: mworld,X16: mworld,X13: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $false
= ( v16 @ X13 ) )
| ( $false
= ( v13 @ X16 ) ) )
| ~ spl40_13 ),
inference(trivial_inequality_removal,[],[f5719]) ).
thf(f5730,definition,
( spl40_31
<=> ! [X13: mworld] :
( $false
= ( v16 @ X13 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_31])],[avatar_definition]) ).
thf(f5731,plain,
( ! [X13: mworld] :
( $false
= ( v16 @ X13 ) )
| ~ spl40_31 ),
inference(avatar_component_clause,[],[f5730]) ).
thf(f5732,plain,
( spl40_14
| spl40_31
| spl40_12
| ~ spl40_13 ),
inference(avatar_split_clause,[],[f5720,f4839,f4836,f5730,f4889]) ).
thf(f5734,plain,
( ( $true = $false )
| ~ spl40_31 ),
inference(constrained_superposition,[],[f5731,f4521]) ).
thf(f5738,plain,
( $false
| ~ spl40_31 ),
inference(trivial_inequality_removal,[],[f5734]) ).
thf(f5739,plain,
~ spl40_31,
inference(avatar_contradiction_clause,[],[f5738]) ).
thf(f5763,plain,
( ( $true = $false )
| ~ spl40_4 ),
inference(constrained_superposition,[],[f4575,f4465]) ).
thf(f5767,plain,
( $false
| ~ spl40_4 ),
inference(trivial_inequality_removal,[],[f5763]) ).
thf(f5768,plain,
~ spl40_4,
inference(avatar_contradiction_clause,[],[f5767]) ).
thf(f5832,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f1824,f193]) ).
thf(f5833,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5832]) ).
thf(f5834,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5833,f193]) ).
thf(f5835,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: 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
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5834]) ).
thf(f5836,plain,
! [X24: 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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5835,f193]) ).
thf(f5837,plain,
! [X24: 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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5836]) ).
thf(f5838,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5837,f193]) ).
thf(f5839,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5838]) ).
thf(f5840,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5839,f193]) ).
thf(f5841,plain,
! [X24: mworld,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,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5840]) ).
thf(f5842,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5841,f193]) ).
thf(f5843,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5842]) ).
thf(f5844,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5843,f193]) ).
thf(f5845,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5844]) ).
thf(f5846,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5845,f193]) ).
thf(f5847,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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5846]) ).
thf(f5848,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5847,f193]) ).
thf(f5849,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5848]) ).
thf(f5850,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5849,f193]) ).
thf(f5851,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5850]) ).
thf(f5852,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5851,f193]) ).
thf(f5853,plain,
! [X21: mworld,X11: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5852]) ).
thf(f5854,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5853,f193]) ).
thf(f5855,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( 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
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5854]) ).
thf(f5856,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5855,f193]) ).
thf(f5857,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5856]) ).
thf(f5858,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5857,f193]) ).
thf(f5859,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $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
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5858]) ).
thf(f5860,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5859,f193]) ).
thf(f5861,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5860]) ).
thf(f5862,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5861,f193]) ).
thf(f5863,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5862]) ).
thf(f5864,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X17: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5863,f193]) ).
thf(f5865,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X17: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5864]) ).
thf(f5866,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5865,f193]) ).
thf(f5867,plain,
! [X21: mworld,X18: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5866]) ).
thf(f5868,plain,
! [X21: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5867,f193]) ).
thf(f5869,plain,
! [X21: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5868]) ).
thf(f5870,plain,
! [X21: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(forward_demodulation,[],[f5869,f193]) ).
thf(f5871,plain,
! [X21: mworld,X19: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v10 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) ),
inference(trivial_inequality_removal,[],[f5870]) ).
thf(f5872,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5871,f5583]) ).
thf(f5873,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5872]) ).
thf(f5874,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5873,f193]) ).
thf(f5875,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5874]) ).
thf(f5876,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5875,f5205]) ).
thf(f5877,plain,
( ! [X21: mworld,X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X21 @ X22 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5876]) ).
thf(f5878,plain,
( ! [X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5877,f193]) ).
thf(f5879,plain,
( ! [X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5878]) ).
thf(f5880,plain,
( ! [X7: mworld,X24: mworld,X23: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5879,f193]) ).
thf(f5881,plain,
( ! [X7: mworld,X24: mworld,X23: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5880]) ).
thf(f5882,plain,
( ! [X7: mworld,X24: mworld] :
( ( $true = $false )
| ( $false
= ( v22 @ X7 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(forward_demodulation,[],[f5881,f193]) ).
thf(f5883,plain,
( ! [X7: mworld,X24: mworld] :
( ( $false
= ( v22 @ X7 ) )
| ( $true
= ( v5 @ X24 ) ) )
| ~ spl40_20
| ~ spl40_29 ),
inference(trivial_inequality_removal,[],[f5882]) ).
thf(f5885,definition,
( spl40_33
<=> ! [X24: mworld] :
( $true
= ( v5 @ X24 ) ) ),
introduced(definition,[new_symbols(definition,[spl40_33])],[avatar_definition]) ).
thf(f5886,plain,
( ! [X24: mworld] :
( $true
= ( v5 @ X24 ) )
| ~ spl40_33 ),
inference(avatar_component_clause,[],[f5885]) ).
thf(f5887,plain,
( spl40_33
| spl40_23
| ~ spl40_20
| ~ spl40_29 ),
inference(avatar_split_clause,[],[f5883,f5582,f5204,f5256,f5885]) ).
thf(f5888,plain,
( ( $true = $false )
| ~ spl40_33 ),
inference(constrained_superposition,[],[f5886,f5527]) ).
thf(f5892,plain,
( $false
| ~ spl40_33 ),
inference(trivial_inequality_removal,[],[f5888]) ).
thf(f5893,plain,
~ spl40_33,
inference(avatar_contradiction_clause,[],[f5892]) ).
thf(f5894,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f4190,f193]) ).
thf(f5895,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5894]) ).
thf(f5898,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 )
| ( $true
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) ),
inference(forward_demodulation,[],[f5895,f193]) ).
thf(f5899,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
= ( v28 @ X1 ) )
| ( $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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5898]) ).
thf(f5902,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5899,f4581]) ).
thf(f5903,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5902]) ).
thf(f5906,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5903,f193]) ).
thf(f5907,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5906]) ).
thf(f5908,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5907,f193]) ).
thf(f5909,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5908]) ).
thf(f5910,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5909,f193]) ).
thf(f5911,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5910]) ).
thf(f5912,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5911,f193]) ).
thf(f5913,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5912]) ).
thf(f5914,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5913,f193]) ).
thf(f5915,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5914]) ).
thf(f5916,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5915,f193]) ).
thf(f5917,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5916]) ).
thf(f5918,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5917,f193]) ).
thf(f5919,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5918]) ).
thf(f5920,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5919,f193]) ).
thf(f5921,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5920]) ).
thf(f5922,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5921,f193]) ).
thf(f5923,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5922]) ).
thf(f5924,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5923,f193]) ).
thf(f5925,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5924]) ).
thf(f5926,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5925,f193]) ).
thf(f5927,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5926]) ).
thf(f5928,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5927,f193]) ).
thf(f5929,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5928]) ).
thf(f5930,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5929,f193]) ).
thf(f5931,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5930]) ).
thf(f5932,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5931,f193]) ).
thf(f5933,plain,
( ! [X18: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5932]) ).
thf(f5934,plain,
( ! [X18: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5933,f193]) ).
thf(f5935,plain,
( ! [X18: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5934]) ).
thf(f5936,plain,
( ! [X18: mworld,X19: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5935,f193]) ).
thf(f5937,plain,
( ! [X18: mworld,X19: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5936]) ).
thf(f5938,plain,
( ! [X19: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5937,f193]) ).
thf(f5939,plain,
( ! [X19: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5938]) ).
thf(f5940,plain,
( ! [X14: mworld,X15: mworld,X20: mworld] :
( ( $true = $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(forward_demodulation,[],[f5939,f193]) ).
thf(f5941,plain,
( ! [X14: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $true
= ( v9 @ X20 ) ) )
| ~ spl40_6 ),
inference(trivial_inequality_removal,[],[f5940]) ).
thf(f5943,plain,
( ( $true = $false )
| ~ spl40_22 ),
inference(constrained_superposition,[],[f5211,f4608]) ).
thf(f5947,plain,
( $false
| ~ spl40_22 ),
inference(trivial_inequality_removal,[],[f5943]) ).
thf(f5948,plain,
~ spl40_22,
inference(avatar_contradiction_clause,[],[f5947]) ).
thf(f6051,plain,
( spl40_20
| spl40_11
| spl40_22
| ~ spl40_6 ),
inference(avatar_split_clause,[],[f5941,f4580,f5210,f4833,f5204]) ).
cnf(s152,plain,
( spl40_3
| spl40_4
| spl40_5
| spl40_6 ),
inference(sat_conversion,[],[f4582]) ).
cnf(s178,plain,
( spl40_9
| spl40_11
| spl40_12
| spl40_13 ),
inference(sat_conversion,[],[f4841]) ).
cnf(s182,plain,
~ spl40_9,
inference(sat_conversion,[],[f4848]) ).
cnf(s186,plain,
~ spl40_11,
inference(sat_conversion,[],[f4855]) ).
cnf(s195,plain,
~ spl40_14,
inference(sat_conversion,[],[f4904]) ).
cnf(s204,plain,
~ spl40_5,
inference(sat_conversion,[],[f4953]) ).
cnf(s227,plain,
( ~ spl40_20
| spl40_23
| spl40_24
| spl40_25 ),
inference(sat_conversion,[],[f5264]) ).
cnf(s231,plain,
~ spl40_23,
inference(sat_conversion,[],[f5271]) ).
cnf(s235,plain,
~ spl40_24,
inference(sat_conversion,[],[f5278]) ).
cnf(s248,plain,
~ spl40_18,
inference(sat_conversion,[],[f5425]) ).
cnf(s261,plain,
( spl40_18
| ~ spl40_25
| spl40_28
| spl40_29 ),
inference(sat_conversion,[],[f5584]) ).
cnf(s265,plain,
~ spl40_28,
inference(sat_conversion,[],[f5591]) ).
cnf(s270,plain,
( ~ spl40_3
| ~ spl40_12
| spl40_28
| spl40_30 ),
inference(sat_conversion,[],[f5646]) ).
cnf(s274,plain,
~ spl40_30,
inference(sat_conversion,[],[f5653]) ).
cnf(s278,plain,
( spl40_12
| ~ spl40_13
| spl40_14
| spl40_31 ),
inference(sat_conversion,[],[f5732]) ).
cnf(s282,plain,
~ spl40_31,
inference(sat_conversion,[],[f5739]) ).
cnf(s288,plain,
~ spl40_4,
inference(sat_conversion,[],[f5768]) ).
cnf(s306,plain,
( ~ spl40_20
| spl40_23
| ~ spl40_29
| spl40_33 ),
inference(sat_conversion,[],[f5887]) ).
cnf(s310,plain,
~ spl40_33,
inference(sat_conversion,[],[f5893]) ).
cnf(s316,plain,
~ spl40_22,
inference(sat_conversion,[],[f5948]) ).
cnf(s332,plain,
( ~ spl40_6
| spl40_11
| spl40_20
| spl40_22 ),
inference(sat_conversion,[],[f6051]) ).
cnf(s333,plain,
( ~ spl40_20
| spl40_23
| ~ spl40_29 ),
inference(rat,[],[s306,s310]) ).
cnf(s334,plain,
( spl40_12
| ~ spl40_13
| spl40_14 ),
inference(rat,[],[s278,s282]) ).
cnf(s335,plain,
( ~ spl40_3
| ~ spl40_12
| spl40_28 ),
inference(rat,[],[s270,s274]) ).
cnf(s336,plain,
( spl40_18
| ~ spl40_25
| spl40_29 ),
inference(rat,[],[s261,s265]) ).
cnf(s338,plain,
( ~ spl40_20
| spl40_25 ),
inference(rat,[],[s227,s235,s231]) ).
cnf(s342,plain,
( spl40_12
| spl40_13 ),
inference(rat,[],[s178,s186,s182]) ).
cnf(s344,plain,
( spl40_3
| spl40_6 ),
inference(rat,[],[s152,s204,s288]) ).
cnf(s345,plain,
~ spl40_20,
inference(rat,[],[s336,s338,s333,s248,s231]) ).
cnf(s347,plain,
~ spl40_6,
inference(rat,[],[s332,s316,s186,s345]) ).
cnf(s348,plain,
spl40_3,
inference(rat,[],[s344,s347]) ).
cnf(s349,plain,
~ spl40_12,
inference(rat,[],[s335,s265,s348]) ).
cnf(s350,plain,
~ spl40_13,
inference(rat,[],[s334,s195,s349]) ).
cnf(s351,plain,
$false,
inference(rat,[],[s342,s350,s349]) ).
thf(f6052,plain,
$false,
inference(avatar_sat_refutation,[],[s351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO904^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:32:36 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
% 3.69/0.88 % (1558917)Will run a generic schedule for satisfiability detection.
% 3.69/0.88 % (1558923)% WARNING: option uhcvi not known.
% 3.69/0.88 % (1558923)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3044735124:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.69/0.88 % (1558924)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2060597425:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.69/0.88 % (1558922)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1996440065_2999 on theBenchmark for (2999ds/0Mi)
% 3.69/0.88 % (1558925)dis+10_1_sil=32000:sp=arity:random_seed=3672834639:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.69/0.88 % (1558926)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3847537535:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.69/0.88 % (1558927)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1181619441:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.69/0.88 % (1558928)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4129658789:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.69/0.88 % (1558923)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.88 % (1558926)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.88 % (1558923)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.69/0.88 % (1558925)Instruction limit reached!
% 3.69/0.88 % (1558925)------------------------------
% 3.69/0.88 % (1558925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.88 % (1558925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.88 % (1558925)CaDiCaL version: 2.1.3
% 3.69/0.88 % (1558925)Termination reason: Instruction limit
% 3.69/0.88 % (1558925)Termination phase: Property scanning
% 3.69/0.88 % (1558925)Time elapsed: 0.036 s
% 3.69/0.88 % (1558925)Peak memory usage: 10 MB
% 3.69/0.88 % (1558925)Instructions burned: 104 (million)
% 3.69/0.88 % (1558926)Instruction limit reached!
% 3.69/0.88 % (1558926)------------------------------
% 3.69/0.88 % (1558926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.88 % (1558926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.88 % (1558926)CaDiCaL version: 2.1.3
% 3.69/0.88 % (1558926)Termination reason: Instruction limit
% 3.69/0.88 % (1558926)Termination phase: Property scanning
% 3.69/0.88 % (1558926)Time elapsed: 0.041 s
% 3.69/0.88 % (1558926)Peak memory usage: 10 MB
% 3.69/0.88 % (1558926)Instructions burned: 117 (million)
% 3.69/0.88 % (1558927)Instruction limit reached!
% 3.69/0.88 % (1558927)------------------------------
% 3.69/0.88 % (1558927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.88 % (1558927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.88 % (1558927)CaDiCaL version: 2.1.3
% 3.69/0.88 % (1558927)Termination reason: Instruction limit
% 3.69/0.88 % (1558927)Termination phase: Property scanning
% 3.69/0.88 % (1558927)Time elapsed: 0.047 s
% 3.69/0.88 % (1558927)Peak memory usage: 10 MB
% 3.69/0.88 % (1558927)Instructions burned: 133 (million)
% 3.69/0.88 % Exception at run slice level
% 3.69/0.88 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558936)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2997151316:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.69/0.89 % (1558928)Instruction limit reached!
% 3.69/0.89 % (1558928)------------------------------
% 3.69/0.89 % (1558928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558928)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558928)Termination reason: Instruction limit
% 3.69/0.89 % (1558928)Termination phase: Saturation
% 3.69/0.89 % (1558928)Time elapsed: 0.058 s
% 3.69/0.89 % (1558928)Peak memory usage: 12 MB
% 3.69/0.89 % (1558928)Instructions burned: 161 (million)
% 3.69/0.89 % (1558937)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2078789711:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.69/0.89 % (1558938)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=3474690412:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.69/0.89 % (1558939)ott-21_1_sil=16000:fs=off:random_seed=3561881883:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.69/0.89 % (1558941)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3545845929:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.69/0.89 % (1558938)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.89 % (1558937)Instruction limit reached!
% 3.69/0.89 % (1558937)------------------------------
% 3.69/0.89 % (1558937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558937)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558937)Termination reason: Instruction limit
% 3.69/0.89 % (1558937)Termination phase: Property scanning
% 3.69/0.89 % (1558937)Time elapsed: 0.047 s
% 3.69/0.89 % (1558937)Peak memory usage: 10 MB
% 3.69/0.89 % (1558937)Instructions burned: 133 (million)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558938)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.69/0.89 % (1558946)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2274551165:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.69/0.89 % (1558947)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3201495658:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.69/0.89 % (1558939)Instruction limit reached!
% 3.69/0.89 % (1558939)------------------------------
% 3.69/0.89 % (1558939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558939)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558939)Termination reason: Instruction limit
% 3.69/0.89 % (1558939)Termination phase: Saturation
% 3.69/0.89 % (1558939)Time elapsed: 0.067 s
% 3.69/0.89 % (1558939)Peak memory usage: 12 MB
% 3.69/0.89 % (1558939)Instructions burned: 182 (million)
% 3.69/0.89 % (1558950)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1736836966:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558952)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=2576325736: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)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558952)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.89 % (1558954)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3635395812:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.69/0.89 % (1558954)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.89 % (1558941)Instruction limit reached!
% 3.69/0.89 % (1558941)------------------------------
% 3.69/0.89 % (1558941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558941)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558941)Termination reason: Instruction limit
% 3.69/0.89 % (1558941)Termination phase: Saturation
% 3.69/0.89 % (1558941)Time elapsed: 0.180 s
% 3.69/0.89 % (1558941)Peak memory usage: 13 MB
% 3.69/0.89 % (1558941)Instructions burned: 483 (million)
% 3.69/0.89 % (1558956)fmb+10_1_sil=64000:random_seed=1386647130:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.69/0.89 % (1558956)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.69/0.89 % (1558938)Instruction limit reached!
% 3.69/0.89 % (1558938)------------------------------
% 3.69/0.89 % (1558938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558938)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558938)Termination reason: Instruction limit
% 3.69/0.89 % (1558938)Termination phase: Saturation
% 3.69/0.89 % (1558938)Time elapsed: 0.257 s
% 3.69/0.89 % (1558938)Peak memory usage: 14 MB
% 3.69/0.89 % (1558938)Instructions burned: 687 (million)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558958)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3415892720:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.69/0.89 % (1558959)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1650158632:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558924) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1558917-1558924"...
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558962)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3901318555:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.69/0.89 % (1558963)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4130446952:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.69/0.89 % (1558962)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.89 % (1558963)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.69/0.89 % (1558963)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.69/0.89 % (1558952)Instruction limit reached!
% 3.69/0.89 % (1558952)------------------------------
% 3.69/0.89 % (1558952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558952)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558952)Termination reason: Instruction limit
% 3.69/0.89 % (1558952)Termination phase: Saturation
% 3.69/0.89 % (1558952)Time elapsed: 0.259 s
% 3.69/0.89 % (1558952)Peak memory usage: 14 MB
% 3.69/0.89 % (1558952)Instructions burned: 693 (million)
% 3.69/0.89 % (1558966)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4126260357:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.69/0.89 % Exception at run slice level
% 3.69/0.89 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.69/0.89 % (1558968)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1738932942:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.69/0.89 % (1558954)Instruction limit reached!
% 3.69/0.89 % (1558954)------------------------------
% 3.69/0.89 % (1558954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558954)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558954)Termination reason: Instruction limit
% 3.69/0.89 % (1558954)Termination phase: Saturation
% 3.69/0.89 % (1558954)Time elapsed: 0.329 s
% 3.69/0.89 % (1558954)Peak memory usage: 14 MB
% 3.69/0.89 % (1558954)Instructions burned: 881 (million)
% 3.69/0.89 % (1558947)Instruction limit reached!
% 3.69/0.89 % (1558947)------------------------------
% 3.69/0.89 % (1558947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.69/0.89 % (1558947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/0.89 % (1558947)CaDiCaL version: 2.1.3
% 3.69/0.89 % (1558947)Termination reason: Instruction limit
% 3.69/0.89 % (1558947)Termination phase: Saturation
% 3.69/0.89 % (1558947)Time elapsed: 0.436 s
% 3.69/0.89 % (1558947)Peak memory usage: 16 MB
% 3.69/0.89 % (1558947)Instructions burned: 1180 (million)
% 3.69/0.89 % (1558970)ott-2_1_sil=16000:newcnf=on:random_seed=460751545:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 3.69/0.89 % (1558971)ott+10_1_sil=32000:tgt=ground:random_seed=3146518034:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 3.69/0.89 % (1558970)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.69/0.89 % (1558924)...printing done.
% 3.69/0.89 % (1558924)Refutation found. Thanks to Tanya!
% 3.69/0.89 % SZS status ContradictoryAxioms for theBenchmark
% 3.69/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 4.64/0.92 % (1558924)------------------------------
% 4.64/0.92 % (1558924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.64/0.92 % (1558924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/0.92 % (1558924)CaDiCaL version: 2.1.3
% 4.64/0.92 % (1558924)Termination reason: Refutation
% 4.64/0.92 % (1558924)Time elapsed: 0.604 s
% 4.64/0.92 % (1558924)Peak memory usage: 17 MB
% 4.64/0.92 % (1558924)Instructions burned: 1563 (million)
% 4.64/0.92 % (1558917)Success in time 0.68 s
% 4.64/0.92 % Vampire exiting
%------------------------------------------------------------------------------