%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO905^6 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:38 AM UTC 2026
% Result : ContradictoryAxioms 15.21s 2.73s
% Output : Refutation 15.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 144
% Number of leaves : 30
% Syntax : Number of formulae : 1247 ( 111 unt; 0 typ; 15 def)
% Number of atoms : 58209 (12600 equ; 0 cnn)
% Maximal formula atoms : 159 ( 46 avg)
% Number of connectives : 90378 (1491 ~;12309 |;4179 &;58522 @)
% ( 15 <=>;6026 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 20 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 388 ( 388 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 106 usr; 22 con; 0-4 aty)
% (5709 !!;2127 ??; 0 @@+; 0 @@-)
% Number of variables : 20808 ( 80 sgn12024 !; 2 ?;20808 :)
% 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_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: 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 > mworld ).
thf(func_def_92,type,
sK40: mworld > mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(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,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X1: mworld,X0: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f28,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod19) ).
thf(f31,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod22) ).
thf(f33,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod24) ).
thf(f40,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod31) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod36) ).
thf(f46,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod37) ).
thf(f47,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod38) ).
thf(f60,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X0: mworld] : $true ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alt1) ).
thf(f71,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f72,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f83,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f84,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f87,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f88,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f90,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f101,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(f102,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
@ ^ [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 ) ) )
= $true ),
inference(fool_elimination,[],[f101]) ).
thf(f107,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f115,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f116,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f115]) ).
thf(f121,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f122,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f133,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f134,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f133]) ).
thf(f137,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f138,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f137]) ).
thf(f161,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f162,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f161]) ).
thf(f163,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f168,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
inference(rectify,[],[f8]) ).
thf(f169,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f168]) ).
thf(f170,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X1 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f171,plain,
! [X1: mworld,X0: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(fool_elimination,[],[f170]) ).
thf(f180,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f181,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f180]) ).
thf(f185,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(rectify,[],[f171]) ).
thf(f186,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f190,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
@ ^ [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 ) ) )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f191,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f72]) ).
thf(f208,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mnot @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f134]) ).
thf(f209,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f185]) ).
thf(f212,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f181]) ).
thf(f220,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f224,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f84]) ).
thf(f225,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f227,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f169]) ).
thf(f235,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v19 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f237,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f238,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f245,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f246,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mor @ ( mnot @ v20 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v15 @ ( mbox @ ( mbox @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f162]) ).
thf(f252,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v5 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v5 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v6 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v8 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v13 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v14 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v23 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v23 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
= $true ),
inference(definition_unfolding,[],[f190,f225,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f245,f238,f227,f227,f227,f227,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f227,f227,f227,f227,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f227,f227,f227,f227,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f245,f227,f227,f186,f227,f227,f227,f227]) ).
thf(f253,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v19 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v15
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f191,f225,f238,f238,f238,f238,f238,f237,f186,f238,f238,f238,f238,f238,f237,f186,f238,f238,f238,f238,f237,f238,f238,f238,f238,f238,f186]) ).
thf(f268,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v25
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v13
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f208,f225,f238,f238,f238,f238,f237,f238,f237,f186,f238,f238,f238,f238,f238,f238,f238,f238,f238,f238,f238,f237,f238,f186]) ).
thf(f271,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v21
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v20
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f212,f225,f238,f238,f238,f238,f238,f238,f238,f238,f237,f238,f237,f238,f238,f238,f238,f238,f237,f186,f238,f238,f238,f238,f238,f186]) ).
thf(f279,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v25
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v20
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f220,f225,f238,f238,f238,f238,f237,f238,f238,f238,f238,f238,f237,f238,f238,f238,f238,f238,f238,f237,f186,f238,f238,f238,f238,f238,f238,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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v19 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v10
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f224,f225,f238,f238,f238,f238,f238,f238,f238,f238,f237,f186,f238,f238,f237,f186,f238,f238,f238,f238,f238,f238,f238,f238,f238,f237,f238,f238]) ).
thf(f292,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v25 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v19
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f235,f225,f238,f238,f238,f238,f237,f186,f238,f237,f186,f238,f238,f238,f238,f238,f237,f238,f238,f238,f238,f238,f238,f238,f238,f238,f238,f238,f186]) ).
thf(f300,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v21
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v20 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v15
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f246,f225,f238,f238,f238,f238,f238,f238,f238,f238,f237,f238,f237,f186,f238,f238,f238,f238,f238,f237,f238,f238,f238]) ).
thf(f449,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f450,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f449]) ).
thf(f451,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f450]) ).
thf(f452,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f452]) ).
thf(f454,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f453]) ).
thf(f455,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f455]) ).
thf(f457,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ 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 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f456]) ).
thf(f458,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f457]) ).
thf(f459,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f459]) ).
thf(f461,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ 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 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f460]) ).
thf(f462,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f461]) ).
thf(f463,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f462]) ).
thf(f464,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f463]) ).
thf(f465,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f465]) ).
thf(f467,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f466]) ).
thf(f468,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f468]) ).
thf(f470,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X7 @ X8 )
=> ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f471]) ).
thf(f473,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f474]) ).
thf(f476,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f475]) ).
thf(f477,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(or_proxy_clausification,[],[f477]) ).
thf(f479,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 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f478]) ).
thf(f480,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 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f479]) ).
thf(f481,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f480]) ).
thf(f482,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f481]) ).
thf(f483,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f482]) ).
thf(f484,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f483]) ).
thf(f485,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 @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f484]) ).
thf(f486,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f485]) ).
thf(f487,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f486]) ).
thf(f488,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 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f487]) ).
thf(f489,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f488]) ).
thf(f490,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f489]) ).
thf(f491,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 @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ~ ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f490]) ).
thf(f492,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ~ ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f491]) ).
thf(f493,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ~ ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f492]) ).
thf(f494,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $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 ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f493]) ).
thf(f495,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f494]) ).
thf(f496,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f495]) ).
thf(f497,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 @ X12 @ X13 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ X14 )
= $false ) ),
inference(beta-eta_normalization,[],[f496]) ).
thf(f498,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f497]) ).
thf(f499,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f498]) ).
thf(f500,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f499]) ).
thf(f501,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f500]) ).
thf(f502,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f501]) ).
thf(f503,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f502]) ).
thf(f504,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f503]) ).
thf(f505,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f504]) ).
thf(f506,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X1: mworld,X14: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f505]) ).
thf(f507,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f506]) ).
thf(f508,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X8: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f507]) ).
thf(f509,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X19: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ~ ( v10 @ X19 ) ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f508]) ).
thf(f510,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ~ ( v10 @ X19 ) )
= $true )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f509]) ).
thf(f511,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f510]) ).
thf(f1016,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f1017,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( v10 @ Y18 )
| ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1016]) ).
thf(f1018,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1017]) ).
thf(f1019,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1018]) ).
thf(f1020,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( v10 @ Y17 )
| ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1019]) ).
thf(f1021,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1020]) ).
thf(f1022,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1021]) ).
thf(f1023,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( v10 @ Y16 )
| ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1022]) ).
thf(f1024,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1023]) ).
thf(f1025,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1024]) ).
thf(f1026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v10 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1025]) ).
thf(f1027,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1026]) ).
thf(f1028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1027]) ).
thf(f1029,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v10 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1028]) ).
thf(f1030,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1029]) ).
thf(f1031,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1030]) ).
thf(f1032,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v10 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1031]) ).
thf(f1033,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1032]) ).
thf(f1034,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1033]) ).
thf(f1035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v10 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1034]) ).
thf(f1036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1035]) ).
thf(f1037,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1036]) ).
thf(f1038,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ~ ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v10 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1037]) ).
thf(f1039,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ~ ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f1038]) ).
thf(f1040,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ~ ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1039]) ).
thf(f1041,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ~ ( v21 @ X8 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f1040]) ).
thf(f1042,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1041]) ).
thf(f1043,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v10 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1042]) ).
thf(f1044,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f1043]) ).
thf(f1045,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f1044]) ).
thf(f1046,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v10 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1045]) ).
thf(f1047,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1046]) ).
thf(f1048,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1047]) ).
thf(f1049,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(or_proxy_clausification,[],[f1048]) ).
thf(f1050,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
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1049]) ).
thf(f1051,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v10 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(not_proxy_clausification,[],[f1050]) ).
thf(f1052,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1051]) ).
thf(f1053,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 @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1052]) ).
thf(f1054,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v10 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1053]) ).
thf(f1055,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 @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1054]) ).
thf(f1056,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
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ 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 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1055]) ).
thf(f1057,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v10 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1056]) ).
thf(f1058,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f1057]) ).
thf(f1059,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 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f1058]) ).
thf(f1060,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v10 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1059]) ).
thf(f1061,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1060]) ).
thf(f1062,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 @ X11 @ X12 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f1061]) ).
thf(f1063,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 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v10 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1062]) ).
thf(f1064,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 @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f1063]) ).
thf(f1065,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f1064]) ).
thf(f1066,plain,
! [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 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v10 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( v19 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1065]) ).
thf(f1067,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1066]) ).
thf(f1068,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f1067]) ).
thf(f1069,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v10 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X17 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f1068]) ).
thf(f1070,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f1069]) ).
thf(f1071,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1070]) ).
thf(f1072,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v10 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v8 @ Y3 ) ) ) ) ) ) ) ) )
@ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f1071]) ).
thf(f1073,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f1072]) ).
thf(f1074,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X6: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f1073]) ).
thf(f1075,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X16: mworld,X4: mworld,X7: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( v10 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v8 @ Y2 ) ) ) ) ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1074]) ).
thf(f1076,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( ( mrel @ X18 @ X19 )
=> ( ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f1075]) ).
thf(f1077,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X6: mworld,X1: mworld,X4: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( ( v10 @ X19 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f1076]) ).
thf(f1078,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X1: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1077]) ).
thf(f1079,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v8 @ Y1 ) ) ) )
@ X20 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f1078]) ).
thf(f1080,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f1079]) ).
thf(f1081,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X19: mworld,X8: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f1080]) ).
thf(f1082,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X1: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( v8 @ Y0 ) )
@ X21 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1081]) ).
thf(f1083,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X6: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( ( mrel @ X20 @ X21 )
=> ( v8 @ X21 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1082]) ).
thf(f1084,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X9: mworld,X14: mworld,X8: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1083]) ).
thf(f1508,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v14 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f1509,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ~ ( v14 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1508]) ).
thf(f1510,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1509]) ).
thf(f1511,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1510]) ).
thf(f1512,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ~ ( v14 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1511]) ).
thf(f1513,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1512]) ).
thf(f1514,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1513]) ).
thf(f1515,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ~ ( v14 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1514]) ).
thf(f1516,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1515]) ).
thf(f1517,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1516]) ).
thf(f1518,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ~ ( v14 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1517]) ).
thf(f1519,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X3 @ X4 )
=> ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1518]) ).
thf(f1520,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1519]) ).
thf(f1521,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f1520]) ).
thf(f1522,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ~ ( v14 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1521]) ).
thf(f1523,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1522]) ).
thf(f1524,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1523]) ).
thf(f1525,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v14 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1524]) ).
thf(f1526,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f1525]) ).
thf(f1527,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1526]) ).
thf(f1528,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v14 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1527]) ).
thf(f1529,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f1528]) ).
thf(f1530,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1529]) ).
thf(f1531,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v14 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1530]) ).
thf(f1532,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1531]) ).
thf(f1533,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f1532]) ).
thf(f1534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v14 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1533]) ).
thf(f1535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1534]) ).
thf(f1536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1535]) ).
thf(f1537,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f1536]) ).
thf(f1538,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v14 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1537]) ).
thf(f1539,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f1538]) ).
thf(f1540,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1539]) ).
thf(f1541,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v14 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1540]) ).
thf(f1542,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1541]) ).
thf(f1543,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 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f1542]) ).
thf(f1544,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 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v14 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1543]) ).
thf(f1545,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f1544]) ).
thf(f1546,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] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f1545]) ).
thf(f1547,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 @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v14 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f1546]) ).
thf(f1548,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f1547]) ).
thf(f1549,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 @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f1548]) ).
thf(f1550,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 @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v14 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1549]) ).
thf(f1551,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f1550]) ).
thf(f1552,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1551]) ).
thf(f1553,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ~ ( v14 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f1552]) ).
thf(f1554,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
= ( v20 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( ~ ( v14 @ X15 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1553]) ).
thf(f1555,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v14 @ X15 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1554]) ).
thf(f1556,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 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( ~ ( v14 @ X15 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f1555]) ).
thf(f1557,plain,
! [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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ~ ( v14 @ X15 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f1556]) ).
thf(f1558,plain,
! [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
= ( v20 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[],[f1557]) ).
thf(f1559,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f1558]) ).
thf(f1560,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1559]) ).
thf(f1561,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f1560]) ).
thf(f1562,plain,
! [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
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f1561]) ).
thf(f1563,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f1562]) ).
thf(f1564,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) )
@ X18 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f1563]) ).
thf(f1565,plain,
! [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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f1564]) ).
thf(f1566,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X18: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1565]) ).
thf(f1567,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X4: mworld,X7: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1566]) ).
thf(f1568,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X19: mworld,X6: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f1567]) ).
thf(f1569,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X18: mworld,X19: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1568]) ).
thf(f1570,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) )
@ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(pi_proxy_clausification,[],[f1569]) ).
thf(f1571,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X18: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f1570]) ).
thf(f1572,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(imp_proxy_clausification,[],[f1571]) ).
thf(f1573,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X18: mworld,X4: mworld,X19: mworld,X14: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) )
@ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f1572]) ).
thf(f1574,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,X19: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ~ ( v8 @ X21 ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f1573]) ).
thf(f1575,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X16: mworld,X4: mworld,X7: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ~ ( v8 @ X21 ) )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(imp_proxy_clausification,[],[f1574]) ).
thf(f1576,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X18: mworld,X4: mworld,X16: mworld,X6: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f1575]) ).
thf(f2404,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ mactual @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) )
& ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f2405,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) )
& ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2404]) ).
thf(f2411,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) )
& ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f2405]) ).
thf(f2412,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f2411]) ).
thf(f2413,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2412]) ).
thf(f2414,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2413]) ).
thf(f2420,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) )
& ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2414]) ).
thf(f2421,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2420]) ).
thf(f2422,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2421]) ).
thf(f2423,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2422]) ).
thf(f2429,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) )
& ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2423]) ).
thf(f2430,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2429]) ).
thf(f2431,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2430]) ).
thf(f2432,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2431]) ).
thf(f2438,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) )
& ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2432]) ).
thf(f2439,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2438]) ).
thf(f2440,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2439]) ).
thf(f2441,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f2440]) ).
thf(f2442,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2440]) ).
thf(f2443,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2442]) ).
thf(f2450,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) )
@ ( sK6 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2443]) ).
thf(f2451,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( v24 @ ( sK6 @ X4 ) )
& ( mrel @ X4 @ ( sK6 @ X4 ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2450]) ).
thf(f2453,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2451]) ).
thf(f2454,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) )
& ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( $true
& ( mrel @ Y22 @ Y23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2441]) ).
thf(f2455,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] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2454]) ).
thf(f2456,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2455]) ).
thf(f2457,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2456]) ).
thf(f2470,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) )
& ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( $true
& ( mrel @ Y21 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2457]) ).
thf(f2471,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2470]) ).
thf(f2472,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2471]) ).
thf(f2473,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f2472]) ).
thf(f2486,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) )
& ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( $true
& ( mrel @ Y20 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2473]) ).
thf(f2487,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X6 @ X7 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2486]) ).
thf(f2488,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2487]) ).
thf(f2489,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2488]) ).
thf(f2490,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f2488]) ).
thf(f2491,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f2490]) ).
thf(f2492,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f2490]) ).
thf(f2493,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) )
@ ( sK11 @ X7 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2492]) ).
thf(f2494,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ~ ( v21 @ ( sK11 @ X7 ) )
& ( mrel @ X7 @ ( sK11 @ X7 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2493]) ).
thf(f2496,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v21 @ ( sK11 @ X7 ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f2494]) ).
thf(f2497,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f2496]) ).
thf(f2498,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) )
@ ( sK12 @ X7 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f2491]) ).
thf(f2499,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( v21 @ ( sK12 @ X7 ) )
& ( mrel @ X7 @ ( sK12 @ X7 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2498]) ).
thf(f2501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f2499]) ).
thf(f2502,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) )
& ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( $true
& ( mrel @ Y19 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2489]) ).
thf(f2503,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X8 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2502]) ).
thf(f2504,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X8 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f2503]) ).
thf(f2505,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(and_proxy_clausification,[],[f2504]) ).
thf(f2511,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) )
& ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2505]) ).
thf(f2512,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X9 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2511]) ).
thf(f2513,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X9 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2512]) ).
thf(f2514,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f2513]) ).
thf(f2520,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) )
& ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2514]) ).
thf(f2521,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X10 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2520]) ).
thf(f2522,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X10 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2521]) ).
thf(f2523,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(and_proxy_clausification,[],[f2522]) ).
thf(f2529,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) )
& ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2523]) ).
thf(f2530,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X11 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2529]) ).
thf(f2531,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X11 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2530]) ).
thf(f2532,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2531]) ).
thf(f2538,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) )
& ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2532]) ).
thf(f2539,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2538]) ).
thf(f2540,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2539]) ).
thf(f2541,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f2540]) ).
thf(f2554,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) )
& ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( $true
& ( mrel @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2541]) ).
thf(f2555,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f2554]) ).
thf(f2556,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2555]) ).
thf(f2557,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2556]) ).
thf(f2558,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2556]) ).
thf(f2559,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(and_proxy_clausification,[],[f2558]) ).
thf(f2560,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2558]) ).
thf(f2561,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) )
@ ( sK19 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(sigma_proxy_clausification,[],[f2560]) ).
thf(f2562,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v15 @ ( sK19 @ X13 ) )
& ( mrel @ X13 @ ( sK19 @ X13 ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f2561]) ).
thf(f2564,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 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ~ ( v15 @ ( sK19 @ X13 ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2562]) ).
thf(f2565,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(not_proxy_clausification,[],[f2564]) ).
thf(f2566,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) )
@ ( sK20 @ X13 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2559]) ).
thf(f2567,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( v15 @ ( sK20 @ X13 ) )
& ( mrel @ X13 @ ( sK20 @ X13 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2566]) ).
thf(f2569,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2567]) ).
thf(f2570,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 @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) )
& ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( $true
& ( mrel @ Y13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2557]) ).
thf(f2571,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2570]) ).
thf(f2572,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2571]) ).
thf(f2573,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 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2572]) ).
thf(f2574,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(and_proxy_clausification,[],[f2572]) ).
thf(f2575,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(and_proxy_clausification,[],[f2574]) ).
thf(f2582,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) )
@ ( sK22 @ X14 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f2575]) ).
thf(f2583,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( v14 @ ( sK22 @ X14 ) )
& ( mrel @ X14 @ ( sK22 @ X14 ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f2582]) ).
thf(f2585,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(and_proxy_clausification,[],[f2583]) ).
thf(f2586,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) )
& ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( $true
& ( mrel @ Y12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2573]) ).
thf(f2587,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 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2586]) ).
thf(f2588,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f2587]) ).
thf(f2589,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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2588]) ).
thf(f2590,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 @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f2588]) ).
thf(f2592,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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(and_proxy_clausification,[],[f2590]) ).
thf(f2593,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) )
@ ( sK23 @ X15 ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f2592]) ).
thf(f2594,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ~ ( v13 @ ( sK23 @ X15 ) )
& ( mrel @ X15 @ ( sK23 @ X15 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2593]) ).
thf(f2596,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 @ X12 @ X13 ) )
| ( $true
= ( ~ ( v13 @ ( sK23 @ X15 ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(and_proxy_clausification,[],[f2594]) ).
thf(f2597,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f2596]) ).
thf(f2602,plain,
! [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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) )
& ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( $true
& ( mrel @ Y11 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f2589]) ).
thf(f2603,plain,
! [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
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X16 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2602]) ).
thf(f2604,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X16 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(imp_proxy_clausification,[],[f2603]) ).
thf(f2605,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(and_proxy_clausification,[],[f2604]) ).
thf(f2611,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) )
& ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2605]) ).
thf(f2612,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X17 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2611]) ).
thf(f2613,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X17 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
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,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2613]) ).
thf(f2620,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) )
& ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2614]) ).
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,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X18 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2620]) ).
thf(f2622,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X18 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2621]) ).
thf(f2623,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X9: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(and_proxy_clausification,[],[f2622]) ).
thf(f2629,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X19: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) )
& ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2623]) ).
thf(f2630,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X1: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ( mrel @ X18 @ X19 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X19 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f2629]) ).
thf(f2631,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X7: mworld,X16: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ X19 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2630]) ).
thf(f2632,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f2631]) ).
thf(f2638,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X18: mworld,X7: mworld,X19: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) )
& ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X20 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(pi_proxy_clausification,[],[f2632]) ).
thf(f2639,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2638]) ).
thf(f2640,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( ?? @ mworld
@ ^ [Y4: mworld] :
( $true
& ( mrel @ Y3 @ Y4 ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( ?? @ mworld
@ ^ [Y5: mworld] :
( $true
& ( mrel @ Y4 @ Y5 ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( ?? @ mworld
@ ^ [Y6: mworld] :
( $true
& ( mrel @ Y5 @ Y6 ) ) )
& ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( $true
& ( mrel @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f2639]) ).
thf(f2642,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X14: mworld,X4: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(and_proxy_clausification,[],[f2640]) ).
thf(f2643,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X4: mworld,X7: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(and_proxy_clausification,[],[f2642]) ).
thf(f2644,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f2642]) ).
thf(f2645,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X19: mworld,X18: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) )
@ ( sK29 @ X20 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(sigma_proxy_clausification,[],[f2644]) ).
thf(f2646,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ~ ( v8 @ ( sK29 @ X20 ) )
& ( mrel @ X20 @ ( sK29 @ X20 ) ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2645]) ).
thf(f2648,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( ( ~ ( v8 @ ( sK29 @ X20 ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f2646]) ).
thf(f2649,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(not_proxy_clausification,[],[f2648]) ).
thf(f2650,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) )
@ ( sK30 @ X20 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(sigma_proxy_clausification,[],[f2643]) ).
thf(f2651,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,X1: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ( v8 @ ( sK30 @ X20 ) )
& ( mrel @ X20 @ ( sK30 @ X20 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2650]) ).
thf(f2653,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f2651]) ).
thf(f3310,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f3311,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v8 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f3310]) ).
thf(f3312,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3311]) ).
thf(f3313,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3312]) ).
thf(f3314,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v8 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3313]) ).
thf(f3315,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3314]) ).
thf(f3316,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3315]) ).
thf(f3317,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v8 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3316]) ).
thf(f3318,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3317]) ).
thf(f3319,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3318]) ).
thf(f3320,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ~ ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v8 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3319]) ).
thf(f3321,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ X3 @ X4 )
=> ( ~ ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3320]) ).
thf(f3322,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ~ ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3321]) ).
thf(f3323,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f3322]) ).
thf(f3324,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( v25 @ X4 ) ) ) ),
inference(pi_proxy_clausification,[],[f3323]) ).
thf(f3325,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v8 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( $false
= ( v25 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f3324]) ).
thf(f3326,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3325]) ).
thf(f3327,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3326]) ).
thf(f3328,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f3327]) ).
thf(f3329,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f3328]) ).
thf(f3330,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v8 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3329]) ).
thf(f3331,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3330]) ).
thf(f3332,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3331]) ).
thf(f3333,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v8 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3332]) ).
thf(f3334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ 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 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3333]) ).
thf(f3335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f3334]) ).
thf(f3336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v8 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3335]) ).
thf(f3337,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f3336]) ).
thf(f3338,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f3337]) ).
thf(f3339,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v8 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f3338]) ).
thf(f3340,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3339]) ).
thf(f3341,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3340]) ).
thf(f3342,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v8 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f3341]) ).
thf(f3343,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X9 @ X10 )
=> ( ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3342]) ).
thf(f3344,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3343]) ).
thf(f3345,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(or_proxy_clausification,[],[f3344]) ).
thf(f3346,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 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v8 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f3345]) ).
thf(f3347,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
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3346]) ).
thf(f3348,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
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3347]) ).
thf(f3349,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 @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f3348]) ).
thf(f3350,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3349]) ).
thf(f3351,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3350]) ).
thf(f3352,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 @ X2 @ X3 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v8 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3351]) ).
thf(f3353,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 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f3352]) ).
thf(f3354,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f3353]) ).
thf(f3355,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 @ X8 @ X9 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f3354]) ).
thf(f3356,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f3355]) ).
thf(f3357,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3356]) ).
thf(f3358,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
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v8 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f3357]) ).
thf(f3359,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] :
( ( ( v19 @ X10 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3358]) ).
thf(f3360,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f3359]) ).
thf(f3361,plain,
! [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 @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v8 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f3360]) ).
thf(f3362,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f3361]) ).
thf(f3363,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3362]) ).
thf(f3364,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v8 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3363]) ).
thf(f3365,plain,
! [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 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3364]) ).
thf(f3366,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3365]) ).
thf(f3367,plain,
! [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 @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v8 @ Y3 ) ) ) ) ) ) ) )
@ X18 ) ) ),
inference(pi_proxy_clausification,[],[f3366]) ).
thf(f3368,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v19 @ X10 )
= $true ) ),
inference(beta-eta_normalization,[],[f3367]) ).
thf(f3369,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) ) ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f3368]) ).
thf(f3370,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v8 @ Y2 ) ) ) ) ) )
@ X19 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v19 @ X10 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3369]) ).
thf(f3371,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f3370]) ).
thf(f3372,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X19: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v19 @ X10 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f3371]) ).
thf(f3373,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X19: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v8 @ Y1 ) ) ) )
@ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f3372]) ).
thf(f3374,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v19 @ X10 )
= $true ) ),
inference(beta-eta_normalization,[],[f3373]) ).
thf(f3375,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X6: mworld,X18: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v19 @ X10 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3374]) ).
thf(f3376,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X6: mworld,X7: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ~ ( v8 @ Y0 ) )
@ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3375]) ).
thf(f3377,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X8: mworld,X6: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ~ ( v8 @ X21 ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(beta-eta_normalization,[],[f3376]) ).
thf(f3378,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( ~ ( v8 @ X21 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f3377]) ).
thf(f3379,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X1: mworld,X7: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(not_proxy_clausification,[],[f3378]) ).
thf(f4008,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f4009,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ~ ( v19 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f4008]) ).
thf(f4010,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f4009]) ).
thf(f4011,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4010]) ).
thf(f4012,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v19 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4011]) ).
thf(f4013,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4012]) ).
thf(f4014,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4013]) ).
thf(f4015,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v19 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4014]) ).
thf(f4016,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4015]) ).
thf(f4017,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4016]) ).
thf(f4018,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v19 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4017]) ).
thf(f4019,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4018]) ).
thf(f4020,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4019]) ).
thf(f4021,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v19 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4020]) ).
thf(f4022,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4021]) ).
thf(f4023,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4022]) ).
thf(f4024,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f4023]) ).
thf(f4025,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f4024]) ).
thf(f4026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v19 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4025]) ).
thf(f4027,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4026]) ).
thf(f4028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f4027]) ).
thf(f4029,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v19 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f4028]) ).
thf(f4030,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f4029]) ).
thf(f4031,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4030]) ).
thf(f4032,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v19 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4031]) ).
thf(f4033,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f4032]) ).
thf(f4034,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4033]) ).
thf(f4035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v19 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4034]) ).
thf(f4036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4035]) ).
thf(f4037,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4036]) ).
thf(f4038,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ~ ( v19 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f4037]) ).
thf(f4039,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f4038]) ).
thf(f4040,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ~ ( v19 @ X10 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f4039]) ).
thf(f4041,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ~ ( v19 @ X10 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f4040]) ).
thf(f4042,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f4041]) ).
thf(f4043,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4042]) ).
thf(f4044,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4043]) ).
thf(f4045,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 @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f4044]) ).
thf(f4046,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 @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f4045]) ).
thf(f4047,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
= ( v24 @ X5 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f4046]) ).
thf(f4048,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f4047]) ).
thf(f4049,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4048]) ).
thf(f4050,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f4049]) ).
thf(f4051,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 @ X10 @ X11 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f4050]) ).
thf(f4052,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4051]) ).
thf(f4053,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f4052]) ).
thf(f4054,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4053]) ).
thf(f4055,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $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 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f4054]) ).
thf(f4056,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f4055]) ).
thf(f4057,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f4056]) ).
thf(f4058,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 @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $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 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f4057]) ).
thf(f4059,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v10 @ Y3 ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f4058]) ).
thf(f4060,plain,
! [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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f4059]) ).
thf(f4061,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4060]) ).
thf(f4062,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v10 @ Y2 ) ) ) ) ) )
@ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4061]) ).
thf(f4063,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f4062]) ).
thf(f4064,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f4063]) ).
thf(f4065,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v10 @ Y1 ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f4064]) ).
thf(f4066,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4065]) ).
thf(f4067,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f4066]) ).
thf(f4068,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ~ ( v10 @ Y0 ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f4067]) ).
thf(f4069,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X1: mworld,X14: mworld,X4: mworld,X6: mworld,X16: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ~ ( v10 @ X19 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(beta-eta_normalization,[],[f4068]) ).
thf(f4070,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X1: mworld,X9: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ~ ( v10 @ X19 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f4069]) ).
thf(f4071,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X18: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(not_proxy_clausification,[],[f4070]) ).
thf(f4072,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v13 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f4073,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v25 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v24 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( v13 @ Y15 )
| ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f4072]) ).
thf(f4074,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f4073]) ).
thf(f4075,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f4074]) ).
thf(f4076,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v25 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v24 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( v13 @ Y14 )
| ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4075]) ).
thf(f4077,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4076]) ).
thf(f4078,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4077]) ).
thf(f4079,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v25 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v24 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v13 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4078]) ).
thf(f4080,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4079]) ).
thf(f4081,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4080]) ).
thf(f4082,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( v25 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v24 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v13 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4081]) ).
thf(f4083,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4082]) ).
thf(f4084,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( v25 @ X4 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4083]) ).
thf(f4085,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f4084]) ).
thf(f4086,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ~ ( v24 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v13 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4085]) ).
thf(f4087,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( ( mrel @ X4 @ X5 )
=> ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4086]) ).
thf(f4088,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v24 @ X5 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4087]) ).
thf(f4089,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( ~ ( v24 @ X5 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f4088]) ).
thf(f4090,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ~ ( v24 @ X5 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4089]) ).
thf(f4091,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v13 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f4090]) ).
thf(f4092,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $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 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4091]) ).
thf(f4093,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v13 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4092]) ).
thf(f4094,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v13 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4093]) ).
thf(f4095,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4094]) ).
thf(f4096,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ 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 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4095]) ).
thf(f4097,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v13 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4096]) ).
thf(f4098,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4097]) ).
thf(f4099,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4098]) ).
thf(f4100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v13 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4099]) ).
thf(f4101,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4100]) ).
thf(f4102,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f4101]) ).
thf(f4103,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v13 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f4102]) ).
thf(f4104,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4103]) ).
thf(f4105,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f4104]) ).
thf(f4106,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v13 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4105]) ).
thf(f4107,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f4106]) ).
thf(f4108,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 @ X9 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4107]) ).
thf(f4109,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 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v13 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4108]) ).
thf(f4110,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 @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f4109]) ).
thf(f4111,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] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f4110]) ).
thf(f4112,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v13 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4111]) ).
thf(f4113,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 @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4112]) ).
thf(f4114,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
= ( v24 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f4113]) ).
thf(f4115,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] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v13 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f4114]) ).
thf(f4116,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
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4115]) ).
thf(f4117,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] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4116]) ).
thf(f4118,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] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v13 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v12 @ Y2 ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4117]) ).
thf(f4119,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f4118]) ).
thf(f4120,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
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f4119]) ).
thf(f4121,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( v13 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v12 @ Y1 ) ) ) ) )
@ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4120]) ).
thf(f4122,plain,
! [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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ( mrel @ X15 @ X16 )
=> ( ( v13 @ X16 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f4121]) ).
thf(f4123,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( v13 @ X16 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4122]) ).
thf(f4124,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f4123]) ).
thf(f4125,plain,
! [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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ~ ( v12 @ Y0 ) )
@ X17 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4124]) ).
thf(f4126,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ~ ( v12 @ X17 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f4125]) ).
thf(f4127,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( ~ ( v12 @ X17 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f4126]) ).
thf(f4128,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(not_proxy_clausification,[],[f4127]) ).
thf(f4295,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f4296,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v21 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ~ ( v20 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( v15 @ Y13 )
| ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v12 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f4295]) ).
thf(f4297,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f4296]) ).
thf(f4298,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f4297]) ).
thf(f4299,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v21 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ~ ( v20 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( v15 @ Y12 )
| ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v12 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4298]) ).
thf(f4300,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4299]) ).
thf(f4301,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ 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 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4300]) ).
thf(f4302,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v21 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ~ ( v20 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( v15 @ Y11 )
| ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v12 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4301]) ).
thf(f4303,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f4302]) ).
thf(f4304,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f4303]) ).
thf(f4305,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v21 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ~ ( v20 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( v15 @ Y10 )
| ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f4304]) ).
thf(f4306,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f4305]) ).
thf(f4307,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4306]) ).
thf(f4308,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v21 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ~ ( v20 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( v15 @ Y9 )
| ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v12 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4307]) ).
thf(f4309,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4308]) ).
thf(f4310,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f4309]) ).
thf(f4311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v21 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ~ ( v20 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( v15 @ Y8 )
| ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v12 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4310]) ).
thf(f4312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4311]) ).
thf(f4313,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f4312]) ).
thf(f4314,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v21 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ~ ( v20 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( v15 @ Y7 )
| ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v12 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4313]) ).
thf(f4315,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f4314]) ).
thf(f4316,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4315]) ).
thf(f4317,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( v21 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ~ ( v20 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( v15 @ Y6 )
| ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v12 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4316]) ).
thf(f4318,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X7 @ X8 )
=> ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f4317]) ).
thf(f4319,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( v21 @ X8 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4318]) ).
thf(f4320,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f4319]) ).
thf(f4321,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ~ ( v20 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( v15 @ Y5 )
| ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v12 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4320]) ).
thf(f4322,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ~ ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4321]) ).
thf(f4323,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ~ ( v20 @ X9 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f4322]) ).
thf(f4324,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ~ ( v20 @ X9 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(or_proxy_clausification,[],[f4323]) ).
thf(f4325,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f4324]) ).
thf(f4326,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 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( v15 @ Y4 )
| ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v12 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f4325]) ).
thf(f4327,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f4326]) ).
thf(f4328,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f4327]) ).
thf(f4329,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( v15 @ Y3 )
| ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v12 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f4328]) ).
thf(f4330,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f4329]) ).
thf(f4331,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f4330]) ).
thf(f4332,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 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( v15 @ Y2 )
| ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v12 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4331]) ).
thf(f4333,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 @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f4332]) ).
thf(f4334,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
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f4333]) ).
thf(f4335,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( v15 @ Y1 )
| ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v12 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f4334]) ).
thf(f4336,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v20 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f4335]) ).
thf(f4337,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 @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f4336]) ).
thf(f4338,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( v15 @ Y0 )
| ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v12 @ Y3 ) ) ) ) ) ) ) ) )
@ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f4337]) ).
thf(f4339,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 @ X7 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f4338]) ).
thf(f4340,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 @ X6 @ X7 ) )
| ( $true
= ( ( v15 @ X14 )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f4339]) ).
thf(f4341,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) ) ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(or_proxy_clausification,[],[f4340]) ).
thf(f4342,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v12 @ Y2 ) ) ) ) ) )
@ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(pi_proxy_clausification,[],[f4341]) ).
thf(f4343,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 @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f4342]) ).
thf(f4344,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f4343]) ).
thf(f4345,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v12 @ Y1 ) ) ) )
@ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4344]) ).
thf(f4346,plain,
! [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] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) ) ) )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f4345]) ).
thf(f4347,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f4346]) ).
thf(f4348,plain,
! [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 @ X2 @ X3 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v12 @ Y0 ) )
@ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(pi_proxy_clausification,[],[f4347]) ).
thf(f4349,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( v12 @ X17 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(beta-eta_normalization,[],[f4348]) ).
thf(f4350,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f4349]) ).
thf(f4587,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v24 @ ( sK6 @ X4 ) )
= $true ) ),
inference(forward_demodulation,[],[f2453,f209]) ).
thf(f4588,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4587]) ).
thf(f4589,plain,
! [X2: mworld,X1: mworld,X4: mworld] :
( ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4588,f209]) ).
thf(f4590,plain,
! [X2: mworld,X1: mworld,X4: mworld] :
( ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4589]) ).
thf(f4591,plain,
! [X1: mworld,X4: mworld] :
( ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4590,f209]) ).
thf(f4592,plain,
! [X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v24 @ ( sK6 @ X4 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4591]) ).
thf(f4593,plain,
! [X4: mworld] :
( ( ( v24 @ ( sK6 @ X4 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4592,f209]) ).
thf(f4594,plain,
! [X4: mworld] :
( ( v24 @ ( sK6 @ X4 ) )
= $true ),
inference(trivial_inequality_removal,[],[f4593]) ).
thf(f4689,definition,
( spl41_5
<=> ! [X14: mworld] :
( ( v15 @ X14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl41_5])],[avatar_definition]) ).
thf(f4690,plain,
( ! [X14: mworld] :
( ( v15 @ X14 )
= $false )
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f4689]) ).
thf(f4692,definition,
( spl41_6
<=> ! [X16: mworld] :
( ( v13 @ X16 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_6])],[avatar_definition]) ).
thf(f4693,plain,
( ! [X16: mworld] :
( ( v13 @ X16 )
= $true )
| ~ spl41_6 ),
inference(avatar_component_clause,[],[f4692]) ).
thf(f4695,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f2497,f209]) ).
thf(f4696,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4695]) ).
thf(f4697,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4696,f209]) ).
thf(f4698,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4697]) ).
thf(f4699,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f4698,f209]) ).
thf(f4700,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4699]) ).
thf(f4701,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f4700,f209]) ).
thf(f4702,plain,
! [X2: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4701]) ).
thf(f4703,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4702,f209]) ).
thf(f4704,plain,
! [X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4703]) ).
thf(f4705,plain,
! [X6: mworld,X7: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4704,f209]) ).
thf(f4706,plain,
! [X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v21 @ ( sK11 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4705]) ).
thf(f4707,plain,
! [X7: mworld] :
( ( $false
= ( v21 @ ( sK11 @ X7 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4706,f209]) ).
thf(f4708,plain,
! [X7: mworld] :
( $false
= ( v21 @ ( sK11 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4707]) ).
thf(f4711,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f2501,f209]) ).
thf(f4712,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4711]) ).
thf(f4713,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4712,f209]) ).
thf(f4714,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4713]) ).
thf(f4715,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X5: mworld] :
( ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4714,f209]) ).
thf(f4716,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4715]) ).
thf(f4717,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4716,f209]) ).
thf(f4718,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4717]) ).
thf(f4719,plain,
! [X1: mworld,X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) ) ),
inference(forward_demodulation,[],[f4718,f209]) ).
thf(f4720,plain,
! [X1: mworld,X6: mworld,X7: mworld] :
( ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4719]) ).
thf(f4721,plain,
! [X6: mworld,X7: mworld] :
( ( $false = $true )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f4720,f209]) ).
thf(f4722,plain,
! [X6: mworld,X7: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ ( sK12 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[],[f4721]) ).
thf(f4723,plain,
! [X7: mworld] :
( ( $true
= ( v21 @ ( sK12 @ X7 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4722,f209]) ).
thf(f4724,plain,
! [X7: mworld] :
( $true
= ( v21 @ ( sK12 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4723]) ).
thf(f4725,plain,
! [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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4128,f209]) ).
thf(f4726,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v12 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4725]) ).
thf(f4727,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false = $true )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4726,f209]) ).
thf(f4728,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4727]) ).
thf(f4729,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f4728,f209]) ).
thf(f4730,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4729]) ).
thf(f4731,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(forward_demodulation,[],[f4730,f209]) ).
thf(f4732,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4731]) ).
thf(f4733,plain,
! [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 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v12 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4732,f209]) ).
thf(f4734,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4733]) ).
thf(f4735,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false = $true )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4734,f209]) ).
thf(f4736,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4735]) ).
thf(f4737,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v12 @ X17 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f4736,f209]) ).
thf(f4738,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4737]) ).
thf(f4739,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v12 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f4738,f209]) ).
thf(f4740,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4739]) ).
thf(f4741,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4740,f209]) ).
thf(f4742,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4741]) ).
thf(f4743,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4742,f209]) ).
thf(f4744,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4743]) ).
thf(f4745,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f4744,f209]) ).
thf(f4746,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v12 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4745]) ).
thf(f4747,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4746,f209]) ).
thf(f4748,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4747]) ).
thf(f4749,plain,
! [X2: mworld,X3: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f4748,f209]) ).
thf(f4750,plain,
! [X2: mworld,X3: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4749]) ).
thf(f4751,plain,
! [X2: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( v12 @ X17 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4750,f209]) ).
thf(f4752,plain,
! [X2: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( v12 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4751]) ).
thf(f4753,plain,
! [X2: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v12 @ X17 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4752,f209]) ).
thf(f4754,plain,
! [X2: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v12 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4753]) ).
thf(f4755,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v13 @ X16 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v12 @ X17 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4754,f209]) ).
thf(f4756,plain,
! [X16: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X13: mworld] :
( ( ( v13 @ X16 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4755]) ).
thf(f4757,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( v13 @ X16 )
= $true )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v12 @ X17 ) ) ),
inference(forward_demodulation,[],[f4756,f209]) ).
thf(f4758,plain,
! [X16: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( v13 @ X16 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v12 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f4757]) ).
thf(f4760,definition,
( spl41_7
<=> ! [X5: mworld] :
( $false
= ( v24 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_7])],[avatar_definition]) ).
thf(f4761,plain,
( ! [X5: mworld] :
( $false
= ( v24 @ X5 ) )
| ~ spl41_7 ),
inference(avatar_component_clause,[],[f4760]) ).
thf(f4763,definition,
( spl41_8
<=> ! [X17: mworld] :
( $false
= ( v12 @ X17 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_8])],[avatar_definition]) ).
thf(f4764,plain,
( ! [X17: mworld] :
( $false
= ( v12 @ X17 ) )
| ~ spl41_8 ),
inference(avatar_component_clause,[],[f4763]) ).
thf(f4766,definition,
( spl41_9
<=> ! [X4: mworld] :
( ( v25 @ X4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_9])],[avatar_definition]) ).
thf(f4767,plain,
( ! [X4: mworld] :
( ( v25 @ X4 )
= $true )
| ~ spl41_9 ),
inference(avatar_component_clause,[],[f4766]) ).
thf(f4768,plain,
( spl41_7
| spl41_8
| spl41_6
| spl41_9 ),
inference(avatar_split_clause,[],[f4758,f4766,f4692,f4763,f4760]) ).
thf(f4795,plain,
! [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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4350,f209]) ).
thf(f4796,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4795]) ).
thf(f4797,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v20 @ X9 ) ) ),
inference(forward_demodulation,[],[f4796,f209]) ).
thf(f4798,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v12 @ X17 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4797]) ).
thf(f4799,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4798,f209]) ).
thf(f4800,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4799]) ).
thf(f4801,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4800,f209]) ).
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,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4801]) ).
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,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4802,f209]) ).
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,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4803]) ).
thf(f4805,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v12 @ X17 )
= $true ) ),
inference(forward_demodulation,[],[f4804,f209]) ).
thf(f4806,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4805]) ).
thf(f4807,plain,
! [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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f4806,f209]) ).
thf(f4808,plain,
! [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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4807]) ).
thf(f4809,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v12 @ X17 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4808,f209]) ).
thf(f4810,plain,
! [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 @ X14 @ X15 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v12 @ X17 )
= $true )
| ( $true
= ( v21 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4809]) ).
thf(f4811,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4810,f209]) ).
thf(f4812,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( v20 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4811]) ).
thf(f4813,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4812,f209]) ).
thf(f4814,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f4813]) ).
thf(f4815,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v12 @ X17 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4814,f209]) ).
thf(f4816,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4815]) ).
thf(f4817,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v12 @ X17 )
= $true ) ),
inference(forward_demodulation,[],[f4816,f209]) ).
thf(f4818,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $true
= ( v21 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4817]) ).
thf(f4819,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v12 @ X17 )
= $true ) ),
inference(forward_demodulation,[],[f4818,f209]) ).
thf(f4820,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v12 @ X17 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4819]) ).
thf(f4821,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v12 @ X17 )
= $true )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f4820,f209]) ).
thf(f4822,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4821]) ).
thf(f4823,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $false = $true )
| ( ( v12 @ X17 )
= $true )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(forward_demodulation,[],[f4822,f209]) ).
thf(f4824,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v12 @ X17 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4823]) ).
thf(f4825,plain,
! [X8: mworld,X6: mworld,X9: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false = $true )
| ( ( v15 @ X14 )
= $true ) ),
inference(forward_demodulation,[],[f4824,f209]) ).
thf(f4826,plain,
! [X8: mworld,X6: mworld,X9: mworld,X14: mworld,X17: mworld,X5: mworld] :
( ( ( v12 @ X17 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4825]) ).
thf(f4827,plain,
! [X8: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( $false = $true )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v20 @ X9 ) )
| ( ( v12 @ X17 )
= $true )
| ( $true
= ( v21 @ X8 ) ) ),
inference(forward_demodulation,[],[f4826,f209]) ).
thf(f4828,plain,
! [X8: mworld,X9: mworld,X14: mworld,X17: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( ( v12 @ X17 )
= $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( v20 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4827]) ).
thf(f4830,definition,
( spl41_10
<=> ! [X9: mworld] :
( $false
= ( v20 @ X9 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_10])],[avatar_definition]) ).
thf(f4831,plain,
( ! [X9: mworld] :
( $false
= ( v20 @ X9 ) )
| ~ spl41_10 ),
inference(avatar_component_clause,[],[f4830]) ).
thf(f4833,definition,
( spl41_11
<=> ! [X14: mworld] :
( ( v15 @ X14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_11])],[avatar_definition]) ).
thf(f4834,plain,
( ! [X14: mworld] :
( ( v15 @ X14 )
= $true )
| ~ spl41_11 ),
inference(avatar_component_clause,[],[f4833]) ).
thf(f4836,definition,
( spl41_12
<=> ! [X8: mworld] :
( $true
= ( v21 @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_12])],[avatar_definition]) ).
thf(f4837,plain,
( ! [X8: mworld] :
( $true
= ( v21 @ X8 ) )
| ~ spl41_12 ),
inference(avatar_component_clause,[],[f4836]) ).
thf(f4839,definition,
( spl41_13
<=> ! [X17: mworld] :
( ( v12 @ X17 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_13])],[avatar_definition]) ).
thf(f4840,plain,
( ! [X17: mworld] :
( ( v12 @ X17 )
= $true )
| ~ spl41_13 ),
inference(avatar_component_clause,[],[f4839]) ).
thf(f4841,plain,
( spl41_10
| spl41_11
| spl41_12
| spl41_13 ),
inference(avatar_split_clause,[],[f4828,f4839,f4836,f4833,f4830]) ).
thf(f4868,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 @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f2565,f209]) ).
thf(f4869,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 @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4868]) ).
thf(f4870,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
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f4869,f209]) ).
thf(f4871,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4870]) ).
thf(f4872,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4871,f209]) ).
thf(f4873,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4872]) ).
thf(f4874,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4873,f209]) ).
thf(f4875,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4874]) ).
thf(f4876,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4875,f209]) ).
thf(f4877,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4876]) ).
thf(f4878,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4877,f209]) ).
thf(f4879,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4878]) ).
thf(f4880,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4879,f209]) ).
thf(f4881,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4880]) ).
thf(f4882,plain,
! [X2: mworld,X3: mworld,X10: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4881,f209]) ).
thf(f4883,plain,
! [X2: mworld,X3: mworld,X10: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4882]) ).
thf(f4884,plain,
! [X2: mworld,X3: mworld,X10: mworld,X6: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4883,f209]) ).
thf(f4885,plain,
! [X2: mworld,X3: mworld,X10: mworld,X6: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4884]) ).
thf(f4886,plain,
! [X2: mworld,X3: mworld,X10: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4885,f209]) ).
thf(f4887,plain,
! [X2: mworld,X3: mworld,X10: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) ) ),
inference(trivial_inequality_removal,[],[f4886]) ).
thf(f4888,plain,
! [X2: mworld,X3: mworld,X10: mworld,X9: mworld,X13: mworld] :
( ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4887,f209]) ).
thf(f4889,plain,
! [X2: mworld,X3: mworld,X10: mworld,X9: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4888]) ).
thf(f4890,plain,
! [X10: mworld,X9: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v15 @ ( sK19 @ X13 ) ) ) ),
inference(forward_demodulation,[],[f4889,f209]) ).
thf(f4891,plain,
! [X10: mworld,X9: mworld,X13: mworld] :
( ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4890]) ).
thf(f4892,plain,
! [X13: mworld] :
( ( $false
= ( v15 @ ( sK19 @ X13 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4891,f209]) ).
thf(f4893,plain,
! [X13: mworld] :
( $false
= ( v15 @ ( sK19 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4892]) ).
thf(f4896,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] :
( ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f2569,f209]) ).
thf(f4897,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 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4896]) ).
thf(f4898,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f4897,f209]) ).
thf(f4899,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4898]) ).
thf(f4900,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4899,f209]) ).
thf(f4901,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 @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4900]) ).
thf(f4902,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4901,f209]) ).
thf(f4903,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4902]) ).
thf(f4904,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4903,f209]) ).
thf(f4905,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4904]) ).
thf(f4906,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true ) ),
inference(forward_demodulation,[],[f4905,f209]) ).
thf(f4907,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4906]) ).
thf(f4908,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4907,f209]) ).
thf(f4909,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4908]) ).
thf(f4910,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4909,f209]) ).
thf(f4911,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4910]) ).
thf(f4912,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f4911,f209]) ).
thf(f4913,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4912]) ).
thf(f4914,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4913,f209]) ).
thf(f4915,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4914]) ).
thf(f4916,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true ) ),
inference(forward_demodulation,[],[f4915,f209]) ).
thf(f4917,plain,
! [X10: mworld,X11: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ ( sK20 @ X13 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4916]) ).
thf(f4918,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4917,f209]) ).
thf(f4919,plain,
! [X11: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4918]) ).
thf(f4920,plain,
! [X13: mworld] :
( ( ( v15 @ ( sK20 @ X13 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4919,f209]) ).
thf(f4921,plain,
! [X13: mworld] :
( ( v15 @ ( sK20 @ X13 ) )
= $true ),
inference(trivial_inequality_removal,[],[f4920]) ).
thf(f4967,plain,
( ( $false = $true )
| ~ spl41_7 ),
inference(constrained_superposition,[],[f4594,f4761]) ).
thf(f4971,plain,
( $false
| ~ spl41_7 ),
inference(trivial_inequality_removal,[],[f4967]) ).
thf(f4972,plain,
~ spl41_7,
inference(avatar_contradiction_clause,[],[f4971]) ).
thf(f5018,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f2585,f209]) ).
thf(f5019,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5018]) ).
thf(f5020,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5019,f209]) ).
thf(f5021,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5020]) ).
thf(f5022,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 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5021,f209]) ).
thf(f5023,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5022]) ).
thf(f5024,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 @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5023,f209]) ).
thf(f5025,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 @ X10 @ X11 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5024]) ).
thf(f5026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5025,f209]) ).
thf(f5027,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5026]) ).
thf(f5028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f5027,f209]) ).
thf(f5029,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5028]) ).
thf(f5030,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5029,f209]) ).
thf(f5031,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5030]) ).
thf(f5032,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5031,f209]) ).
thf(f5033,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld] :
( ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5032]) ).
thf(f5034,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5033,f209]) ).
thf(f5035,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5034]) ).
thf(f5036,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5035,f209]) ).
thf(f5037,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5036]) ).
thf(f5038,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(forward_demodulation,[],[f5037,f209]) ).
thf(f5039,plain,
! [X2: mworld,X3: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5038]) ).
thf(f5040,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X14: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5039,f209]) ).
thf(f5041,plain,
! [X2: mworld,X3: mworld,X6: mworld,X7: mworld,X14: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5040]) ).
thf(f5042,plain,
! [X6: mworld,X7: mworld,X14: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(forward_demodulation,[],[f5041,f209]) ).
thf(f5043,plain,
! [X6: mworld,X7: mworld,X14: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5042]) ).
thf(f5044,plain,
! [X14: mworld] :
( ( $false = $true )
| ( ( v14 @ ( sK22 @ X14 ) )
= $true ) ),
inference(forward_demodulation,[],[f5043,f209]) ).
thf(f5045,plain,
! [X14: mworld] :
( ( v14 @ ( sK22 @ X14 ) )
= $true ),
inference(trivial_inequality_removal,[],[f5044]) ).
thf(f5046,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X1: mworld,X19: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f511,f209]) ).
thf(f5047,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X9: mworld,X16: mworld,X4: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f5046]) ).
thf(f5048,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5047,f209]) ).
thf(f5049,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X8: mworld,X16: mworld,X9: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5048]) ).
thf(f5050,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v10 @ X19 )
= $false ) ),
inference(forward_demodulation,[],[f5049,f209]) ).
thf(f5051,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5050]) ).
thf(f5052,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(forward_demodulation,[],[f5051,f209]) ).
thf(f5053,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5052]) ).
thf(f5054,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5053,f209]) ).
thf(f5055,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5054]) ).
thf(f5056,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5055,f209]) ).
thf(f5057,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5056]) ).
thf(f5058,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5057,f209]) ).
thf(f5059,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5058]) ).
thf(f5060,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X6: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ X14 )
= $false ) ),
inference(forward_demodulation,[],[f5059,f209]) ).
thf(f5061,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5060]) ).
thf(f5062,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X6: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f5061,f209]) ).
thf(f5063,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X9: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5062]) ).
thf(f5064,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X6: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5063,f209]) ).
thf(f5065,plain,
! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5064]) ).
thf(f5066,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X16: mworld,X7: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5065,f209]) ).
thf(f5067,plain,
! [X10: mworld,X11: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X6: mworld,X16: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ X14 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5066]) ).
thf(f5068,plain,
! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X19: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $false ) ),
inference(forward_demodulation,[],[f5067,f209]) ).
thf(f5069,plain,
! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X19: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5068]) ).
thf(f5070,plain,
! [X10: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X9: mworld,X16: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5069,f209]) ).
thf(f5071,plain,
! [X10: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X9: mworld,X14: mworld,X16: mworld,X15: mworld,X5: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5070]) ).
thf(f5072,plain,
! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X16: mworld,X14: mworld,X15: mworld,X5: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5071,f209]) ).
thf(f5073,plain,
! [X10: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X6: mworld,X15: mworld,X5: mworld] :
( ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5072]) ).
thf(f5074,plain,
! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X16: mworld,X15: mworld,X5: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f5073,f209]) ).
thf(f5075,plain,
! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X16: mworld,X14: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5074]) ).
thf(f5076,plain,
! [X10: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X9: mworld,X15: mworld,X5: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) ) ),
inference(forward_demodulation,[],[f5075,f209]) ).
thf(f5077,plain,
! [X10: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X14: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v15 @ X14 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5076]) ).
thf(f5078,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X16: mworld,X15: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5077,f4831]) ).
thf(f5079,plain,
( ! [X10: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X9: mworld,X15: mworld,X5: mworld] :
( ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5078]) ).
thf(f5080,plain,
( ! [X10: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v15 @ X14 )
= $false )
| ( $true
= ( v21 @ X8 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5079,f209]) ).
thf(f5081,plain,
( ! [X10: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X15: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5080]) ).
thf(f5082,plain,
( ! [X8: mworld,X19: mworld,X16: mworld,X14: mworld,X15: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( $false = $true ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5081,f209]) ).
thf(f5083,plain,
( ! [X8: mworld,X19: mworld,X16: mworld,X14: mworld,X15: mworld] :
( ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v21 @ X8 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5082]) ).
thf(f5084,plain,
( ! [X8: mworld,X19: mworld,X14: mworld] :
( ( $false = $true )
| ( $true
= ( v21 @ X8 ) )
| ( ( v15 @ X14 )
= $false )
| ( ( v10 @ X19 )
= $false ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5083,f209]) ).
thf(f5085,plain,
( ! [X8: mworld,X19: mworld,X14: mworld] :
( ( $true
= ( v21 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $false ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5084]) ).
thf(f5087,definition,
( spl41_16
<=> ! [X19: mworld] :
( ( v10 @ X19 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl41_16])],[avatar_definition]) ).
thf(f5088,plain,
( ! [X19: mworld] :
( ( v10 @ X19 )
= $false )
| ~ spl41_16 ),
inference(avatar_component_clause,[],[f5087]) ).
thf(f5089,plain,
( spl41_12
| spl41_16
| spl41_5
| ~ spl41_10 ),
inference(avatar_split_clause,[],[f5085,f4830,f4689,f5087,f4836]) ).
thf(f5090,plain,
( ( $false = $true )
| ~ spl41_5 ),
inference(constrained_superposition,[],[f4690,f4921]) ).
thf(f5095,plain,
( $false
| ~ spl41_5 ),
inference(trivial_inequality_removal,[],[f5090]) ).
thf(f5096,plain,
~ spl41_5,
inference(avatar_contradiction_clause,[],[f5095]) ).
thf(f5108,plain,
( ( $false = $true )
| ~ spl41_11 ),
inference(constrained_superposition,[],[f4834,f4893]) ).
thf(f5112,plain,
( $false
| ~ spl41_11 ),
inference(trivial_inequality_removal,[],[f5108]) ).
thf(f5113,plain,
~ spl41_11,
inference(avatar_contradiction_clause,[],[f5112]) ).
thf(f5115,plain,
( ( $false = $true )
| ~ spl41_12 ),
inference(constrained_superposition,[],[f4708,f4837]) ).
thf(f5118,plain,
( $false
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5115]) ).
thf(f5119,plain,
~ spl41_12,
inference(avatar_contradiction_clause,[],[f5118]) ).
thf(f5170,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f2597,f209]) ).
thf(f5171,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5170]) ).
thf(f5172,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f5171,f209]) ).
thf(f5173,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5172]) ).
thf(f5174,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f5173,f209]) ).
thf(f5175,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5174]) ).
thf(f5176,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 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5175,f209]) ).
thf(f5177,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 @ X4 @ X5 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5176]) ).
thf(f5178,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,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5177,f209]) ).
thf(f5179,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,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5178]) ).
thf(f5180,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5179,f209]) ).
thf(f5181,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5180]) ).
thf(f5182,plain,
! [X2: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f5181,f209]) ).
thf(f5183,plain,
! [X2: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5182]) ).
thf(f5184,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) ) ),
inference(forward_demodulation,[],[f5183,f209]) ).
thf(f5185,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5184]) ).
thf(f5186,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5185,f209]) ).
thf(f5187,plain,
! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5186]) ).
thf(f5188,plain,
! [X2: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f5187,f209]) ).
thf(f5189,plain,
! [X2: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v13 @ ( sK23 @ X15 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5188]) ).
thf(f5190,plain,
( ! [X2: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true ) )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5189,f4693]) ).
thf(f5191,plain,
( ! [X2: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5190]) ).
thf(f5192,plain,
( ! [X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5191,f209]) ).
thf(f5193,plain,
( ! [X1: mworld,X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5192]) ).
thf(f5194,plain,
( ! [X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5193,f209]) ).
thf(f5195,plain,
( ! [X8: mworld,X9: mworld,X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5194]) ).
thf(f5196,plain,
( ! [X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true ) )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5195,f209]) ).
thf(f5197,plain,
( ! [X14: mworld,X15: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5196]) ).
thf(f5198,plain,
( ! [X14: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5197,f209]) ).
thf(f5199,plain,
( ! [X14: mworld,X13: mworld] :
( $false
= ( mrel @ X13 @ X14 ) )
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5198]) ).
thf(f5200,plain,
( ( $false = $true )
| ~ spl41_6 ),
inference(forward_demodulation,[],[f5199,f209]) ).
thf(f5201,plain,
( $false
| ~ spl41_6 ),
inference(trivial_inequality_removal,[],[f5200]) ).
thf(f5202,plain,
~ spl41_6,
inference(avatar_contradiction_clause,[],[f5201]) ).
thf(f5245,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f2649,f209]) ).
thf(f5246,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X18: mworld,X4: mworld,X14: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5245]) ).
thf(f5247,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X7: mworld,X1: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5246,f209]) ).
thf(f5248,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5247]) ).
thf(f5249,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5248,f209]) ).
thf(f5250,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X9: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5249]) ).
thf(f5251,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X1: mworld,X16: mworld,X4: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f5250,f209]) ).
thf(f5252,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X8: mworld,X4: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5251]) ).
thf(f5253,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X1: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5252,f209]) ).
thf(f5254,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5253]) ).
thf(f5255,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X4: mworld,X7: mworld,X8: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5254,f209]) ).
thf(f5256,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5255]) ).
thf(f5257,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5256,f209]) ).
thf(f5258,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X1: mworld,X4: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5257]) ).
thf(f5259,plain,
! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5258,f209]) ).
thf(f5260,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5259]) ).
thf(f5261,plain,
! [X10: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f5260,f209]) ).
thf(f5262,plain,
! [X10: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5261]) ).
thf(f5263,plain,
! [X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5262,f209]) ).
thf(f5264,plain,
! [X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5263]) ).
thf(f5265,plain,
! [X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f5264,f209]) ).
thf(f5266,plain,
! [X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5265]) ).
thf(f5267,plain,
! [X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5266,f209]) ).
thf(f5268,plain,
! [X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5267]) ).
thf(f5269,plain,
! [X10: mworld,X18: mworld,X19: mworld,X6: mworld,X7: mworld,X9: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5268,f209]) ).
thf(f5270,plain,
! [X10: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5269]) ).
thf(f5271,plain,
! [X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5270,f209]) ).
thf(f5272,plain,
! [X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5271]) ).
thf(f5273,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5272,f209]) ).
thf(f5274,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5273]) ).
thf(f5275,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5274,f209]) ).
thf(f5276,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5275]) ).
thf(f5277,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5276,f209]) ).
thf(f5278,plain,
! [X18: mworld,X6: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5277]) ).
thf(f5279,plain,
! [X18: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false = $true )
| ( ( mrel @ X17 @ X18 )
= $false ) ),
inference(forward_demodulation,[],[f5278,f209]) ).
thf(f5280,plain,
! [X18: mworld,X14: mworld,X17: mworld,X15: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5279]) ).
thf(f5281,plain,
! [X14: mworld,X15: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5280,f209]) ).
thf(f5282,plain,
! [X14: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ ( sK29 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5281]) ).
thf(f5283,plain,
! [X20: mworld] :
( ( $false
= ( v8 @ ( sK29 @ X20 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5282,f209]) ).
thf(f5284,plain,
! [X20: mworld] :
( $false
= ( v8 @ ( sK29 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5283]) ).
thf(f5287,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X7: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f2653,f209]) ).
thf(f5288,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X9: mworld,X7: mworld,X8: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5287]) ).
thf(f5289,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X8: mworld,X9: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5288,f209]) ).
thf(f5290,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X6: mworld,X4: mworld,X7: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5289]) ).
thf(f5291,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X8: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5290,f209]) ).
thf(f5292,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X9: mworld,X14: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5291]) ).
thf(f5293,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5292,f209]) ).
thf(f5294,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5293]) ).
thf(f5295,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f5294,f209]) ).
thf(f5296,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5295]) ).
thf(f5297,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5296,f209]) ).
thf(f5298,plain,
! [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,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5297]) ).
thf(f5299,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5298,f209]) ).
thf(f5300,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5299]) ).
thf(f5301,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5300,f209]) ).
thf(f5302,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5301]) ).
thf(f5303,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5302,f209]) ).
thf(f5304,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5303]) ).
thf(f5305,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X8: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5304,f209]) ).
thf(f5306,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X8: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f5305]) ).
thf(f5307,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5306,f209]) ).
thf(f5308,plain,
! [X2: mworld,X3: mworld,X11: mworld,X1: mworld,X8: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5307]) ).
thf(f5309,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f5308,f209]) ).
thf(f5310,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5309]) ).
thf(f5311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f5310,f209]) ).
thf(f5312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5311]) ).
thf(f5313,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5312,f209]) ).
thf(f5314,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5313]) ).
thf(f5315,plain,
! [X3: mworld,X1: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5314,f209]) ).
thf(f5316,plain,
! [X3: mworld,X1: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X17: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5315]) ).
thf(f5317,plain,
! [X3: mworld,X1: mworld,X8: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f5316,f209]) ).
thf(f5318,plain,
! [X3: mworld,X1: mworld,X8: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X20: mworld] :
( ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5317]) ).
thf(f5319,plain,
! [X1: mworld,X8: mworld,X7: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5318,f209]) ).
thf(f5320,plain,
! [X1: mworld,X8: mworld,X7: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5319]) ).
thf(f5321,plain,
! [X1: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5320,f209]) ).
thf(f5322,plain,
! [X1: mworld,X16: mworld,X17: mworld,X20: mworld] :
( ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5321]) ).
thf(f5323,plain,
! [X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(forward_demodulation,[],[f5322,f209]) ).
thf(f5324,plain,
! [X16: mworld,X17: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v8 @ ( sK30 @ X20 ) ) ) ),
inference(trivial_inequality_removal,[],[f5323]) ).
thf(f5325,plain,
! [X20: mworld] :
( ( $true
= ( v8 @ ( sK30 @ X20 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5324,f209]) ).
thf(f5326,plain,
! [X20: mworld] :
( $true
= ( v8 @ ( sK30 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5325]) ).
thf(f5560,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X1: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f1084,f209]) ).
thf(f5561,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X7: mworld,X4: mworld,X6: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5560]) ).
thf(f5562,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X16: mworld,X14: mworld,X7: mworld,X19: mworld,X9: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5561,f209]) ).
thf(f5563,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X6: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5562]) ).
thf(f5564,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X19: mworld,X14: mworld,X1: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v21 @ X8 ) ) ),
inference(forward_demodulation,[],[f5563,f209]) ).
thf(f5565,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X9: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5564]) ).
thf(f5566,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X18: mworld,X7: mworld,X6: mworld,X4: mworld,X9: mworld,X14: mworld,X16: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5565,f209]) ).
thf(f5567,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X19: mworld,X7: mworld,X4: mworld,X8: mworld,X14: mworld,X17: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5566]) ).
thf(f5568,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v8 @ X21 )
= $true ) ),
inference(forward_demodulation,[],[f5567,f209]) ).
thf(f5569,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X8: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5568]) ).
thf(f5570,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X18: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(forward_demodulation,[],[f5569,f209]) ).
thf(f5571,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X8: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5570]) ).
thf(f5572,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X1: mworld,X14: mworld,X4: mworld,X6: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( v21 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true ) ),
inference(forward_demodulation,[],[f5571,f209]) ).
thf(f5573,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X1: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5572]) ).
thf(f5574,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v8 @ X21 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5573,f209]) ).
thf(f5575,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X7: mworld,X18: mworld,X4: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5574]) ).
thf(f5576,plain,
! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5575,f209]) ).
thf(f5577,plain,
! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X9: mworld,X7: mworld,X4: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5576]) ).
thf(f5578,plain,
! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X4: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( v21 @ X8 ) ) ),
inference(forward_demodulation,[],[f5577,f209]) ).
thf(f5579,plain,
! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X6: mworld,X4: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v8 @ X21 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5578]) ).
thf(f5580,plain,
( ! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5579,f5088]) ).
thf(f5581,plain,
( ! [X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5580]) ).
thf(f5582,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5581,f209]) ).
thf(f5583,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5582]) ).
thf(f5584,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false = $true ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5583,f209]) ).
thf(f5585,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5584]) ).
thf(f5586,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5585,f209]) ).
thf(f5587,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5586]) ).
thf(f5588,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5587,f209]) ).
thf(f5589,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X9: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v8 @ X21 )
= $true ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5588]) ).
thf(f5590,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5589,f209]) ).
thf(f5591,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v8 @ X21 )
= $true ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5590]) ).
thf(f5592,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false = $true )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5591,f209]) ).
thf(f5593,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5592]) ).
thf(f5594,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5593,f209]) ).
thf(f5595,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v21 @ X8 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5594]) ).
thf(f5596,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5595,f209]) ).
thf(f5597,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5596]) ).
thf(f5598,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( ( v8 @ X21 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5597,f209]) ).
thf(f5599,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v21 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v8 @ X21 )
= $true ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5598]) ).
thf(f5600,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X9: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5599,f209]) ).
thf(f5601,plain,
( ! [X21: mworld,X10: mworld,X8: mworld,X9: mworld] :
( ( ( v8 @ X21 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5600]) ).
thf(f5602,plain,
( ! [X21: mworld,X10: mworld,X8: mworld] :
( ( ( v8 @ X21 )
= $true )
| ( $false
= ( v21 @ X8 ) )
| ( $false = $true )
| ( $false
= ( v19 @ X10 ) ) )
| ~ spl41_16 ),
inference(forward_demodulation,[],[f5601,f209]) ).
thf(f5603,plain,
( ! [X21: mworld,X10: mworld,X8: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( ( v8 @ X21 )
= $true )
| ( $false
= ( v21 @ X8 ) ) )
| ~ spl41_16 ),
inference(trivial_inequality_removal,[],[f5602]) ).
thf(f5605,definition,
( spl41_21
<=> ! [X8: mworld] :
( $false
= ( v21 @ X8 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_21])],[avatar_definition]) ).
thf(f5606,plain,
( ! [X8: mworld] :
( $false
= ( v21 @ X8 ) )
| ~ spl41_21 ),
inference(avatar_component_clause,[],[f5605]) ).
thf(f5608,definition,
( spl41_22
<=> ! [X21: mworld] :
( ( v8 @ X21 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_22])],[avatar_definition]) ).
thf(f5609,plain,
( ! [X21: mworld] :
( ( v8 @ X21 )
= $true )
| ~ spl41_22 ),
inference(avatar_component_clause,[],[f5608]) ).
thf(f5611,definition,
( spl41_23
<=> ! [X10: mworld] :
( $false
= ( v19 @ X10 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_23])],[avatar_definition]) ).
thf(f5612,plain,
( ! [X10: mworld] :
( $false
= ( v19 @ X10 ) )
| ~ spl41_23 ),
inference(avatar_component_clause,[],[f5611]) ).
thf(f5613,plain,
( spl41_21
| spl41_22
| spl41_23
| ~ spl41_16 ),
inference(avatar_split_clause,[],[f5603,f5087,f5611,f5608,f5605]) ).
thf(f5614,plain,
( ( $false = $true )
| ~ spl41_21 ),
inference(constrained_superposition,[],[f5606,f4724]) ).
thf(f5620,plain,
( $false
| ~ spl41_21 ),
inference(trivial_inequality_removal,[],[f5614]) ).
thf(f5621,plain,
~ spl41_21,
inference(avatar_contradiction_clause,[],[f5620]) ).
thf(f5624,plain,
( ( $false = $true )
| ~ spl41_8
| ~ spl41_13 ),
inference(forward_demodulation,[],[f4840,f4764]) ).
thf(f5625,plain,
( $false
| ~ spl41_8
| ~ spl41_13 ),
inference(trivial_inequality_removal,[],[f5624]) ).
thf(f5626,plain,
( ~ spl41_8
| ~ spl41_13 ),
inference(avatar_contradiction_clause,[],[f5625]) ).
thf(f5627,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X16: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f4071,f209]) ).
thf(f5628,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X1: mworld,X14: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5627]) ).
thf(f5633,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X18: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5628,f209]) ).
thf(f5634,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5633]) ).
thf(f5639,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X19: mworld,X6: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5634,f209]) ).
thf(f5640,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X14: mworld,X16: mworld,X1: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5639]) ).
thf(f5645,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5640,f209]) ).
thf(f5646,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5645]) ).
thf(f5651,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X7: mworld,X16: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5646,f209]) ).
thf(f5652,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X18: mworld,X7: mworld,X4: mworld,X14: mworld,X16: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5651]) ).
thf(f5657,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5652,f209]) ).
thf(f5658,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5657]) ).
thf(f5663,plain,
! [X2: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5658,f209]) ).
thf(f5664,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X18: mworld,X4: mworld,X9: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5663]) ).
thf(f5669,plain,
! [X2: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X1: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5664,f209]) ).
thf(f5670,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X18: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5669]) ).
thf(f5675,plain,
! [X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X9: mworld,X16: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5670,f209]) ).
thf(f5676,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X6: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5675]) ).
thf(f5681,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5676,f209]) ).
thf(f5682,plain,
! [X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f5681]) ).
thf(f5687,plain,
! [X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X8: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(forward_demodulation,[],[f5682,f209]) ).
thf(f5688,plain,
! [X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X7: mworld,X14: mworld,X6: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5687]) ).
thf(f5693,plain,
! [X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X1: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5688,f209]) ).
thf(f5694,plain,
! [X10: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X14: mworld,X6: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5693]) ).
thf(f5701,plain,
! [X10: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5694,f209]) ).
thf(f5702,plain,
! [X10: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5701]) ).
thf(f5705,plain,
! [X10: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5702,f209]) ).
thf(f5706,plain,
! [X10: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v10 @ X19 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5705]) ).
thf(f5709,plain,
! [X10: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false = $true )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(forward_demodulation,[],[f5706,f209]) ).
thf(f5710,plain,
! [X10: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5709]) ).
thf(f5713,plain,
! [X10: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v19 @ X10 ) ) ),
inference(forward_demodulation,[],[f5710,f209]) ).
thf(f5714,plain,
! [X10: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v15 @ X14 )
= $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5713]) ).
thf(f5717,plain,
! [X10: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(forward_demodulation,[],[f5714,f209]) ).
thf(f5718,plain,
! [X10: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v19 @ X10 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5717]) ).
thf(f5721,plain,
! [X10: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v19 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(forward_demodulation,[],[f5718,f209]) ).
thf(f5722,plain,
! [X10: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5721]) ).
thf(f5725,plain,
! [X10: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false = $true )
| ( $false
= ( v19 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true ) ),
inference(forward_demodulation,[],[f5722,f209]) ).
thf(f5726,plain,
! [X10: mworld,X19: mworld,X14: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( v15 @ X14 )
= $true )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( v19 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5725]) ).
thf(f5729,plain,
( spl41_11
| spl41_16
| spl41_7
| spl41_23 ),
inference(avatar_split_clause,[],[f5726,f5611,f4760,f5087,f4833]) ).
thf(f5741,plain,
( ( $false = $true )
| ~ spl41_22 ),
inference(constrained_superposition,[],[f5284,f5609]) ).
thf(f5744,plain,
( $false
| ~ spl41_22 ),
inference(trivial_inequality_removal,[],[f5741]) ).
thf(f5745,plain,
~ spl41_22,
inference(avatar_contradiction_clause,[],[f5744]) ).
thf(f5748,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X6: mworld,X4: mworld,X1: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v19 @ X10 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(forward_demodulation,[],[f3379,f209]) ).
thf(f5749,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X18: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5748]) ).
thf(f5750,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X19: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f5749,f209]) ).
thf(f5751,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X6: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5750]) ).
thf(f5752,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X8: mworld,X6: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(forward_demodulation,[],[f5751,f209]) ).
thf(f5753,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f5752]) ).
thf(f5754,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v19 @ X10 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5753,f209]) ).
thf(f5755,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X1: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5754]) ).
thf(f5756,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X18: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5755,f209]) ).
thf(f5757,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X19: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v8 @ X21 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5756]) ).
thf(f5758,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X18: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5757,f209]) ).
thf(f5759,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v25 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5758]) ).
thf(f5760,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X8: mworld,X4: mworld,X9: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f5759,f209]) ).
thf(f5761,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v25 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5760]) ).
thf(f5762,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X16: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5761,f4767]) ).
thf(f5763,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X1: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5762]) ).
thf(f5764,plain,
( ! [X2: mworld,X21: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5763,f209]) ).
thf(f5765,plain,
( ! [X2: mworld,X21: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5764]) ).
thf(f5766,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X14: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5765,f209]) ).
thf(f5767,plain,
( ! [X21: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5766]) ).
thf(f5768,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X9: mworld,X14: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5767,f209]) ).
thf(f5769,plain,
( ! [X21: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X7: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5768]) ).
thf(f5770,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5769,f209]) ).
thf(f5771,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5770]) ).
thf(f5772,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5771,f209]) ).
thf(f5773,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5772]) ).
thf(f5774,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v19 @ X10 )
= $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5773,f209]) ).
thf(f5775,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v19 @ X10 )
= $true ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5774]) ).
thf(f5776,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5775,f209]) ).
thf(f5777,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v19 @ X10 )
= $true )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5776]) ).
thf(f5778,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v19 @ X10 )
= $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f5777,f209]) ).
thf(f5779,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( ( v19 @ X10 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f5778]) ).
thf(f5780,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5779,f5612]) ).
thf(f5781,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5780]) ).
thf(f5782,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false = $true ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5781,f209]) ).
thf(f5783,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X7: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5782]) ).
thf(f5784,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5783,f209]) ).
thf(f5785,plain,
( ! [X21: mworld,X10: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5784]) ).
thf(f5786,plain,
( ! [X21: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5785,f209]) ).
thf(f5787,plain,
( ! [X21: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5786]) ).
thf(f5788,plain,
( ! [X21: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5787,f209]) ).
thf(f5789,plain,
( ! [X21: mworld,X1: mworld,X8: mworld,X9: mworld,X5: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5788]) ).
thf(f5790,plain,
( ! [X21: mworld,X1: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false = $true ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5789,f209]) ).
thf(f5791,plain,
( ! [X21: mworld,X1: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5790]) ).
thf(f5792,plain,
( ! [X21: mworld,X5: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(forward_demodulation,[],[f5791,f209]) ).
thf(f5793,plain,
( ! [X21: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_9
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5792]) ).
thf(f5795,definition,
( spl41_25
<=> ! [X21: mworld] :
( $false
= ( v8 @ X21 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_25])],[avatar_definition]) ).
thf(f5796,plain,
( ! [X21: mworld] :
( $false
= ( v8 @ X21 ) )
| ~ spl41_25 ),
inference(avatar_component_clause,[],[f5795]) ).
thf(f5797,plain,
( spl41_7
| spl41_25
| ~ spl41_9
| ~ spl41_23 ),
inference(avatar_split_clause,[],[f5793,f5611,f4766,f5795,f4760]) ).
thf(f5798,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X18: mworld,X4: mworld,X19: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f1576,f209]) ).
thf(f5799,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5798]) ).
thf(f5804,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X6: mworld,X4: mworld,X16: mworld,X14: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5799,f209]) ).
thf(f5805,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X14: mworld,X1: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5804]) ).
thf(f5810,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f5805,f209]) ).
thf(f5811,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X4: mworld,X7: mworld,X14: mworld,X8: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5810]) ).
thf(f5816,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X6: mworld,X7: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(forward_demodulation,[],[f5811,f209]) ).
thf(f5817,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X19: mworld,X6: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X6 @ X7 ) ) ),
inference(trivial_inequality_removal,[],[f5816]) ).
thf(f5822,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v8 @ X21 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(forward_demodulation,[],[f5817,f209]) ).
thf(f5823,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X7: mworld,X8: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5822]) ).
thf(f5828,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X1: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5823,f209]) ).
thf(f5829,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X6: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5828]) ).
thf(f5834,plain,
! [X2: mworld,X21: mworld,X3: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5829,f209]) ).
thf(f5835,plain,
! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X18: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5834]) ).
thf(f5840,plain,
! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X8: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5835,f209]) ).
thf(f5841,plain,
! [X2: mworld,X21: mworld,X3: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X6: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $true
= ( v20 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5840]) ).
thf(f5846,plain,
! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X16: mworld,X8: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $true
= ( v20 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5841,f209]) ).
thf(f5847,plain,
! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X7: mworld,X16: mworld,X8: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v20 @ X9 ) )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5846]) ).
thf(f5852,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5847,f4831]) ).
thf(f5853,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X7: mworld,X8: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5852]) ).
thf(f5858,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5853,f209]) ).
thf(f5859,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5858]) ).
thf(f5864,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5859,f209]) ).
thf(f5865,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( $false
= ( v8 @ X21 ) )
| ( ( mrel @ X17 @ X18 )
= $false ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5864]) ).
thf(f5870,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X8: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X17 @ X18 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5865,f209]) ).
thf(f5871,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X6 @ X7 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5870]) ).
thf(f5876,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5871,f209]) ).
thf(f5877,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v8 @ X21 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5876]) ).
thf(f5882,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false = $true )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5877,f209]) ).
thf(f5883,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v8 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5882]) ).
thf(f5888,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5883,f209]) ).
thf(f5889,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5888]) ).
thf(f5896,plain,
( ! [X21: mworld,X18: mworld,X8: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5889,f209]) ).
thf(f5897,plain,
( ! [X21: mworld,X18: mworld,X8: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5896]) ).
thf(f5900,plain,
( ! [X21: mworld,X1: mworld,X18: mworld,X8: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ X21 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5897,f209]) ).
thf(f5901,plain,
( ! [X21: mworld,X18: mworld,X8: mworld,X1: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5900]) ).
thf(f5904,plain,
( ! [X21: mworld,X1: mworld,X8: mworld,X18: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v14 @ X15 ) )
| ( $false = $true )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5901,f209]) ).
thf(f5905,plain,
( ! [X21: mworld,X18: mworld,X8: mworld,X1: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5904]) ).
thf(f5908,plain,
( ! [X21: mworld,X1: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5905,f209]) ).
thf(f5909,plain,
( ! [X21: mworld,X1: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5908]) ).
thf(f5912,plain,
( ! [X21: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( $false
= ( v14 @ X15 ) )
| ( $false = $true )
| ( ( v25 @ X4 )
= $true ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5909,f209]) ).
thf(f5913,plain,
( ! [X21: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false
= ( v14 @ X15 ) )
| ( ( mrel @ X17 @ X18 )
= $false )
| ( ( v25 @ X4 )
= $true ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5912]) ).
thf(f5916,plain,
( ! [X21: mworld,X4: mworld,X15: mworld] :
( ( $false
= ( v8 @ X21 ) )
| ( $false = $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v14 @ X15 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5913,f209]) ).
thf(f5917,plain,
( ! [X21: mworld,X4: mworld,X15: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( v14 @ X15 ) )
| ( $false
= ( v8 @ X21 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5916]) ).
thf(f5923,definition,
( spl41_28
<=> ! [X15: mworld] :
( $false
= ( v14 @ X15 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_28])],[avatar_definition]) ).
thf(f5924,plain,
( ! [X15: mworld] :
( $false
= ( v14 @ X15 ) )
| ~ spl41_28 ),
inference(avatar_component_clause,[],[f5923]) ).
thf(f5925,plain,
( spl41_9
| spl41_28
| spl41_25
| ~ spl41_10 ),
inference(avatar_split_clause,[],[f5917,f4830,f5795,f5923,f4766]) ).
thf(f5928,plain,
( ( $false = $true )
| ~ spl41_25 ),
inference(constrained_superposition,[],[f5326,f5796]) ).
thf(f5931,plain,
( $false
| ~ spl41_25 ),
inference(trivial_inequality_removal,[],[f5928]) ).
thf(f5932,plain,
~ spl41_25,
inference(avatar_contradiction_clause,[],[f5931]) ).
thf(f5938,plain,
( ( $false = $true )
| ~ spl41_28 ),
inference(constrained_superposition,[],[f5045,f5924]) ).
thf(f5941,plain,
( $false
| ~ spl41_28 ),
inference(trivial_inequality_removal,[],[f5938]) ).
thf(f5942,plain,
~ spl41_28,
inference(avatar_contradiction_clause,[],[f5941]) ).
cnf(s4,plain,
( spl41_6
| spl41_7
| spl41_8
| spl41_9 ),
inference(sat_conversion,[],[f4768]) ).
cnf(s5,plain,
( spl41_10
| spl41_11
| spl41_12
| spl41_13 ),
inference(sat_conversion,[],[f4841]) ).
cnf(s8,plain,
~ spl41_7,
inference(sat_conversion,[],[f4972]) ).
cnf(s10,plain,
( spl41_5
| ~ spl41_10
| spl41_12
| spl41_16 ),
inference(sat_conversion,[],[f5089]) ).
cnf(s12,plain,
~ spl41_5,
inference(sat_conversion,[],[f5096]) ).
cnf(s15,plain,
~ spl41_11,
inference(sat_conversion,[],[f5113]) ).
cnf(s17,plain,
~ spl41_12,
inference(sat_conversion,[],[f5119]) ).
cnf(s19,plain,
~ spl41_6,
inference(sat_conversion,[],[f5202]) ).
cnf(s23,plain,
( ~ spl41_16
| spl41_21
| spl41_22
| spl41_23 ),
inference(sat_conversion,[],[f5613]) ).
cnf(s25,plain,
~ spl41_21,
inference(sat_conversion,[],[f5621]) ).
cnf(s26,plain,
( ~ spl41_8
| ~ spl41_13 ),
inference(sat_conversion,[],[f5626]) ).
cnf(s28,plain,
( spl41_7
| spl41_11
| spl41_16
| spl41_23 ),
inference(sat_conversion,[],[f5729]) ).
cnf(s32,plain,
~ spl41_22,
inference(sat_conversion,[],[f5745]) ).
cnf(s33,plain,
( spl41_7
| ~ spl41_9
| ~ spl41_23
| spl41_25 ),
inference(sat_conversion,[],[f5797]) ).
cnf(s36,plain,
( spl41_9
| ~ spl41_10
| spl41_25
| spl41_28 ),
inference(sat_conversion,[],[f5925]) ).
cnf(s38,plain,
~ spl41_25,
inference(sat_conversion,[],[f5932]) ).
cnf(s40,plain,
~ spl41_28,
inference(sat_conversion,[],[f5942]) ).
cnf(s41,plain,
( spl41_9
| ~ spl41_10 ),
inference(rat,[],[s36,s40,s38]) ).
cnf(s43,plain,
( spl41_7
| ~ spl41_9
| ~ spl41_23 ),
inference(rat,[],[s33,s38]) ).
cnf(s45,plain,
( ~ spl41_16
| spl41_23 ),
inference(rat,[],[s23,s32,s25]) ).
cnf(s48,plain,
( ~ spl41_10
| spl41_16 ),
inference(rat,[],[s10,s17,s12]) ).
cnf(s50,plain,
( spl41_10
| spl41_13 ),
inference(rat,[],[s5,s17,s15]) ).
cnf(s51,plain,
( spl41_8
| spl41_9 ),
inference(rat,[],[s4,s8,s19]) ).
cnf(s54,plain,
~ spl41_10,
inference(rat,[],[s45,s43,s48,s41,s8]) ).
cnf(s56,plain,
spl41_13,
inference(rat,[],[s50,s54]) ).
cnf(s58,plain,
~ spl41_8,
inference(rat,[],[s26,s56]) ).
cnf(s59,plain,
spl41_9,
inference(rat,[],[s51,s58]) ).
cnf(s60,plain,
~ spl41_23,
inference(rat,[],[s43,s8,s59]) ).
cnf(s62,plain,
~ spl41_16,
inference(rat,[],[s45,s60]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s28,s8,s15,s60,s62]) ).
thf(f5944,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO905^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n005.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 17:26:32 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.24/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.48 % (1957387)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.48 % (1957401)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.48 % (1957401)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.68/0.48 % (1957401)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2325038287:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.48 % (1957396)lrs+10_16_si=on:nwc=1.5:random_seed=1480486202:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.48 % (1957395)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=418128259:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.48 % (1957399)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=748469746:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.48 % (1957398)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1119204020:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.68/0.48 % (1957400)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=484053275:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.48 % (1957397)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=596050381:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.48 % (1957396)Instruction limit reached!
% 0.68/0.48 % (1957396)------------------------------
% 0.68/0.48 % (1957396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.48 % (1957396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.48 % (1957396)CaDiCaL version: 2.1.3
% 0.68/0.48 % (1957396)Termination reason: Instruction limit
% 0.68/0.48 % (1957396)Termination phase: shuffling
% 0.68/0.48 % (1957396)Time elapsed: 0.012 s
% 0.68/0.48 % (1957396)Peak memory usage: 10 MB
% 0.68/0.48 % (1957396)Instructions burned: 19 (million)
% 0.68/0.48 % (1957397)Instruction limit reached!
% 0.68/0.48 % (1957397)------------------------------
% 0.68/0.48 % (1957397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.48 % (1957397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.48 % (1957397)CaDiCaL version: 2.1.3
% 0.68/0.48 % (1957397)Termination reason: Instruction limit
% 0.68/0.48 % (1957397)Termination phase: shuffling
% 0.68/0.48 % (1957397)Time elapsed: 0.006 s
% 0.68/0.48 % (1957397)Peak memory usage: 10 MB
% 0.68/0.48 % (1957397)Instructions burned: 3 (million)
% 0.68/0.48 % (1957399)Instruction limit reached!
% 0.68/0.48 % (1957399)------------------------------
% 0.68/0.48 % (1957399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.48 % (1957399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.48 % (1957399)CaDiCaL version: 2.1.3
% 0.68/0.48 % (1957399)Termination reason: Instruction limit
% 0.68/0.48 % (1957399)Termination phase: shuffling
% 0.68/0.48 % (1957399)Time elapsed: 0.015 s
% 0.68/0.48 % (1957399)Peak memory usage: 10 MB
% 0.68/0.48 % (1957399)Instructions burned: 24 (million)
% 0.68/0.48 % (1957411)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3365734484:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.48 % (1957411)Instruction limit reached!
% 0.68/0.48 % (1957411)------------------------------
% 0.68/0.48 % (1957411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.48 % (1957411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.48 % (1957411)CaDiCaL version: 2.1.3
% 0.68/0.48 % (1957411)Termination reason: Instruction limit
% 0.68/0.48 % (1957411)Termination phase: shuffling
% 0.68/0.48 % (1957411)Time elapsed: 0.002 s
% 0.68/0.48 % (1957411)Peak memory usage: 10 MB
% 0.68/0.48 % (1957411)Instructions burned: 4 (million)
% 0.68/0.48 % (1957401)Instruction limit reached!
% 0.68/0.48 % (1957401)------------------------------
% 0.68/0.48 % (1957401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.52 % (1957401)CaDiCaL version: 2.1.3
% 1.44/0.52 % (1957401)Termination reason: Instruction limit
% 1.44/0.52 % (1957401)Termination phase: Saturation
% 1.44/0.52 % (1957401)Time elapsed: 0.058 s
% 1.44/0.52 % (1957401)Peak memory usage: 12 MB
% 1.44/0.52 % (1957401)Instructions burned: 158 (million)
% 1.44/0.52 % (1957400)Instruction limit reached!
% 1.44/0.52 % (1957400)------------------------------
% 1.44/0.52 % (1957400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.52 % (1957400)CaDiCaL version: 2.1.3
% 1.44/0.52 % (1957400)Termination reason: Instruction limit
% 1.44/0.52 % (1957400)Termination phase: Function definition elimination
% 1.44/0.52 % (1957400)Time elapsed: 0.050 s
% 1.44/0.52 % (1957400)Peak memory usage: 10 MB
% 1.44/0.52 % (1957400)Instructions burned: 76 (million)
% 1.44/0.52 % (1957414)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.44/0.52 % (1957414)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3961228341:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.44/0.52 % (1957395)Instruction limit reached!
% 1.44/0.52 % (1957395)------------------------------
% 1.44/0.52 % (1957395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.52 % (1957395)CaDiCaL version: 2.1.3
% 1.44/0.52 % (1957395)Termination reason: Instruction limit
% 1.44/0.52 % (1957395)Termination phase: Property scanning
% 1.44/0.52 % (1957395)Time elapsed: 0.058 s
% 1.44/0.52 % (1957395)Peak memory usage: 11 MB
% 1.44/0.52 % (1957395)Instructions burned: 87 (million)
% 1.44/0.52 % (1957412)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=431395186:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.44/0.52 % (1957414)Instruction limit reached!
% 1.44/0.52 % (1957414)------------------------------
% 1.44/0.52 % (1957414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.52 % (1957414)CaDiCaL version: 2.1.3
% 1.44/0.52 % (1957414)Termination reason: Instruction limit
% 1.44/0.52 % (1957414)Termination phase: Property scanning
% 1.44/0.52 % (1957414)Time elapsed: 0.004 s
% 1.44/0.52 % (1957414)Peak memory usage: 10 MB
% 1.44/0.52 % (1957414)Instructions burned: 9 (million)
% 1.44/0.52 % (1957412)Instruction limit reached!
% 1.44/0.52 % (1957412)------------------------------
% 1.44/0.52 % (1957412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.52 % (1957412)CaDiCaL version: 2.1.3
% 1.44/0.52 % (1957412)Termination reason: Instruction limit
% 1.44/0.52 % (1957412)Termination phase: shuffling
% 1.44/0.52 % (1957412)Time elapsed: 0.003 s
% 1.44/0.52 % (1957412)Peak memory usage: 10 MB
% 1.44/0.52 % (1957412)Instructions burned: 5 (million)
% 1.44/0.52 % (1957417)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.44/0.52 % (1957417)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.44/0.52 % (1957416)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2038809968:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.44/0.52 % (1957417)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1612811335:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.44/0.52 % (1957423)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.44/0.52 % (1957416)Instruction limit reached!
% 1.44/0.52 % (1957416)------------------------------
% 1.44/0.52 % (1957416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.52 % (1957416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957416)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957416)Termination reason: Instruction limit
% 1.44/0.55 % (1957416)Termination phase: shuffling
% 1.44/0.55 % (1957416)Time elapsed: 0.008 s
% 1.44/0.55 % (1957416)Peak memory usage: 10 MB
% 1.44/0.55 % (1957416)Instructions burned: 13 (million)
% 1.44/0.55 % (1957423)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1768093327:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.44/0.55 % (1957423)Instruction limit reached!
% 1.44/0.55 % (1957423)------------------------------
% 1.44/0.55 % (1957423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.55 % (1957423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957423)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957423)Termination reason: Instruction limit
% 1.44/0.55 % (1957423)Termination phase: shuffling
% 1.44/0.55 % (1957423)Time elapsed: 0.001 s
% 1.44/0.55 % (1957423)Peak memory usage: 10 MB
% 1.44/0.55 % (1957423)Instructions burned: 2 (million)
% 1.44/0.55 % (1957417)Instruction limit reached!
% 1.44/0.55 % (1957417)------------------------------
% 1.44/0.55 % (1957417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.55 % (1957417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957417)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957417)Termination reason: Instruction limit
% 1.44/0.55 % (1957417)Termination phase: Property scanning
% 1.44/0.55 % (1957417)Time elapsed: 0.013 s
% 1.44/0.55 % (1957417)Peak memory usage: 10 MB
% 1.44/0.55 % (1957417)Instructions burned: 29 (million)
% 1.44/0.55 % (1957419)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1849214960:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.44/0.55 % (1957422)lrs+10_1_si=on:cs=on:random_seed=2338078695:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.44/0.55 % (1957424)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2543434030:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.44/0.55 % (1957431)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1952646178:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.55 % (1957428)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1031836261:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.44/0.55 % (1957422)Instruction limit reached!
% 1.44/0.55 % (1957422)------------------------------
% 1.44/0.55 % (1957422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.55 % (1957422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957422)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957422)Termination reason: Instruction limit
% 1.44/0.55 % (1957422)Termination phase: shuffling
% 1.44/0.55 % (1957422)Time elapsed: 0.006 s
% 1.44/0.55 % (1957422)Peak memory usage: 10 MB
% 1.44/0.55 % (1957422)Instructions burned: 10 (million)
% 1.44/0.55 % (1957431)Instruction limit reached!
% 1.44/0.55 % (1957431)------------------------------
% 1.44/0.55 % (1957431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.55 % (1957431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957431)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957431)Termination reason: Instruction limit
% 1.44/0.55 % (1957431)Termination phase: shuffling
% 1.44/0.55 % (1957431)Time elapsed: 0.005 s
% 1.44/0.55 % (1957431)Peak memory usage: 10 MB
% 1.44/0.55 % (1957431)Instructions burned: 18 (million)
% 1.44/0.55 % (1957430)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1551996436:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.44/0.55 % (1957424)Instruction limit reached!
% 1.44/0.55 % (1957424)------------------------------
% 1.44/0.55 % (1957424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.55 % (1957424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.55 % (1957424)CaDiCaL version: 2.1.3
% 1.44/0.55 % (1957424)Termination reason: Instruction limit
% 1.44/0.55 % (1957424)Termination phase: shuffling
% 1.44/0.63 % (1957424)Time elapsed: 0.024 s
% 1.44/0.63 % (1957424)Peak memory usage: 10 MB
% 1.44/0.63 % (1957424)Instructions burned: 39 (million)
% 1.44/0.63 % (1957438)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=777331707:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.63 % (1957438)Instruction limit reached!
% 1.44/0.63 % (1957438)------------------------------
% 1.44/0.63 % (1957438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.63 % (1957438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.63 % (1957438)CaDiCaL version: 2.1.3
% 1.44/0.63 % (1957438)Termination reason: Instruction limit
% 1.44/0.63 % (1957438)Termination phase: shuffling
% 1.44/0.63 % (1957438)Time elapsed: 0.004 s
% 1.44/0.63 % (1957438)Peak memory usage: 10 MB
% 1.44/0.63 % (1957438)Instructions burned: 15 (million)
% 1.44/0.63 % (1957430)Instruction limit reached!
% 1.44/0.63 % (1957430)------------------------------
% 1.44/0.63 % (1957430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.63 % (1957430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.63 % (1957430)CaDiCaL version: 2.1.3
% 2.06/0.63 % (1957430)Termination reason: Instruction limit
% 2.06/0.63 % (1957430)Termination phase: shuffling
% 2.06/0.63 % (1957430)Time elapsed: 0.017 s
% 2.06/0.63 % (1957430)Peak memory usage: 10 MB
% 2.06/0.63 % (1957430)Instructions burned: 26 (million)
% 2.06/0.63 % (1957428)Refutation not found, incomplete strategy
% 2.06/0.63 % (1957428)------------------------------
% 2.06/0.63 % (1957428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.63 % (1957428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.63 % (1957428)CaDiCaL version: 2.1.3
% 2.06/0.63 % (1957428)Termination reason: Refutation not found, incomplete strategy
% 2.06/0.63 % (1957428)Time elapsed: 0.039 s
% 2.06/0.63 % (1957428)Peak memory usage: 12 MB
% 2.06/0.63 % (1957428)Instructions burned: 59 (million)
% 2.06/0.63 % (1957428)------------------------------
% 2.06/0.63 % (1957428)------------------------------
% 2.06/0.63 % (1957437)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2612015001:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.06/0.63 % (1957443)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=883940706:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.06/0.63 % (1957443)Instruction limit reached!
% 2.06/0.63 % (1957443)------------------------------
% 2.06/0.63 % (1957443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.63 % (1957443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.63 % (1957443)CaDiCaL version: 2.1.3
% 2.06/0.63 % (1957443)Termination reason: Instruction limit
% 2.06/0.63 % (1957443)Termination phase: shuffling
% 2.06/0.63 % (1957443)Time elapsed: 0.001 s
% 2.06/0.63 % (1957443)Peak memory usage: 10 MB
% 2.06/0.63 % (1957443)Instructions burned: 3 (million)
% 2.06/0.63 % (1957419)Instruction limit reached!
% 2.06/0.63 % (1957419)------------------------------
% 2.06/0.63 % (1957419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.63 % (1957419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.63 % (1957419)CaDiCaL version: 2.1.3
% 2.06/0.63 % (1957419)Termination reason: Instruction limit
% 2.06/0.63 % (1957419)Termination phase: Property scanning
% 2.06/0.63 % (1957419)Time elapsed: 0.064 s
% 2.06/0.63 % (1957419)Peak memory usage: 10 MB
% 2.06/0.63 % (1957419)Instructions burned: 87 (million)
% 2.06/0.63 % (1957449)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.06/0.63 % (1957449)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.06/0.63 % (1957445)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2953690519:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.06/0.63 % (1957450)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.06/0.63 % (1957449)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1572310416:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.06/0.68 % (1957450)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3811590384:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.06/0.68 % (1957444)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2173055496:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.06/0.68 % (1957450)Instruction limit reached!
% 2.06/0.68 % (1957450)------------------------------
% 2.06/0.68 % (1957450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957450)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957450)Termination reason: Instruction limit
% 2.06/0.68 % (1957450)Termination phase: shuffling
% 2.06/0.68 % (1957450)Time elapsed: 0.003 s
% 2.06/0.68 % (1957450)Peak memory usage: 10 MB
% 2.06/0.68 % (1957450)Instructions burned: 9 (million)
% 2.06/0.68 % (1957449)Instruction limit reached!
% 2.06/0.68 % (1957449)------------------------------
% 2.06/0.68 % (1957449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957449)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957449)Termination reason: Instruction limit
% 2.06/0.68 % (1957449)Termination phase: Property scanning
% 2.06/0.68 % (1957449)Time elapsed: 0.007 s
% 2.06/0.68 % (1957449)Peak memory usage: 10 MB
% 2.06/0.68 % (1957449)Instructions burned: 16 (million)
% 2.06/0.68 % (1957446)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3793874410:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.06/0.68 % (1957445)Instruction limit reached!
% 2.06/0.68 % (1957445)------------------------------
% 2.06/0.68 % (1957445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957445)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957445)Termination reason: Instruction limit
% 2.06/0.68 % (1957445)Termination phase: shuffling
% 2.06/0.68 % (1957445)Time elapsed: 0.014 s
% 2.06/0.68 % (1957445)Peak memory usage: 10 MB
% 2.06/0.68 % (1957445)Instructions burned: 23 (million)
% 2.06/0.68 % (1957437)Refutation not found, incomplete strategy
% 2.06/0.68 % (1957437)------------------------------
% 2.06/0.68 % (1957437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957437)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957437)Termination reason: Refutation not found, incomplete strategy
% 2.06/0.68 % (1957437)Time elapsed: 0.046 s
% 2.06/0.68 % (1957437)Peak memory usage: 12 MB
% 2.06/0.68 % (1957437)Instructions burned: 63 (million)
% 2.06/0.68 % (1957437)------------------------------
% 2.06/0.68 % (1957437)------------------------------
% 2.06/0.68 % (1957444)Instruction limit reached!
% 2.06/0.68 % (1957444)------------------------------
% 2.06/0.68 % (1957444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957444)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957444)Termination reason: Instruction limit
% 2.06/0.68 % (1957444)Termination phase: Property scanning
% 2.06/0.68 % (1957444)Time elapsed: 0.020 s
% 2.06/0.68 % (1957444)Peak memory usage: 10 MB
% 2.06/0.68 % (1957444)Instructions burned: 27 (million)
% 2.06/0.68 % (1957458)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1941292922:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.06/0.68 % (1957458)Instruction limit reached!
% 2.06/0.68 % (1957458)------------------------------
% 2.06/0.68 % (1957458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.68 % (1957458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.68 % (1957458)CaDiCaL version: 2.1.3
% 2.06/0.68 % (1957458)Termination reason: Instruction limit
% 2.06/0.68 % (1957458)Termination phase: shuffling
% 2.06/0.68 % (1957458)Time elapsed: 0.003 s
% 2.06/0.68 % (1957458)Peak memory usage: 10 MB
% 2.06/0.68 % (1957458)Instructions burned: 8 (million)
% 2.54/0.76 % (1957460)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3078731823:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.54/0.76 % (1957446)Instruction limit reached!
% 2.54/0.76 % (1957446)------------------------------
% 2.54/0.76 % (1957446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.76 % (1957446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.76 % (1957446)CaDiCaL version: 2.1.3
% 2.54/0.76 % (1957446)Termination reason: Instruction limit
% 2.54/0.76 % (1957446)Termination phase: Property scanning
% 2.54/0.76 % (1957446)Time elapsed: 0.040 s
% 2.54/0.76 % (1957446)Peak memory usage: 10 MB
% 2.54/0.76 % (1957446)Instructions burned: 61 (million)
% 2.54/0.76 % (1957457)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3652662963:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.54/0.76 % (1957466)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2477114297:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.54/0.76 % (1957464)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1181643249:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.54/0.76 % (1957463)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3112492653:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.54/0.76 % (1957460)Instruction limit reached!
% 2.54/0.76 % (1957460)------------------------------
% 2.54/0.76 % (1957460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.76 % (1957460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.76 % (1957460)CaDiCaL version: 2.1.3
% 2.54/0.76 % (1957460)Termination reason: Instruction limit
% 2.54/0.76 % (1957460)Termination phase: Property scanning
% 2.54/0.76 % (1957460)Time elapsed: 0.018 s
% 2.54/0.76 % (1957460)Peak memory usage: 10 MB
% 2.54/0.76 % (1957460)Instructions burned: 24 (million)
% 2.54/0.76 % (1957468)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3852043665:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.54/0.76 % (1957463)Instruction limit reached!
% 2.54/0.76 % (1957463)------------------------------
% 2.54/0.76 % (1957463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.76 % (1957463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.76 % (1957463)CaDiCaL version: 2.1.3
% 2.54/0.76 % (1957463)Termination reason: Instruction limit
% 2.54/0.76 % (1957463)Termination phase: shuffling
% 2.54/0.76 % (1957463)Time elapsed: 0.013 s
% 2.54/0.76 % (1957463)Peak memory usage: 10 MB
% 2.54/0.76 % (1957463)Instructions burned: 21 (million)
% 2.54/0.76 % (1957457)Instruction limit reached!
% 2.54/0.76 % (1957457)------------------------------
% 2.54/0.76 % (1957457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.76 % (1957457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.76 % (1957457)CaDiCaL version: 2.1.3
% 2.54/0.76 % (1957457)Termination reason: Instruction limit
% 2.54/0.76 % (1957457)Termination phase: Property scanning
% 2.54/0.76 % (1957457)Time elapsed: 0.037 s
% 2.54/0.76 % (1957457)Peak memory usage: 10 MB
% 2.54/0.76 % (1957457)Instructions burned: 31 (million)
% 2.54/0.76 % (1957474)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1887286864:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.54/0.76 % (1957468)Refutation not found, incomplete strategy
% 2.54/0.76 % (1957468)------------------------------
% 2.54/0.76 % (1957468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.76 % (1957468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.76 % (1957468)CaDiCaL version: 2.1.3
% 2.54/0.76 % (1957468)Termination reason: Refutation not found, incomplete strategy
% 2.54/0.76 % (1957468)Time elapsed: 0.028 s
% 2.54/0.76 % (1957468)Peak memory usage: 13 MB
% 2.54/0.76 % (1957468)Instructions burned: 79 (million)
% 2.54/0.76 % (1957468)------------------------------
% 2.54/0.76 % (1957468)------------------------------
% 2.54/0.76 % (1957476)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.54/0.76 % (1957476)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1785682127:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.94/0.87 % (1957476)Instruction limit reached!
% 2.94/0.87 % (1957476)------------------------------
% 2.94/0.87 % (1957476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.87 % (1957476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.87 % (1957476)CaDiCaL version: 2.1.3
% 2.94/0.87 % (1957476)Termination reason: Instruction limit
% 2.94/0.87 % (1957476)Termination phase: shuffling
% 2.94/0.87 % (1957476)Time elapsed: 0.006 s
% 2.94/0.87 % (1957476)Peak memory usage: 10 MB
% 2.94/0.87 % (1957476)Instructions burned: 7 (million)
% 2.94/0.87 % (1957480)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3562083096:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.94/0.87 % (1957474)Instruction limit reached!
% 2.94/0.87 % (1957474)------------------------------
% 2.94/0.87 % (1957474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.87 % (1957474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.87 % (1957474)CaDiCaL version: 2.1.3
% 2.94/0.87 % (1957474)Termination reason: Instruction limit
% 2.94/0.87 % (1957474)Termination phase: shuffling
% 2.94/0.87 % (1957474)Time elapsed: 0.026 s
% 2.94/0.87 % (1957474)Peak memory usage: 10 MB
% 2.94/0.87 % (1957474)Instructions burned: 42 (million)
% 2.94/0.87 % (1957466)Instruction limit reached!
% 2.94/0.87 % (1957466)------------------------------
% 2.94/0.87 % (1957466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.87 % (1957466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.87 % (1957466)CaDiCaL version: 2.1.3
% 2.94/0.87 % (1957466)Termination reason: Instruction limit
% 2.94/0.87 % (1957466)Termination phase: Property scanning
% 2.94/0.87 % (1957466)Time elapsed: 0.071 s
% 2.94/0.87 % (1957466)Peak memory usage: 11 MB
% 2.94/0.87 % (1957466)Instructions burned: 143 (million)
% 2.94/0.87 % (1957478)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2896893461:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.94/0.87 % (1957482)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.94/0.87 % (1957482)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=577262351:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.94/0.87 % (1957482)Instruction limit reached!
% 2.94/0.87 % (1957482)------------------------------
% 2.94/0.87 % (1957482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.87 % (1957482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.87 % (1957482)CaDiCaL version: 2.1.3
% 2.94/0.87 % (1957482)Termination reason: Instruction limit
% 2.94/0.87 % (1957482)Termination phase: Property scanning
% 2.94/0.87 % (1957482)Time elapsed: 0.003 s
% 2.94/0.87 % (1957482)Peak memory usage: 10 MB
% 2.94/0.87 % (1957482)Instructions burned: 8 (million)
% 2.94/0.87 % (1957480)Refutation not found, incomplete strategy
% 2.94/0.87 % (1957480)------------------------------
% 2.94/0.87 % (1957480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.87 % (1957480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.87 % (1957480)CaDiCaL version: 2.1.3
% 2.94/0.87 % (1957480)Termination reason: Refutation not found, incomplete strategy
% 2.94/0.87 % (1957480)Time elapsed: 0.020 s
% 2.94/0.87 % (1957480)Peak memory usage: 12 MB
% 2.94/0.87 % (1957480)Instructions burned: 59 (million)
% 2.94/0.87 % (1957480)------------------------------
% 2.94/0.87 % (1957480)------------------------------
% 2.94/0.87 % (1957484)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2956498162:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.94/0.87 % (1957489)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3503119105:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.46/0.95 % (1957487)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=50417771:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.46/0.95 % (1957478)Refutation not found, incomplete strategy
% 3.46/0.95 % (1957478)------------------------------
% 3.46/0.95 % (1957478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.95 % (1957478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.95 % (1957490)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=549164806:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.46/0.95 % (1957478)CaDiCaL version: 2.1.3
% 3.46/0.95 % (1957478)Termination reason: Refutation not found, incomplete strategy
% 3.46/0.95 % (1957478)Time elapsed: 0.038 s
% 3.46/0.95 % (1957478)Peak memory usage: 12 MB
% 3.46/0.95 % (1957478)Instructions burned: 58 (million)
% 3.46/0.95 % (1957478)------------------------------
% 3.46/0.95 % (1957478)------------------------------
% 3.46/0.95 % (1957484)Instruction limit reached!
% 3.46/0.95 % (1957484)------------------------------
% 3.46/0.95 % (1957484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.95 % (1957484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.95 % (1957484)CaDiCaL version: 2.1.3
% 3.46/0.95 % (1957484)Termination reason: Instruction limit
% 3.46/0.95 % (1957484)Termination phase: shuffling
% 3.46/0.95 % (1957484)Time elapsed: 0.013 s
% 3.46/0.95 % (1957484)Peak memory usage: 10 MB
% 3.46/0.95 % (1957484)Instructions burned: 22 (million)
% 3.46/0.95 % (1957487)Instruction limit reached!
% 3.46/0.95 % (1957487)------------------------------
% 3.46/0.95 % (1957487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.95 % (1957487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.95 % (1957487)CaDiCaL version: 2.1.3
% 3.46/0.95 % (1957487)Termination reason: Instruction limit
% 3.46/0.95 % (1957487)Termination phase: Property scanning
% 3.46/0.95 % (1957487)Time elapsed: 0.016 s
% 3.46/0.95 % (1957487)Peak memory usage: 10 MB
% 3.46/0.95 % (1957487)Instructions burned: 21 (million)
% 3.46/0.95 % (1957495)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2319288367:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.46/0.95 % (1957496)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2234840788:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.46/0.95 % (1957497)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2605624477:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.46/0.95 % (1957497)Instruction limit reached!
% 3.46/0.95 % (1957497)------------------------------
% 3.46/0.95 % (1957497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.95 % (1957497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.95 % (1957497)CaDiCaL version: 2.1.3
% 3.46/0.95 % (1957497)Termination reason: Instruction limit
% 3.46/0.95 % (1957497)Termination phase: shuffling
% 3.46/0.95 % (1957497)Time elapsed: 0.014 s
% 3.46/0.95 % (1957497)Peak memory usage: 10 MB
% 3.46/0.95 % (1957497)Instructions burned: 21 (million)
% 3.46/0.95 % (1957495)Instruction limit reached!
% 3.46/0.95 % (1957495)------------------------------
% 3.46/0.95 % (1957495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.95 % (1957495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.95 % (1957495)CaDiCaL version: 2.1.3
% 3.46/0.95 % (1957495)Termination reason: Instruction limit
% 3.46/0.95 % (1957495)Termination phase: shuffling
% 3.46/0.95 % (1957495)Time elapsed: 0.029 s
% 3.46/0.95 % (1957495)Peak memory usage: 10 MB
% 3.46/0.95 % (1957495)Instructions burned: 45 (million)
% 3.46/0.95 % (1957501)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.46/0.95 % (1957501)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3048453424:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.46/1.04 % (1957502)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2120999550:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.46/1.04 % (1957502)Instruction limit reached!
% 3.46/1.04 % (1957502)------------------------------
% 3.46/1.04 % (1957502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957502)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957502)Termination reason: Instruction limit
% 3.46/1.04 % (1957502)Termination phase: shuffling
% 3.46/1.04 % (1957502)Time elapsed: 0.009 s
% 3.46/1.04 % (1957502)Peak memory usage: 10 MB
% 3.46/1.04 % (1957502)Instructions burned: 14 (million)
% 3.46/1.04 % (1957489)Instruction limit reached!
% 3.46/1.04 % (1957489)------------------------------
% 3.46/1.04 % (1957489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957489)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957489)Termination reason: Instruction limit
% 3.46/1.04 % (1957489)Termination phase: Saturation
% 3.46/1.04 % (1957489)Time elapsed: 0.117 s
% 3.46/1.04 % (1957489)Peak memory usage: 12 MB
% 3.46/1.04 % (1957489)Instructions burned: 322 (million)
% 3.46/1.04 % (1957496)Refutation not found, incomplete strategy
% 3.46/1.04 % (1957496)------------------------------
% 3.46/1.04 % (1957496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957496)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957496)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.04 % (1957496)Time elapsed: 0.084 s
% 3.46/1.04 % (1957496)Peak memory usage: 13 MB
% 3.46/1.04 % (1957496)Instructions burned: 114 (million)
% 3.46/1.04 % (1957496)------------------------------
% 3.46/1.04 % (1957496)------------------------------
% 3.46/1.04 % (1957505)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2245293595:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.46/1.04 % (1957506)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1788096919:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.46/1.04 % (1957507)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3055842465:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 3.46/1.04 % (1957501)Instruction limit reached!
% 3.46/1.04 % (1957501)------------------------------
% 3.46/1.04 % (1957501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957501)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957501)Termination reason: Instruction limit
% 3.46/1.04 % (1957501)Termination phase: Saturation
% 3.46/1.04 % (1957501)Time elapsed: 0.083 s
% 3.46/1.04 % (1957501)Peak memory usage: 12 MB
% 3.46/1.04 % (1957501)Instructions burned: 201 (million)
% 3.46/1.04 % (1957398)Instruction limit reached!
% 3.46/1.04 % (1957398)------------------------------
% 3.46/1.04 % (1957398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957398)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957398)Termination reason: Instruction limit
% 3.46/1.04 % (1957398)Termination phase: Saturation
% 3.46/1.04 % (1957398)Time elapsed: 0.506 s
% 3.46/1.04 % (1957398)Peak memory usage: 16 MB
% 3.46/1.04 % (1957398)Instructions burned: 634 (million)
% 3.46/1.04 % (1957506)Instruction limit reached!
% 3.46/1.04 % (1957506)------------------------------
% 3.46/1.04 % (1957506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/1.04 % (1957506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.04 % (1957506)CaDiCaL version: 2.1.3
% 3.46/1.04 % (1957506)Termination reason: Instruction limit
% 3.46/1.04 % (1957506)Termination phase: Property scanning
% 3.46/1.04 % (1957506)Time elapsed: 0.035 s
% 3.46/1.04 % (1957506)Peak memory usage: 10 MB
% 3.46/1.04 % (1957506)Instructions burned: 51 (million)
% 3.46/1.04 % (1957511)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3496367062:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 5.63/1.15 % (1957507)Instruction limit reached!
% 5.63/1.15 % (1957507)------------------------------
% 5.63/1.15 % (1957507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957507)CaDiCaL version: 2.1.3
% 5.63/1.15 % (1957507)Termination reason: Instruction limit
% 5.63/1.15 % (1957507)Termination phase: Function definition elimination
% 5.63/1.15 % (1957507)Time elapsed: 0.023 s
% 5.63/1.15 % (1957507)Peak memory usage: 10 MB
% 5.63/1.15 % (1957507)Instructions burned: 31 (million)
% 5.63/1.15 % (1957505)Instruction limit reached!
% 5.63/1.15 % (1957505)------------------------------
% 5.63/1.15 % (1957505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957505)CaDiCaL version: 2.1.3
% 5.63/1.15 % (1957505)Termination reason: Instruction limit
% 5.63/1.15 % (1957505)Termination phase: Property scanning
% 5.63/1.15 % (1957505)Time elapsed: 0.051 s
% 5.63/1.15 % (1957505)Peak memory usage: 11 MB
% 5.63/1.15 % (1957505)Instructions burned: 67 (million)
% 5.63/1.15 % (1957514)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=552208663:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 5.63/1.15 % (1957515)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.63/1.15 % (1957512)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2592858801:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 5.63/1.15 % (1957515)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=716998039:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 5.63/1.15 % (1957514)Instruction limit reached!
% 5.63/1.15 % (1957514)------------------------------
% 5.63/1.15 % (1957514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957514)CaDiCaL version: 2.1.3
% 5.63/1.15 % (1957514)Termination reason: Instruction limit
% 5.63/1.15 % (1957514)Termination phase: Function definition elimination
% 5.63/1.15 % (1957514)Time elapsed: 0.024 s
% 5.63/1.15 % (1957514)Peak memory usage: 10 MB
% 5.63/1.15 % (1957514)Instructions burned: 69 (million)
% 5.63/1.15 % (1957516)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3475764751:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.63/1.15 % (1957512)Instruction limit reached!
% 5.63/1.15 % (1957512)------------------------------
% 5.63/1.15 % (1957512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957512)CaDiCaL version: 2.1.3
% 5.63/1.15 % (1957512)Termination reason: Instruction limit
% 5.63/1.15 % (1957512)Termination phase: Function definition elimination
% 5.63/1.15 % (1957512)Time elapsed: 0.026 s
% 5.63/1.15 % (1957512)Peak memory usage: 10 MB
% 5.63/1.15 % (1957512)Instructions burned: 35 (million)
% 5.63/1.15 % (1957520)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1181373322:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.63/1.15 % (1957511)Instruction limit reached!
% 5.63/1.15 % (1957511)------------------------------
% 5.63/1.15 % (1957511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957511)CaDiCaL version: 2.1.3
% 5.63/1.15 % (1957511)Termination reason: Instruction limit
% 5.63/1.15 % (1957511)Termination phase: Saturation
% 5.63/1.15 % (1957511)Time elapsed: 0.068 s
% 5.63/1.15 % (1957511)Peak memory usage: 12 MB
% 5.63/1.15 % (1957511)Instructions burned: 137 (million)
% 5.63/1.15 % (1957516)Refutation not found, incomplete strategy
% 5.63/1.15 % (1957516)------------------------------
% 5.63/1.15 % (1957516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.15 % (1957516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.15 % (1957516)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957516)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.35 % (1957516)Time elapsed: 0.039 s
% 6.35/1.35 % (1957516)Peak memory usage: 12 MB
% 6.35/1.35 % (1957516)Instructions burned: 60 (million)
% 6.35/1.35 % (1957516)------------------------------
% 6.35/1.35 % (1957516)------------------------------
% 6.35/1.35 % (1957524)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=162996721:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 6.35/1.35 % (1957522)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=495580301:i=427:sd=1:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/427Mi)
% 6.35/1.35 % (1957520)Instruction limit reached!
% 6.35/1.35 % (1957520)------------------------------
% 6.35/1.35 % (1957520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.35/1.35 % (1957520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.35 % (1957520)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957520)Termination reason: Instruction limit
% 6.35/1.35 % (1957520)Termination phase: Property scanning
% 6.35/1.35 % (1957520)Time elapsed: 0.034 s
% 6.35/1.35 % (1957520)Peak memory usage: 11 MB
% 6.35/1.35 % (1957520)Instructions burned: 97 (million)
% 6.35/1.35 % (1957528)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1957344378:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 6.35/1.35 % (1957525)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2495522408:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 6.35/1.35 % (1957528)Refutation not found, incomplete strategy
% 6.35/1.35 % (1957528)------------------------------
% 6.35/1.35 % (1957528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.35/1.35 % (1957528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.35 % (1957528)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957528)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.35 % (1957528)Time elapsed: 0.011 s
% 6.35/1.35 % (1957528)Peak memory usage: 12 MB
% 6.35/1.35 % (1957528)Instructions burned: 25 (million)
% 6.35/1.35 % (1957528)------------------------------
% 6.35/1.35 % (1957528)------------------------------
% 6.35/1.35 % (1957524)Refutation not found, incomplete strategy
% 6.35/1.35 % (1957524)------------------------------
% 6.35/1.35 % (1957524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.35/1.35 % (1957524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.35 % (1957524)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957524)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.35 % (1957524)Time elapsed: 0.038 s
% 6.35/1.35 % (1957524)Peak memory usage: 12 MB
% 6.35/1.35 % (1957524)Instructions burned: 63 (million)
% 6.35/1.35 % (1957524)------------------------------
% 6.35/1.35 % (1957524)------------------------------
% 6.35/1.35 % (1957522)Refutation not found, incomplete strategy
% 6.35/1.35 % (1957522)------------------------------
% 6.35/1.35 % (1957522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.35/1.35 % (1957522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.35 % (1957522)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957522)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.35 % (1957522)Time elapsed: 0.038 s
% 6.35/1.35 % (1957522)Peak memory usage: 12 MB
% 6.35/1.35 % (1957522)Instructions burned: 58 (million)
% 6.35/1.35 % (1957522)------------------------------
% 6.35/1.35 % (1957522)------------------------------
% 6.35/1.35 % (1957531)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1644143769:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 6.35/1.35 % (1957532)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3316147836:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.35/1.35 % (1957531)Instruction limit reached!
% 6.35/1.35 % (1957531)------------------------------
% 6.35/1.35 % (1957531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.35/1.35 % (1957531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.35 % (1957531)CaDiCaL version: 2.1.3
% 6.35/1.35 % (1957531)Termination reason: Instruction limit
% 6.35/1.35 % (1957531)Termination phase: Function definition elimination
% 6.35/1.35 % (1957531)Time elapsed: 0.017 s
% 6.35/1.35 % (1957531)Peak memory usage: 10 MB
% 6.35/1.35 % (1957531)Instructions burned: 45 (million)
% 7.51/1.40 % (1957515)Instruction limit reached!
% 7.51/1.40 % (1957515)------------------------------
% 7.51/1.40 % (1957515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.51/1.40 % (1957515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.40 % (1957515)CaDiCaL version: 2.1.3
% 7.51/1.40 % (1957515)Termination reason: Instruction limit
% 7.51/1.40 % (1957515)Termination phase: Saturation
% 7.51/1.40 % (1957515)Time elapsed: 0.130 s
% 7.51/1.40 % (1957515)Peak memory usage: 12 MB
% 7.51/1.40 % (1957515)Instructions burned: 180 (million)
% 7.51/1.40 % (1957533)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=161995259:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 7.51/1.40 % (1957536)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1930068975:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 7.51/1.40 % (1957538)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=2164787082:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 7.51/1.40 % (1957536)Instruction limit reached!
% 7.51/1.40 % (1957536)------------------------------
% 7.51/1.40 % (1957536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.51/1.40 % (1957536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.40 % (1957536)CaDiCaL version: 2.1.3
% 7.51/1.40 % (1957536)Termination reason: Instruction limit
% 7.51/1.40 % (1957536)Termination phase: Property scanning
% 7.51/1.40 % (1957536)Time elapsed: 0.034 s
% 7.51/1.40 % (1957536)Peak memory usage: 10 MB
% 7.51/1.40 % (1957536)Instructions burned: 97 (million)
% 7.51/1.40 % (1957541)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2806511223:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 7.51/1.40 % (1957538)Instruction limit reached!
% 7.51/1.40 % (1957538)------------------------------
% 7.51/1.40 % (1957538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.51/1.40 % (1957538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.40 % (1957538)CaDiCaL version: 2.1.3
% 7.51/1.40 % (1957538)Termination reason: Instruction limit
% 7.51/1.40 % (1957538)Termination phase: Property scanning
% 7.51/1.40 % (1957538)Time elapsed: 0.047 s
% 7.51/1.40 % (1957538)Peak memory usage: 11 MB
% 7.51/1.40 % (1957538)Instructions burned: 65 (million)
% 7.51/1.40 % (1957532)Refutation not found, incomplete strategy
% 7.51/1.40 % (1957532)------------------------------
% 7.51/1.40 % (1957532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.51/1.40 % (1957532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.40 % (1957532)CaDiCaL version: 2.1.3
% 7.51/1.40 % (1957532)Termination reason: Refutation not found, incomplete strategy
% 7.51/1.40 % (1957532)Time elapsed: 0.087 s
% 7.51/1.40 % (1957532)Peak memory usage: 13 MB
% 7.51/1.40 % (1957532)Instructions burned: 115 (million)
% 7.51/1.40 % (1957532)------------------------------
% 7.51/1.40 % (1957532)------------------------------
% 7.51/1.40 % (1957543)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3455491227:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 7.51/1.40 % (1957541)Instruction limit reached!
% 7.51/1.40 % (1957541)------------------------------
% 7.51/1.40 % (1957541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.51/1.40 % (1957541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.51/1.40 % (1957541)CaDiCaL version: 2.1.3
% 7.51/1.40 % (1957541)Termination reason: Instruction limit
% 7.51/1.40 % (1957541)Termination phase: Property scanning
% 7.51/1.40 % (1957541)Time elapsed: 0.040 s
% 7.51/1.40 % (1957541)Peak memory usage: 10 MB
% 7.51/1.40 % (1957541)Instructions burned: 106 (million)
% 7.51/1.40 % (1957544)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=676012768:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 7.83/1.55 % (1957543)Refutation not found, incomplete strategy
% 7.83/1.55 % (1957543)------------------------------
% 7.83/1.55 % (1957543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.55 % (1957543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.55 % (1957543)CaDiCaL version: 2.1.3
% 7.83/1.55 % (1957543)Termination reason: Refutation not found, incomplete strategy
% 7.83/1.55 % (1957543)Time elapsed: 0.026 s
% 7.83/1.55 % (1957543)Peak memory usage: 13 MB
% 7.83/1.55 % (1957543)Instructions burned: 61 (million)
% 7.83/1.55 % (1957543)------------------------------
% 7.83/1.55 % (1957543)------------------------------
% 7.83/1.55 % (1957546)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2933319397:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 7.83/1.55 % (1957548)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1703926233:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 7.83/1.55 % (1957548)Instruction limit reached!
% 7.83/1.55 % (1957548)------------------------------
% 7.83/1.55 % (1957548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.55 % (1957548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.55 % (1957548)CaDiCaL version: 2.1.3
% 7.83/1.55 % (1957548)Termination reason: Instruction limit
% 7.83/1.55 % (1957548)Termination phase: Function definition elimination
% 7.83/1.55 % (1957548)Time elapsed: 0.026 s
% 7.83/1.55 % (1957548)Peak memory usage: 10 MB
% 7.83/1.55 % (1957548)Instructions burned: 35 (million)
% 7.83/1.55 % (1957551)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4064591273:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 7.83/1.55 % (1957551)Instruction limit reached!
% 7.83/1.55 % (1957551)------------------------------
% 7.83/1.55 % (1957551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.55 % (1957551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.55 % (1957551)CaDiCaL version: 2.1.3
% 7.83/1.55 % (1957551)Termination reason: Instruction limit
% 7.83/1.56 % (1957551)Termination phase: Property scanning
% 7.83/1.56 % (1957551)Time elapsed: 0.035 s
% 7.83/1.56 % (1957551)Peak memory usage: 11 MB
% 7.83/1.56 % (1957551)Instructions burned: 92 (million)
% 7.83/1.56 % (1957553)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3823080802:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2990 on theBenchmark for (2990ds/66Mi)
% 7.83/1.56 % (1957546)Instruction limit reached!
% 7.83/1.56 % (1957546)------------------------------
% 7.83/1.56 % (1957546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.56 % (1957546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.56 % (1957546)CaDiCaL version: 2.1.3
% 7.83/1.56 % (1957546)Termination reason: Instruction limit
% 7.83/1.56 % (1957546)Termination phase: Saturation
% 7.83/1.56 % (1957546)Time elapsed: 0.173 s
% 7.83/1.56 % (1957546)Peak memory usage: 13 MB
% 7.83/1.56 % (1957546)Instructions burned: 495 (million)
% 7.83/1.56 % (1957525)Instruction limit reached!
% 7.83/1.56 % (1957525)------------------------------
% 7.83/1.56 % (1957525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.56 % (1957525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.56 % (1957525)CaDiCaL version: 2.1.3
% 7.83/1.56 % (1957525)Termination reason: Instruction limit
% 7.83/1.56 % (1957525)Termination phase: Saturation
% 7.83/1.56 % (1957525)Time elapsed: 0.356 s
% 7.83/1.56 % (1957525)Peak memory usage: 14 MB
% 7.83/1.56 % (1957525)Instructions burned: 515 (million)
% 7.83/1.56 % (1957533)Instruction limit reached!
% 7.83/1.56 % (1957533)------------------------------
% 7.83/1.56 % (1957533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.83/1.56 % (1957533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.83/1.56 % (1957533)CaDiCaL version: 2.1.3
% 7.83/1.56 % (1957533)Termination reason: Instruction limit
% 7.83/1.56 % (1957533)Termination phase: Saturation
% 7.83/1.56 % (1957533)Time elapsed: 0.315 s
% 7.83/1.56 % (1957533)Peak memory usage: 13 MB
% 7.83/1.56 % (1957533)Instructions burned: 450 (million)
% 7.83/1.56 % (1957553)Refutation not found, incomplete strategy
% 7.83/1.56 % (1957553)------------------------------
% 8.61/1.66 % (1957553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.66 % (1957553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.66 % (1957553)CaDiCaL version: 2.1.3
% 8.61/1.66 % (1957553)Termination reason: Refutation not found, incomplete strategy
% 8.61/1.66 % (1957553)Time elapsed: 0.046 s
% 8.61/1.66 % (1957553)Peak memory usage: 12 MB
% 8.61/1.66 % (1957553)Instructions burned: 57 (million)
% 8.61/1.66 % (1957553)------------------------------
% 8.61/1.66 % (1957553)------------------------------
% 8.61/1.66 % (1957558)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3250535474:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 8.61/1.66 % (1957558)Instruction limit reached!
% 8.61/1.66 % (1957558)------------------------------
% 8.61/1.66 % (1957558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.66 % (1957558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.66 % (1957558)CaDiCaL version: 2.1.3
% 8.61/1.66 % (1957558)Termination reason: Instruction limit
% 8.61/1.66 % (1957558)Termination phase: shuffling
% 8.61/1.66 % (1957558)Time elapsed: 0.009 s
% 8.61/1.66 % (1957558)Peak memory usage: 10 MB
% 8.61/1.66 % (1957558)Instructions burned: 24 (million)
% 8.61/1.66 % (1957559)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2577590388:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 8.61/1.66 % (1957544)Instruction limit reached!
% 8.61/1.66 % (1957544)------------------------------
% 8.61/1.66 % (1957544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.66 % (1957544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.66 % (1957544)CaDiCaL version: 2.1.3
% 8.61/1.66 % (1957544)Termination reason: Instruction limit
% 8.61/1.66 % (1957544)Termination phase: Saturation
% 8.61/1.66 % (1957544)Time elapsed: 0.223 s
% 8.61/1.66 % (1957544)Peak memory usage: 12 MB
% 8.61/1.66 % (1957544)Instructions burned: 375 (million)
% 8.61/1.66 % (1957561)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 8.61/1.66 % (1957490)Instruction limit reached!
% 8.61/1.66 % (1957490)------------------------------
% 8.61/1.66 % (1957490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.66 % (1957490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.66 % (1957490)CaDiCaL version: 2.1.3
% 8.61/1.66 % (1957490)Termination reason: Instruction limit
% 8.61/1.66 % (1957490)Termination phase: Saturation
% 8.61/1.66 % (1957490)Time elapsed: 0.694 s
% 8.61/1.66 % (1957490)Peak memory usage: 17 MB
% 8.61/1.66 % (1957490)Instructions burned: 855 (million)
% 8.61/1.66 % (1957560)lrs+10_1_sil=128000:si=on:urr=on:random_seed=467201777:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/28Mi)
% 8.61/1.66 % (1957561)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2619386094:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2989 on theBenchmark for (2989ds/137Mi)
% 8.61/1.66 % (1957564)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=3648264167:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2989 on theBenchmark for (2989ds/340Mi)
% 8.61/1.66 % (1957568)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 8.61/1.66 % (1957568)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=249750219:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/373Mi)
% 8.61/1.66 % (1957560)Instruction limit reached!
% 8.61/1.66 % (1957560)------------------------------
% 8.61/1.66 % (1957560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.66 % (1957560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.66 % (1957560)CaDiCaL version: 2.1.3
% 8.61/1.66 % (1957560)Termination reason: Instruction limit
% 8.61/1.66 % (1957560)Termination phase: shuffling
% 8.61/1.66 % (1957560)Time elapsed: 0.017 s
% 8.61/1.66 % (1957560)Peak memory usage: 10 MB
% 8.61/1.66 % (1957560)Instructions burned: 28 (million)
% 9.15/1.74 % (1957566)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1731923382:i=227:sd=1:bd=all:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/227Mi)
% 9.15/1.74 % (1957573)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=343709830:i=116:ep=RSTC:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/116Mi)
% 9.15/1.74 % (1957464)Instruction limit reached!
% 9.15/1.74 % (1957464)------------------------------
% 9.15/1.74 % (1957464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.15/1.74 % (1957464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/1.74 % (1957464)CaDiCaL version: 2.1.3
% 9.15/1.74 % (1957464)Termination reason: Instruction limit
% 9.15/1.74 % (1957464)Termination phase: Saturation
% 9.15/1.74 % (1957464)Time elapsed: 0.862 s
% 9.15/1.74 % (1957464)Peak memory usage: 16 MB
% 9.15/1.74 % (1957464)Instructions burned: 1240 (million)
% 9.15/1.74 % (1957566)Refutation not found, incomplete strategy
% 9.15/1.74 % (1957566)------------------------------
% 9.15/1.74 % (1957566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.15/1.74 % (1957566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/1.74 % (1957566)CaDiCaL version: 2.1.3
% 9.15/1.74 % (1957566)Termination reason: Refutation not found, incomplete strategy
% 9.15/1.74 % (1957566)Time elapsed: 0.038 s
% 9.15/1.74 % (1957566)Peak memory usage: 12 MB
% 9.15/1.74 % (1957566)Instructions burned: 58 (million)
% 9.15/1.74 % (1957566)------------------------------
% 9.15/1.74 % (1957566)------------------------------
% 9.15/1.74 % (1957578)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=4117324265:i=575:rtra=on_2988 on theBenchmark for (2988ds/575Mi)
% 9.15/1.74 % (1957579)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1430372141:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2988 on theBenchmark for (2988ds/270Mi)
% 9.15/1.74 % (1957561)Instruction limit reached!
% 9.15/1.74 % (1957561)------------------------------
% 9.15/1.74 % (1957561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.15/1.74 % (1957561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/1.74 % (1957561)CaDiCaL version: 2.1.3
% 9.15/1.74 % (1957561)Termination reason: Instruction limit
% 9.15/1.74 % (1957561)Termination phase: Saturation
% 9.15/1.74 % (1957561)Time elapsed: 0.101 s
% 9.15/1.74 % (1957561)Peak memory usage: 12 MB
% 9.15/1.74 % (1957561)Instructions burned: 137 (million)
% 9.15/1.74 % (1957573)Instruction limit reached!
% 9.15/1.74 % (1957573)------------------------------
% 9.15/1.74 % (1957573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.15/1.74 % (1957573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/1.74 % (1957573)CaDiCaL version: 2.1.3
% 9.15/1.74 % (1957573)Termination reason: Instruction limit
% 9.15/1.74 % (1957573)Termination phase: Property scanning
% 9.15/1.74 % (1957573)Time elapsed: 0.080 s
% 9.15/1.74 % (1957573)Peak memory usage: 11 MB
% 9.15/1.74 % (1957573)Instructions burned: 116 (million)
% 9.15/1.74 % (1957584)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3191824493:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2988 on theBenchmark for (2988ds/9840Mi)
% 9.15/1.74 % (1957568)Instruction limit reached!
% 9.15/1.74 % (1957568)------------------------------
% 9.15/1.74 % (1957568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.15/1.74 % (1957568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/1.74 % (1957568)CaDiCaL version: 2.1.3
% 9.15/1.74 % (1957568)Termination reason: Instruction limit
% 9.15/1.74 % (1957568)Termination phase: Saturation
% 9.15/1.74 % (1957568)Time elapsed: 0.135 s
% 9.15/1.74 % (1957568)Peak memory usage: 12 MB
% 9.15/1.74 % (1957568)Instructions burned: 375 (million)
% 9.15/1.74 % (1957586)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2008545629:i=421:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/421Mi)
% 9.15/1.74 % (1957589)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 9.71/1.98 % (1957589)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2432723113:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/270Mi)
% 9.71/1.98 % (1957564)Instruction limit reached!
% 9.71/1.98 % (1957564)------------------------------
% 9.71/1.98 % (1957564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.71/1.98 % (1957564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/1.98 % (1957564)CaDiCaL version: 2.1.3
% 9.71/1.98 % (1957564)Termination reason: Instruction limit
% 9.71/1.98 % (1957564)Termination phase: Saturation
% 9.71/1.98 % (1957564)Time elapsed: 0.176 s
% 9.71/1.98 % (1957564)Peak memory usage: 12 MB
% 9.71/1.98 % (1957564)Instructions burned: 342 (million)
% 9.71/1.98 % (1957594)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=791736269:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/31Mi)
% 9.71/1.98 % (1957586)Refutation not found, incomplete strategy
% 9.71/1.98 % (1957586)------------------------------
% 9.71/1.98 % (1957586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.71/1.98 % (1957586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/1.98 % (1957586)CaDiCaL version: 2.1.3
% 9.71/1.98 % (1957586)Termination reason: Refutation not found, incomplete strategy
% 9.71/1.98 % (1957586)Time elapsed: 0.038 s
% 9.71/1.98 % (1957586)Peak memory usage: 12 MB
% 9.71/1.98 % (1957586)Instructions burned: 58 (million)
% 9.71/1.98 % (1957586)------------------------------
% 9.71/1.98 % (1957586)------------------------------
% 9.71/1.98 % (1957559)Instruction limit reached!
% 9.71/1.98 % (1957559)------------------------------
% 9.71/1.98 % (1957559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.71/1.98 % (1957559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/1.98 % (1957559)CaDiCaL version: 2.1.3
% 9.71/1.98 % (1957559)Termination reason: Instruction limit
% 9.71/1.98 % (1957559)Termination phase: Saturation
% 9.71/1.98 % (1957559)Time elapsed: 0.219 s
% 9.71/1.98 % (1957559)Peak memory usage: 13 MB
% 9.71/1.98 % (1957559)Instructions burned: 338 (million)
% 9.71/1.98 % (1957594)Instruction limit reached!
% 9.71/1.98 % (1957594)------------------------------
% 9.71/1.98 % (1957594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.71/1.98 % (1957594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/1.98 % (1957594)CaDiCaL version: 2.1.3
% 9.71/1.98 % (1957594)Termination reason: Instruction limit
% 9.71/1.98 % (1957594)Termination phase: Function definition elimination
% 9.71/1.98 % (1957594)Time elapsed: 0.013 s
% 9.71/1.98 % (1957594)Peak memory usage: 10 MB
% 9.71/1.98 % (1957594)Instructions burned: 34 (million)
% 9.71/1.98 % (1957600)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1839045864:i=111:add=on:fgj=on:rtra=on:fdi=1024_2987 on theBenchmark for (2987ds/111Mi)
% 9.71/1.98 % (1957598)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 9.71/1.98 % (1957598)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 9.71/1.98 % (1957598)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=152242443:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2987 on theBenchmark for (2987ds/1440Mi)
% 9.71/1.98 % (1957599)dis+10_2_sil=128000:si=on:random_seed=187294154:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2987 on theBenchmark for (2987ds/339Mi)
% 9.71/1.98 % (1957600)Instruction limit reached!
% 9.71/1.98 % (1957600)------------------------------
% 9.71/1.98 % (1957600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.71/1.98 % (1957600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/1.98 % (1957600)CaDiCaL version: 2.1.3
% 9.71/1.98 % (1957600)Termination reason: Instruction limit
% 9.71/1.98 % (1957600)Termination phase: Property scanning
% 9.71/1.98 % (1957600)Time elapsed: 0.039 s
% 9.71/1.98 % (1957600)Peak memory usage: 10 MB
% 9.71/1.98 % (1957600)Instructions burned: 111 (million)
% 9.71/1.98 % (1957589)Instruction limit reached!
% 9.71/1.98 % (1957589)------------------------------
% 12.14/2.09 % (1957589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.14/2.09 % (1957589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.14/2.09 % (1957589)CaDiCaL version: 2.1.3
% 12.14/2.09 % (1957589)Termination reason: Instruction limit
% 12.14/2.09 % (1957589)Termination phase: Saturation
% 12.14/2.09 % (1957589)Time elapsed: 0.102 s
% 12.14/2.09 % (1957589)Peak memory usage: 12 MB
% 12.14/2.09 % (1957589)Instructions burned: 272 (million)
% 12.14/2.09 % (1957599)Refutation not found, incomplete strategy
% 12.14/2.09 % (1957599)------------------------------
% 12.14/2.09 % (1957599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.14/2.09 % (1957599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.14/2.09 % (1957599)CaDiCaL version: 2.1.3
% 12.14/2.09 % (1957599)Termination reason: Refutation not found, incomplete strategy
% 12.14/2.09 % (1957599)Time elapsed: 0.040 s
% 12.14/2.09 % (1957599)Peak memory usage: 12 MB
% 12.14/2.09 % (1957599)Instructions burned: 61 (million)
% 12.14/2.09 % (1957599)------------------------------
% 12.14/2.09 % (1957599)------------------------------
% 12.14/2.09 % (1957579)Instruction limit reached!
% 12.14/2.09 % (1957579)------------------------------
% 12.14/2.09 % (1957579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.14/2.09 % (1957579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.14/2.09 % (1957579)CaDiCaL version: 2.1.3
% 12.14/2.09 % (1957579)Termination reason: Instruction limit
% 12.14/2.09 % (1957579)Termination phase: Saturation
% 12.14/2.09 % (1957579)Time elapsed: 0.190 s
% 12.14/2.09 % (1957579)Peak memory usage: 12 MB
% 12.14/2.09 % (1957579)Instructions burned: 271 (million)
% 12.14/2.09 % (1957608)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2640759605:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2986 on theBenchmark for (2986ds/122Mi)
% 12.14/2.09 % (1957609)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=2997539723:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/136Mi)
% 12.14/2.09 % (1957608)Refutation not found, incomplete strategy
% 12.14/2.09 % (1957608)------------------------------
% 12.14/2.09 % (1957608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.14/2.09 % (1957608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.14/2.09 % (1957608)CaDiCaL version: 2.1.3
% 12.14/2.09 % (1957608)Termination reason: Refutation not found, incomplete strategy
% 12.14/2.09 % (1957608)Time elapsed: 0.020 s
% 12.14/2.09 % (1957608)Peak memory usage: 12 MB
% 12.14/2.09 % (1957608)Instructions burned: 59 (million)
% 12.14/2.09 % (1957608)------------------------------
% 12.14/2.09 % (1957608)------------------------------
% 12.14/2.09 % (1957610)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=589713065:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2986 on theBenchmark for (2986ds/232Mi)
% 12.14/2.09 % (1957611)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=248267899:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2986 on theBenchmark for (2986ds/1254Mi)
% 12.14/2.09 % (1957616)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 12.14/2.09 % (1957616)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=1657138859:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2986 on theBenchmark for (2986ds/281Mi)
% 12.14/2.09 % (1957609)Instruction limit reached!
% 12.14/2.09 % (1957609)------------------------------
% 12.14/2.09 % (1957609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.14/2.09 % (1957609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.14/2.09 % (1957609)CaDiCaL version: 2.1.3
% 12.14/2.09 % (1957609)Termination reason: Instruction limit
% 12.14/2.09 % (1957609)Termination phase: Property scanning
% 12.14/2.09 % (1957609)Time elapsed: 0.053 s
% 12.14/2.09 % (1957609)Peak memory usage: 10 MB
% 12.14/2.09 % (1957609)Instructions burned: 138 (million)
% 12.14/2.09 % (1957610)Refutation not found, incomplete strategy
% 12.14/2.09 % (1957610)------------------------------
% 12.14/2.09 % (1957610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957610)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957610)Termination reason: Refutation not found, incomplete strategy
% 13.02/2.23 % (1957610)Time elapsed: 0.039 s
% 13.02/2.23 % (1957610)Peak memory usage: 12 MB
% 13.02/2.23 % (1957610)Instructions burned: 59 (million)
% 13.02/2.23 % (1957610)------------------------------
% 13.02/2.23 % (1957610)------------------------------
% 13.02/2.23 % (1957623)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2532112794:i=619:add=on:rtra=on_2985 on theBenchmark for (2985ds/619Mi)
% 13.02/2.23 % (1957625)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3940676905:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/865Mi)
% 13.02/2.23 % (1957578)Refutation not found, incomplete strategy
% 13.02/2.23 % (1957578)------------------------------
% 13.02/2.23 % (1957578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957578)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957578)Termination reason: Refutation not found, incomplete strategy
% 13.02/2.23 % (1957578)Time elapsed: 0.340 s
% 13.02/2.23 % (1957578)Peak memory usage: 15 MB
% 13.02/2.23 % (1957578)Instructions burned: 503 (million)
% 13.02/2.23 % (1957578)------------------------------
% 13.02/2.23 % (1957578)------------------------------
% 13.02/2.23 % (1957632)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3435918865:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2984 on theBenchmark for (2984ds/212Mi)
% 13.02/2.23 % (1957616)Instruction limit reached!
% 13.02/2.23 % (1957616)------------------------------
% 13.02/2.23 % (1957616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957616)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957616)Termination reason: Instruction limit
% 13.02/2.23 % (1957616)Termination phase: Saturation
% 13.02/2.23 % (1957616)Time elapsed: 0.186 s
% 13.02/2.23 % (1957616)Peak memory usage: 12 MB
% 13.02/2.23 % (1957616)Instructions burned: 282 (million)
% 13.02/2.23 % (1957632)Instruction limit reached!
% 13.02/2.23 % (1957632)------------------------------
% 13.02/2.23 % (1957632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957632)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957632)Termination reason: Instruction limit
% 13.02/2.23 % (1957632)Termination phase: Saturation
% 13.02/2.23 % (1957632)Time elapsed: 0.088 s
% 13.02/2.23 % (1957632)Peak memory usage: 12 MB
% 13.02/2.23 % (1957632)Instructions burned: 213 (million)
% 13.02/2.23 % (1957638)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2407998153:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/130Mi)
% 13.02/2.23 % (1957641)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=160464075:st=1.5:i=346:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/346Mi)
% 13.02/2.23 % (1957641)Refutation not found, incomplete strategy
% 13.02/2.23 % (1957641)------------------------------
% 13.02/2.23 % (1957641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957641)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957641)Termination reason: Refutation not found, incomplete strategy
% 13.02/2.23 % (1957641)Time elapsed: 0.011 s
% 13.02/2.23 % (1957641)Peak memory usage: 12 MB
% 13.02/2.23 % (1957641)Instructions burned: 25 (million)
% 13.02/2.23 % (1957641)------------------------------
% 13.02/2.23 % (1957641)------------------------------
% 13.02/2.23 % (1957638)Refutation not found, incomplete strategy
% 13.02/2.23 % (1957638)------------------------------
% 13.02/2.23 % (1957638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.02/2.23 % (1957638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.23 % (1957638)CaDiCaL version: 2.1.3
% 13.02/2.23 % (1957638)Termination reason: Refutation not found, incomplete strategy
% 13.02/2.23 % (1957638)Time elapsed: 0.038 s
% 13.02/2.23 % (1957638)Peak memory usage: 12 MB
% 14.35/2.54 % (1957638)Instructions burned: 60 (million)
% 14.35/2.54 % (1957638)------------------------------
% 14.35/2.54 % (1957638)------------------------------
% 14.35/2.54 % (1957645)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2087860384:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2983 on theBenchmark for (2983ds/152Mi)
% 14.35/2.54 % (1957646)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3177036793:i=75:ep=R:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/75Mi)
% 14.35/2.54 % (1957611)Refutation not found, incomplete strategy
% 14.35/2.54 % (1957611)------------------------------
% 14.35/2.54 % (1957611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.35/2.54 % (1957611)CaDiCaL version: 2.1.3
% 14.35/2.54 % (1957611)Termination reason: Refutation not found, incomplete strategy
% 14.35/2.54 % (1957611)Time elapsed: 0.328 s
% 14.35/2.54 % (1957611)Peak memory usage: 15 MB
% 14.35/2.54 % (1957611)Instructions burned: 470 (million)
% 14.35/2.54 % (1957611)------------------------------
% 14.35/2.54 % (1957611)------------------------------
% 14.35/2.54 % (1957623)Refutation not found, incomplete strategy
% 14.35/2.54 % (1957623)------------------------------
% 14.35/2.54 % (1957623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.35/2.54 % (1957623)CaDiCaL version: 2.1.3
% 14.35/2.54 % (1957623)Termination reason: Refutation not found, incomplete strategy
% 14.35/2.54 % (1957623)Time elapsed: 0.289 s
% 14.35/2.54 % (1957623)Peak memory usage: 15 MB
% 14.35/2.54 % (1957623)Instructions burned: 466 (million)
% 14.35/2.54 % (1957623)------------------------------
% 14.35/2.54 % (1957623)------------------------------
% 14.35/2.54 % (1957652)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=1145950188:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/387Mi)
% 14.35/2.54 % (1957646)Instruction limit reached!
% 14.35/2.54 % (1957646)------------------------------
% 14.35/2.54 % (1957646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.35/2.54 % (1957646)CaDiCaL version: 2.1.3
% 14.35/2.54 % (1957646)Termination reason: Instruction limit
% 14.35/2.54 % (1957646)Termination phase: Property scanning
% 14.35/2.54 % (1957646)Time elapsed: 0.058 s
% 14.35/2.54 % (1957646)Peak memory usage: 10 MB
% 14.35/2.54 % (1957646)Instructions burned: 76 (million)
% 14.35/2.54 % (1957652)Refutation not found, incomplete strategy
% 14.35/2.54 % (1957652)------------------------------
% 14.35/2.54 % (1957652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.35/2.54 % (1957652)CaDiCaL version: 2.1.3
% 14.35/2.54 % (1957652)Termination reason: Refutation not found, incomplete strategy
% 14.35/2.54 % (1957652)Time elapsed: 0.019 s
% 14.35/2.54 % (1957652)Peak memory usage: 12 MB
% 14.35/2.54 % (1957652)Instructions burned: 25 (million)
% 14.35/2.54 % (1957652)------------------------------
% 14.35/2.54 % (1957652)------------------------------
% 14.35/2.54 % (1957654)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3420436456:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2982 on theBenchmark for (2982ds/148Mi)
% 14.35/2.54 % (1957657)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=624352912:i=161:piset=and:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/161Mi)
% 14.35/2.54 % (1957625)Instruction limit reached!
% 14.35/2.54 % (1957625)------------------------------
% 14.35/2.54 % (1957625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.35/2.54 % (1957625)CaDiCaL version: 2.1.3
% 14.35/2.54 % (1957625)Termination reason: Instruction limit
% 14.35/2.54 % (1957625)Termination phase: Saturation
% 14.35/2.54 % (1957625)Time elapsed: 0.324 s
% 14.35/2.54 % (1957625)Peak memory usage: 18 MB
% 14.35/2.54 % (1957625)Instructions burned: 868 (million)
% 14.35/2.54 % (1957645)Instruction limit reached!
% 14.35/2.54 % (1957645)------------------------------
% 14.35/2.54 % (1957645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.35/2.54 % (1957645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957645)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957645)Termination reason: Instruction limit
% 15.21/2.73 % (1957645)Termination phase: Property scanning
% 15.21/2.73 % (1957645)Time elapsed: 0.107 s
% 15.21/2.73 % (1957645)Peak memory usage: 11 MB
% 15.21/2.73 % (1957645)Instructions burned: 153 (million)
% 15.21/2.73 % (1957659)lrs+10_1_sil=128000:si=on:random_seed=3531041384:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/888Mi)
% 15.21/2.73 % (1957663)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=631669463:i=88:s2at=3:nm=2:rtra=on:rawr=on_2982 on theBenchmark for (2982ds/88Mi)
% 15.21/2.73 % (1957661)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=1591895349:i=136:add=on:ins=4:rtra=on:sup=off_2982 on theBenchmark for (2982ds/136Mi)
% 15.21/2.73 % (1957663)Instruction limit reached!
% 15.21/2.73 % (1957663)------------------------------
% 15.21/2.73 % (1957663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957663)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957663)Termination reason: Instruction limit
% 15.21/2.73 % (1957663)Termination phase: Property scanning
% 15.21/2.73 % (1957663)Time elapsed: 0.034 s
% 15.21/2.73 % (1957663)Peak memory usage: 11 MB
% 15.21/2.73 % (1957663)Instructions burned: 90 (million)
% 15.21/2.73 % (1957669)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1233419065:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2981 on theBenchmark for (2981ds/93Mi)
% 15.21/2.73 % (1957657)Instruction limit reached!
% 15.21/2.73 % (1957657)------------------------------
% 15.21/2.73 % (1957657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957657)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957657)Termination reason: Instruction limit
% 15.21/2.73 % (1957657)Termination phase: Saturation
% 15.21/2.73 % (1957657)Time elapsed: 0.093 s
% 15.21/2.73 % (1957657)Peak memory usage: 12 MB
% 15.21/2.73 % (1957657)Instructions burned: 162 (million)
% 15.21/2.73 % (1957661)Instruction limit reached!
% 15.21/2.73 % (1957661)------------------------------
% 15.21/2.73 % (1957661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957661)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957661)Termination reason: Instruction limit
% 15.21/2.73 % (1957661)Termination phase: Property scanning
% 15.21/2.73 % (1957661)Time elapsed: 0.076 s
% 15.21/2.73 % (1957661)Peak memory usage: 11 MB
% 15.21/2.73 % (1957661)Instructions burned: 137 (million)
% 15.21/2.73 % (1957654)Instruction limit reached!
% 15.21/2.73 % (1957654)------------------------------
% 15.21/2.73 % (1957654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957654)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957654)Termination reason: Instruction limit
% 15.21/2.73 % (1957654)Termination phase: Saturation
% 15.21/2.73 % (1957654)Time elapsed: 0.118 s
% 15.21/2.73 % (1957654)Peak memory usage: 12 MB
% 15.21/2.73 % (1957654)Instructions burned: 149 (million)
% 15.21/2.73 % (1957676)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1275673734:i=2186:rtra=on:ixr=off_2981 on theBenchmark for (2981ds/2186Mi)
% 15.21/2.73 % (1957684)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2937294079:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2981 on theBenchmark for (2981ds/805Mi)
% 15.21/2.73 % (1957681)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3527707780:s2a=on:i=240:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/240Mi)
% 15.21/2.73 % (1957669)Instruction limit reached!
% 15.21/2.73 % (1957669)------------------------------
% 15.21/2.73 % (1957669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957669)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957669)Termination reason: Instruction limit
% 15.21/2.73 % (1957669)Termination phase: Property scanning
% 15.21/2.73 % (1957669)Time elapsed: 0.059 s
% 15.21/2.73 % (1957669)Peak memory usage: 11 MB
% 15.21/2.73 % (1957669)Instructions burned: 94 (million)
% 15.21/2.73 % (1957691)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 15.21/2.73 % (1957691)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=74808215:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2980 on theBenchmark for (2980ds/391Mi)
% 15.21/2.73 % (1957691)Refutation not found, incomplete strategy
% 15.21/2.73 % (1957691)------------------------------
% 15.21/2.73 % (1957691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957691)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957691)Termination reason: Refutation not found, incomplete strategy
% 15.21/2.73 % (1957691)Time elapsed: 0.014 s
% 15.21/2.73 % (1957691)Peak memory usage: 12 MB
% 15.21/2.73 % (1957691)Instructions burned: 29 (million)
% 15.21/2.73 % (1957691)------------------------------
% 15.21/2.73 % (1957691)------------------------------
% 15.21/2.73 % (1957699)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=4161206273:i=355:av=off:fsr=off:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/355Mi)
% 15.21/2.73 % (1957681)Instruction limit reached!
% 15.21/2.73 % (1957681)------------------------------
% 15.21/2.73 % (1957681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957681)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957681)Termination reason: Instruction limit
% 15.21/2.73 % (1957681)Termination phase: Saturation
% 15.21/2.73 % (1957681)Time elapsed: 0.127 s
% 15.21/2.73 % (1957681)Peak memory usage: 12 MB
% 15.21/2.73 % (1957681)Instructions burned: 240 (million)
% 15.21/2.73 % (1957598) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1957387-1957598"...
% 15.21/2.73 % (1957711)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=1323105277:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/314Mi)
% 15.21/2.73 % (1957684)Instruction limit reached!
% 15.21/2.73 % (1957684)------------------------------
% 15.21/2.73 % (1957684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957684)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957684)Termination reason: Instruction limit
% 15.21/2.73 % (1957684)Termination phase: Saturation
% 15.21/2.73 % (1957684)Time elapsed: 0.204 s
% 15.21/2.73 % (1957684)Peak memory usage: 14 MB
% 15.21/2.73 % (1957684)Instructions burned: 808 (million)
% 15.21/2.73 % (1957711)Refutation not found, incomplete strategy
% 15.21/2.73 % (1957711)------------------------------
% 15.21/2.73 % (1957711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957711)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957711)Termination reason: Refutation not found, incomplete strategy
% 15.21/2.73 % (1957711)Time elapsed: 0.037 s
% 15.21/2.73 % (1957711)Peak memory usage: 12 MB
% 15.21/2.73 % (1957711)Instructions burned: 62 (million)
% 15.21/2.73 % (1957711)------------------------------
% 15.21/2.73 % (1957711)------------------------------
% 15.21/2.73 % (1957718)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=2687050617:s2a=on:i=251:fsr=off:rtra=on_2978 on theBenchmark for (2978ds/251Mi)
% 15.21/2.73 % (1957719)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=775822966:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2978 on theBenchmark for (2978ds/2470Mi)
% 15.21/2.73 % (1957718)Instruction limit reached!
% 15.21/2.73 % (1957718)------------------------------
% 15.21/2.73 % (1957718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957718)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957718)Termination reason: Instruction limit
% 15.21/2.73 % (1957718)Termination phase: Saturation
% 15.21/2.73 % (1957718)Time elapsed: 0.093 s
% 15.21/2.73 % (1957718)Peak memory usage: 12 MB
% 15.21/2.73 % (1957718)Instructions burned: 253 (million)
% 15.21/2.73 % (1957699)Instruction limit reached!
% 15.21/2.73 % (1957699)------------------------------
% 15.21/2.73 % (1957699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957699)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957699)Termination reason: Instruction limit
% 15.21/2.73 % (1957699)Termination phase: Saturation
% 15.21/2.73 % (1957699)Time elapsed: 0.236 s
% 15.21/2.73 % (1957699)Peak memory usage: 12 MB
% 15.21/2.73 % (1957699)Instructions burned: 355 (million)
% 15.21/2.73 % (1957725)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=2681845465:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2977 on theBenchmark for (2977ds/673Mi)
% 15.21/2.73 % (1957726)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3077140348:i=116:ep=RSTC:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/116Mi)
% 15.21/2.73 % (1957726)Instruction limit reached!
% 15.21/2.73 % (1957726)------------------------------
% 15.21/2.73 % (1957726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957726)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957726)Termination reason: Instruction limit
% 15.21/2.73 % (1957726)Termination phase: Property scanning
% 15.21/2.73 % (1957726)Time elapsed: 0.049 s
% 15.21/2.73 % (1957726)Peak memory usage: 10 MB
% 15.21/2.73 % (1957726)Instructions burned: 117 (million)
% 15.21/2.73 % (1957729)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3036237648:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2977 on theBenchmark for (2977ds/270Mi)
% 15.21/2.73 % (1957659)Instruction limit reached!
% 15.21/2.73 % (1957659)------------------------------
% 15.21/2.73 % (1957659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.73 % (1957659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.73 % (1957659)CaDiCaL version: 2.1.3
% 15.21/2.73 % (1957659)Termination reason: Instruction limit
% 15.21/2.73 % (1957659)Termination phase: Saturation
% 15.21/2.73 % (1957659)Time elapsed: 0.591 s
% 15.21/2.73 % (1957659)Peak memory usage: 15 MB
% 15.21/2.73 % (1957659)Instructions burned: 889 (million)
% 15.21/2.73 % (1957598)...printing done.
% 15.21/2.73 % (1957731)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1790379219:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2976 on theBenchmark for (2976ds/30Mi)
% 15.21/2.73 % (1957598)Refutation found. Thanks to Tanya!
% 15.21/2.73 % SZS status ContradictoryAxioms for theBenchmark
% 15.21/2.73 % SZS output start Proof for theBenchmark
% See solution above
% 15.21/2.78 % (1957598)------------------------------
% 15.21/2.78 % (1957598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.21/2.78 % (1957598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.21/2.78 % (1957598)CaDiCaL version: 2.1.3
% 15.21/2.78 % (1957598)Termination reason: Refutation
% 15.21/2.78 % (1957598)Time elapsed: 1.100 s
% 15.21/2.78 % (1957598)Peak memory usage: 17 MB
% 15.21/2.78 % (1957598)Instructions burned: 1516 (million)
% 15.21/2.78 % (1957387)Success in time 2.448 s
% 15.21/2.78 % Vampire exiting
%------------------------------------------------------------------------------