%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO904^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:37 AM UTC 2026
% Result : ContradictoryAxioms 8.40s 1.68s
% Output : Refutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 158
% Number of leaves : 33
% Syntax : Number of formulae : 1340 ( 113 unt; 0 typ; 18 def)
% Number of atoms : 63731 (14037 equ; 0 cnn)
% Maximal formula atoms : 159 ( 47 avg)
% Number of connectives : 98000 (1726 ~;13759 |;4374 &;63370 @)
% ( 18 <=>;6426 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 21 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 392 ( 392 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 109 usr; 25 con; 0-4 aty)
% (6096 !!;2231 ??; 0 @@+; 0 @@-)
% Number of variables : 23000 ( 80 sgn13707 !; 2 ?;23000 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vIFF: $o > $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: mworld > mworld ).
thf(func_def_54,type,
sK2: mworld > mworld ).
thf(func_def_55,type,
sK3: mworld > mworld ).
thf(func_def_56,type,
sK4: mworld > mworld ).
thf(func_def_57,type,
sK5: mworld > mworld ).
thf(func_def_58,type,
sK6: mworld > mworld ).
thf(func_def_59,type,
sK7: mworld > mworld ).
thf(func_def_60,type,
sK8: mworld > mworld ).
thf(func_def_61,type,
sK9: mworld > mworld ).
thf(func_def_62,type,
sK10: mworld > mworld ).
thf(func_def_63,type,
sK11: mworld > mworld ).
thf(func_def_64,type,
sK12: mworld > mworld ).
thf(func_def_65,type,
sK13: mworld > mworld ).
thf(func_def_66,type,
sK14: mworld > mworld ).
thf(func_def_67,type,
sK15: mworld > mworld ).
thf(func_def_68,type,
sK16: mworld > mworld ).
thf(func_def_69,type,
sK17: mworld > mworld ).
thf(func_def_70,type,
sK18: mworld > mworld ).
thf(func_def_71,type,
sK19: mworld > mworld ).
thf(func_def_72,type,
sK20: mworld > mworld ).
thf(func_def_73,type,
sK21: mworld > mworld ).
thf(func_def_74,type,
sK22: mworld > mworld ).
thf(func_def_75,type,
sK23: mworld > mworld ).
thf(func_def_76,type,
sK24: mworld > mworld ).
thf(func_def_77,type,
sK25: mworld > mworld ).
thf(func_def_78,type,
sK26: mworld > mworld ).
thf(func_def_79,type,
sK27: mworld > mworld ).
thf(func_def_80,type,
sK28: mworld > mworld ).
thf(func_def_81,type,
sK29: mworld > mworld ).
thf(func_def_82,type,
sK30: mworld > mworld ).
thf(func_def_83,type,
sK31: mworld > mworld ).
thf(func_def_84,type,
sK32: mworld > mworld ).
thf(func_def_85,type,
sK33: mworld > mworld ).
thf(func_def_86,type,
sK34: mworld > mworld ).
thf(func_def_87,type,
sK35: mworld > mworld ).
thf(func_def_88,type,
sK36: mworld > mworld ).
thf(func_def_89,type,
sK37: mworld > mworld ).
thf(func_def_90,type,
sK38: mworld > mworld ).
thf(func_def_91,type,
sK39: mworld > mworld ).
thf(func_def_92,type,
sK40: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
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] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ 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(f13,axiom,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod4) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod6) ).
thf(f17,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod8) ).
thf(f32,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod23) ).
thf(f34,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod25) ).
thf(f39,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod30) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod36) ).
thf(f60,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X0: mworld] : $true ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) )
@ ( mdia
@ ^ [X0: mworld] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alt1) ).
thf(f63,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f64,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f68,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f67]) ).
thf(f75,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f92,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f93,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f95,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f97,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f106,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f107,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f106]) ).
thf(f112,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f113,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f118,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) )
= mdia ),
inference(rectify,[],[f8]) ).
thf(f119,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f124,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f125,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f128,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f129,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f128]) ).
thf(f136,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f137,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f136]) ).
thf(f138,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(f139,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,[],[f138]) ).
thf(f176,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X1 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f177,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X1 @ X0 )
= $true ),
inference(fool_elimination,[],[f176]) ).
thf(f182,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f183,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f182]) ).
thf(f185,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f192,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f195,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f137]) ).
thf(f199,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,[],[f139]) ).
thf(f200,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f204,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f68]) ).
thf(f207,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f208,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f107]) ).
thf(f209,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f183]) ).
thf(f230,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f64]) ).
thf(f232,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f234,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f129]) ).
thf(f237,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f241,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f93]) ).
thf(f245,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X1 @ X0 )
= $true ),
inference(cnf_transformation,[],[f177]) ).
thf(f248,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v28
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v14
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f185,f237,f234,f192,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f192,f232,f234,f192,f234,f234,f234,f234,f234]) ).
thf(f256,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v26
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f195,f237,f234,f192,f232,f234,f234,f192,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f192,f232,f234,f234,f234,f232]) ).
thf(f260,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v5 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v5 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v6 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v8 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v13 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v14 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v23 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v23 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) ) ),
inference(definition_unfolding,[],[f199,f237,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f209,f234,f207,f207,f207,f207,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f207,f207,f207,f207,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f207,f207,f207,f207,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f209,f207,f207,f232,f207,f207,f207,f207]) ).
thf(f261,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] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v25 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v13
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v10
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f200,f237,f234,f234,f234,f234,f192,f232,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f192,f234,f234,f234,f192,f234,f234,f234,f234,f232]) ).
thf(f265,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 > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v26 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v18 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f204,f237,f234,f234,f234,f192,f232,f234,f234,f234,f234,f234,f234,f234,f234,f192,f232,f234,f234,f234,f192,f232,f234,f234,f234,f234,f234,f234,f234,f234,f234,f232]) ).
thf(f267,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] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v25
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v23
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f208,f237,f234,f234,f234,f234,f192,f234,f234,f192,f234,f192,f232,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f232]) ).
thf(f288,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v22
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f230,f237,f234,f192,f232,f234,f234,f234,f234,f192,f232,f234,f234,f192,f234,f234,f234,f234]) ).
thf(f296,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 > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v9 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f241,f237,f234,f234,f234,f234,f234,f234,f234,f192,f232,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f234,f192,f232,f234,f192,f232,f234,f234,f234,f234]) ).
thf(f549,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y19 ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f550,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y19 ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f549]) ).
thf(f551,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f550]) ).
thf(f552,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f551]) ).
thf(f553,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f552]) ).
thf(f554,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f553]) ).
thf(f555,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f554]) ).
thf(f556,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f555]) ).
thf(f557,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f556]) ).
thf(f558,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f557]) ).
thf(f559,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f558]) ).
thf(f560,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f559]) ).
thf(f561,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f560]) ).
thf(f562,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f561]) ).
thf(f563,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f562]) ).
thf(f564,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f563]) ).
thf(f565,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f564]) ).
thf(f566,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f565]) ).
thf(f567,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f566]) ).
thf(f568,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f567]) ).
thf(f569,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f568]) ).
thf(f570,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( 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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f569]) ).
thf(f571,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ~ ( v22 @ X7 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f570]) ).
thf(f572,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ~ ( v22 @ X7 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f571]) ).
thf(f573,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(not_proxy_clausification,[],[f572]) ).
thf(f574,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f575,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f575]) ).
thf(f577,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f576]) ).
thf(f578,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f577]) ).
thf(f579,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f578]) ).
thf(f580,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 @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f581,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 )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f580]) ).
thf(f582,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 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f582]) ).
thf(f584,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 )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f583]) ).
thf(f585,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 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f584]) ).
thf(f586,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f585]) ).
thf(f587,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 @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f586]) ).
thf(f588,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 @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f587]) ).
thf(f589,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f588]) ).
thf(f590,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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f589]) ).
thf(f591,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f590]) ).
thf(f592,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 @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f591]) ).
thf(f593,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $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 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f592]) ).
thf(f594,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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f593]) ).
thf(f595,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f594]) ).
thf(f596,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 @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f595]) ).
thf(f597,plain,
! [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 @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f596]) ).
thf(f598,plain,
! [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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f597]) ).
thf(f599,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 @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f598]) ).
thf(f600,plain,
! [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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) )
@ X17 ) ) ),
inference(pi_proxy_clausification,[],[f599]) ).
thf(f601,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f600]) ).
thf(f602,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] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f601]) ).
thf(f603,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) )
@ X18 )
= $true ) ),
inference(pi_proxy_clausification,[],[f602]) ).
thf(f604,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 @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f603]) ).
thf(f605,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(imp_proxy_clausification,[],[f604]) ).
thf(f606,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X1: mworld,X4: mworld,X6: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
| ~ ( v10 @ X19 ) ) ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f606]) ).
thf(f608,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X8: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
| ~ ( v10 @ X19 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X7: mworld,X6: mworld,X4: mworld,X16: mworld,X14: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ~ ( v10 @ X19 ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f608]) ).
thf(f610,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X6: mworld,X4: mworld,X16: mworld,X7: 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 @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ~ ( v10 @ X19 ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) )
@ X20 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(pi_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X19: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) )
@ X20 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(not_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X6: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X19 @ X20 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X20 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f611]) ).
thf(f613,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X20 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X9: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ~ ( v9 @ X20 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f615,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X9: mworld,X1: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) )
@ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v9 @ X20 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f614]) ).
thf(f616,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,X8: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) )
@ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f615]) ).
thf(f617,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(beta-eta_normalization,[],[f616]) ).
thf(f618,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X18: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f617]) ).
thf(f619,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X1: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) )
@ X22 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v10 @ X19 )
= $false ) ),
inference(pi_proxy_clausification,[],[f618]) ).
thf(f620,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X16: mworld,X9: mworld,X4: mworld,X14: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( ( mrel @ X21 @ X22 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(beta-eta_normalization,[],[f619]) ).
thf(f621,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,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f620]) ).
thf(f622,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X14: mworld,X18: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) )
@ X23 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f621]) ).
thf(f623,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X22 @ X23 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(beta-eta_normalization,[],[f622]) ).
thf(f624,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $false ) ),
inference(imp_proxy_clausification,[],[f623]) ).
thf(f625,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( v5 @ Y0 ) )
@ X24 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) ) ),
inference(pi_proxy_clausification,[],[f624]) ).
thf(f626,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v10 @ X19 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( ( mrel @ X23 @ X24 )
=> ( v5 @ X24 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f625]) ).
thf(f627,plain,
! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( ( v10 @ X19 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f626]) ).
thf(f678,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 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& $true ) ) )
= $true ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f680,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 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f678]) ).
thf(f681,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( ( mrel @ Y26 @ Y27 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ( v5 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& ~ ( v5 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v6 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v6 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v7 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v7 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v8 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v8 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v13 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v13 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v14 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v14 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v15 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v15 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v16 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v16 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v21 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v21 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v22 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v22 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v23 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v23 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v24 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v24 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f680]) ).
thf(f682,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 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& $true ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f681]) ).
thf(f683,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 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& $true ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f682]) ).
thf(f685,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 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f683]) ).
thf(f686,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ( v5 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& ~ ( v5 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v6 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v6 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v7 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v7 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v8 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v8 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v14 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v14 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v15 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v15 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v16 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v16 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v21 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v21 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v22 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v22 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v23 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v23 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v24 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v24 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f685]) ).
thf(f687,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f686]) ).
thf(f688,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
& $true ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f690,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 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f688]) ).
thf(f691,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ( v5 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& ~ ( v5 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v6 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v6 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v7 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v7 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v8 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v8 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v13 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v13 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v14 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v14 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v15 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v15 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v16 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v16 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v21 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v21 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v22 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v22 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v23 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v23 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v24 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v24 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f690]) ).
thf(f692,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
& $true ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f691]) ).
thf(f693,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( 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 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
& $true ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f692]) ).
thf(f695,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f693]) ).
thf(f696,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 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ( v5 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& ~ ( v5 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v6 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v6 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v7 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v7 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v8 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v8 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v13 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v13 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v14 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v14 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v15 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v15 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v16 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v16 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v21 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v21 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v22 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v22 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v23 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v23 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v24 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v24 @ Y1 ) ) ) ) )
@ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f695]) ).
thf(f697,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f696]) ).
thf(f698,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f697]) ).
thf(f699,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ~ ( v24 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f698]) ).
thf(f700,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f698]) ).
thf(f701,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( 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 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ( v5 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& ~ ( v5 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v6 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v6 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v7 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v7 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v8 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v8 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v13 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v13 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v14 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v14 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v15 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v15 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v16 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v16 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v21 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v21 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v22 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v22 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v23 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v23 @ Y1 ) ) ) ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f700]) ).
thf(f702,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f701]) ).
thf(f703,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f702]) ).
thf(f704,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ( v23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f703]) ).
thf(f705,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f703]) ).
thf(f706,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ( v5 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& ~ ( v5 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v6 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v6 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v7 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v7 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v8 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v8 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v13 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v13 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v14 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v14 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v15 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v15 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v16 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v16 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v21 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v21 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v22 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v22 @ Y1 ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f705]) ).
thf(f707,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 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f706]) ).
thf(f708,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 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f707]) ).
thf(f709,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f708]) ).
thf(f710,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $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 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f708]) ).
thf(f711,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 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ( v5 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& ~ ( v5 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v6 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v6 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v7 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v7 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v8 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v8 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v13 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v13 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v14 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v14 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v15 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v15 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v16 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v16 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v21 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v21 @ Y1 ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f710]) ).
thf(f712,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 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f711]) ).
thf(f713,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ( v21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
& ~ ( v21 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f712]) ).
thf(f715,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f713]) ).
thf(f716,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ( v5 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& ~ ( v5 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v6 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v6 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v7 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v7 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v8 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v8 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v13 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v13 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v14 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v14 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v15 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v15 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v16 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v16 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f715]) ).
thf(f717,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X7 @ X8 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f716]) ).
thf(f718,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
& $true ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f717]) ).
thf(f720,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(and_proxy_clausification,[],[f718]) ).
thf(f721,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ( v5 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& ~ ( v5 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v6 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v6 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v7 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v7 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v8 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v8 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v13 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v13 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v14 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v14 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v15 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v15 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v16 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v16 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X9 ) ) ),
inference(pi_proxy_clausification,[],[f720]) ).
thf(f722,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ( mrel @ X8 @ X9 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
& $true ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f721]) ).
thf(f723,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
& $true ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f722]) ).
thf(f725,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f723]) ).
thf(f726,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ( v5 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& ~ ( v5 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v6 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v6 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v7 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v7 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v8 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v8 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v13 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v13 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v14 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v14 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v15 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v15 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v16 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v16 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X10 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f725]) ).
thf(f727,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f726]) ).
thf(f728,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 @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
& $true ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f727]) ).
thf(f730,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f728]) ).
thf(f731,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ( v5 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& ~ ( v5 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v6 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v6 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v7 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v7 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v8 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v8 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v13 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v13 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v14 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v14 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v15 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v15 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v16 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v16 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f730]) ).
thf(f732,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 @ X2 @ X3 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f731]) ).
thf(f733,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
& $true ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f732]) ).
thf(f735,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 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f733]) ).
thf(f736,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ( v5 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& ~ ( v5 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v6 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v6 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v7 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v7 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v13 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v13 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v14 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v14 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v15 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v15 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v16 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v16 @ Y1 ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f735]) ).
thf(f737,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( mrel @ X11 @ X12 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f736]) ).
thf(f738,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f737]) ).
thf(f739,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ~ ( v16 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f738]) ).
thf(f740,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
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(and_proxy_clausification,[],[f738]) ).
thf(f741,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ( v5 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& ~ ( v5 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v6 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v6 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v7 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v7 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v8 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v8 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v13 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v13 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v14 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v14 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v15 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v15 @ Y1 ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f740]) ).
thf(f742,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 @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f741]) ).
thf(f743,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f742]) ).
thf(f744,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ~ ( v15 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f743]) ).
thf(f745,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ 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 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f743]) ).
thf(f746,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 @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ( v5 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& ~ ( v5 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v6 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v6 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v8 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v8 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v13 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v13 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v14 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v14 @ Y1 ) ) ) ) )
@ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f745]) ).
thf(f747,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 @ X11 @ X12 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f746]) ).
thf(f748,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 @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f747]) ).
thf(f749,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ( v14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(and_proxy_clausification,[],[f748]) ).
thf(f750,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f748]) ).
thf(f751,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ( v5 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& ~ ( v5 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v6 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v6 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v7 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v7 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v8 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v8 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v13 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v13 @ Y1 ) ) ) ) )
@ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f750]) ).
thf(f752,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f751]) ).
thf(f753,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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $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 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f752]) ).
thf(f754,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f753]) ).
thf(f755,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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $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 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(and_proxy_clausification,[],[f753]) ).
thf(f756,plain,
! [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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ( v5 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& ~ ( v5 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v7 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v7 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v8 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v8 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X16 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f755]) ).
thf(f757,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f756]) ).
thf(f758,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 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
& $true ) ) )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f757]) ).
thf(f760,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(and_proxy_clausification,[],[f758]) ).
thf(f761,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ( v5 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& ~ ( v5 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v6 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v6 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v7 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v7 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v8 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v8 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X17 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f760]) ).
thf(f762,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
& $true ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f761]) ).
thf(f763,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
& $true ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f762]) ).
thf(f765,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f763]) ).
thf(f766,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] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ( v5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& ~ ( v5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v6 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v6 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v7 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v7 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v8 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v8 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(pi_proxy_clausification,[],[f765]) ).
thf(f767,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X1: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
& $true ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f766]) ).
thf(f768,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X7: mworld,X9: mworld,X4: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
& $true ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f767]) ).
thf(f770,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(and_proxy_clausification,[],[f768]) ).
thf(f771,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X19: mworld,X7: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ( v5 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& ~ ( v5 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v6 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v6 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v7 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v7 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v8 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v8 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) )
@ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(pi_proxy_clausification,[],[f770]) ).
thf(f772,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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
& $true ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f771]) ).
thf(f773,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X9: mworld,X1: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
& $true ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f772]) ).
thf(f775,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X14: mworld,X16: mworld,X9: mworld,X6: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(and_proxy_clausification,[],[f773]) ).
thf(f776,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ( v5 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& ~ ( v5 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v6 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v6 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v7 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v7 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v8 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v8 @ Y1 ) ) ) ) )
@ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f775]) ).
thf(f777,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X19 @ X20 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f776]) ).
thf(f778,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X8: mworld,X6: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ( v8 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
& ~ ( v8 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(imp_proxy_clausification,[],[f777]) ).
thf(f780,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(and_proxy_clausification,[],[f778]) ).
thf(f781,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X16: mworld,X7: mworld,X4: mworld,X6: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( v5 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ~ ( v5 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v6 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v6 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v7 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v7 @ Y1 ) ) ) ) )
@ X21 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f780]) ).
thf(f782,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X19: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ( mrel @ X20 @ X21 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ~ ( v7 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f781]) ).
thf(f783,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ( v7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
& ~ ( v7 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f782]) ).
thf(f785,plain,
! [X2: mworld,X21: 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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(and_proxy_clausification,[],[f783]) ).
thf(f786,plain,
! [X2: mworld,X21: 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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( v5 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( v5 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v6 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v6 @ Y1 ) ) ) ) )
@ X22 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f785]) ).
thf(f787,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X1: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( mrel @ X21 @ X22 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f786]) ).
thf(f788,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(imp_proxy_clausification,[],[f787]) ).
thf(f789,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X8: mworld,X4: mworld,X14: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ~ ( v6 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f788]) ).
thf(f790,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X18: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(and_proxy_clausification,[],[f788]) ).
thf(f791,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X4: mworld,X16: mworld,X14: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( v5 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( v5 @ Y1 ) ) ) ) )
@ X23 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(pi_proxy_clausification,[],[f790]) ).
thf(f792,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X1: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( ( mrel @ X22 @ X23 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f791]) ).
thf(f793,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X16: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
& $true ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& $true ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f792]) ).
thf(f794,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X16: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ( v5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(and_proxy_clausification,[],[f793]) ).
thf(f830,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X16: mworld,X7: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(and_proxy_clausification,[],[f794]) ).
thf(f836,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
& ~ ( v5 @ Y0 ) )
@ ( sK6 @ X23 ) )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(sigma_proxy_clausification,[],[f830]) ).
thf(f837,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X8: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( ( mrel @ X23 @ ( sK6 @ X23 ) )
& ~ ( v5 @ ( sK6 @ X23 ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f836]) ).
thf(f838,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X19: mworld,X14: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ~ ( v5 @ ( sK6 @ X23 ) ) )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f837]) ).
thf(f840,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X19: mworld,X7: mworld,X4: mworld,X8: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f838]) ).
thf(f842,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X7: mworld,X8: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(and_proxy_clausification,[],[f789]) ).
thf(f843,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X16: mworld,X8: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
& ( v6 @ Y0 ) )
@ ( sK7 @ X22 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(sigma_proxy_clausification,[],[f842]) ).
thf(f844,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X9: mworld,X4: mworld,X14: mworld,X18: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( ( mrel @ X22 @ ( sK7 @ X22 ) )
& ( v6 @ ( sK7 @ X22 ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f843]) ).
thf(f845,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X14: mworld,X18: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f844]) ).
thf(f890,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
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f754]) ).
thf(f891,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 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(and_proxy_clausification,[],[f754]) ).
thf(f892,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 @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ( v13 @ Y0 ) )
@ ( sK17 @ X15 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(sigma_proxy_clausification,[],[f891]) ).
thf(f893,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X15 @ ( sK17 @ X15 ) )
& ( v13 @ ( sK17 @ X15 ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f892]) ).
thf(f894,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 @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ ( sK17 @ X15 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(and_proxy_clausification,[],[f893]) ).
thf(f896,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
& ~ ( v13 @ Y0 ) )
@ ( sK18 @ X15 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(sigma_proxy_clausification,[],[f890]) ).
thf(f897,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X15 @ ( sK18 @ X15 ) )
& ~ ( v13 @ ( sK18 @ X15 ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f896]) ).
thf(f898,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( ~ ( v13 @ ( sK18 @ X15 ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(and_proxy_clausification,[],[f897]) ).
thf(f900,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(not_proxy_clausification,[],[f898]) ).
thf(f901,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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(and_proxy_clausification,[],[f749]) ).
thf(f907,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] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
& ~ ( v14 @ Y0 ) )
@ ( sK20 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(sigma_proxy_clausification,[],[f901]) ).
thf(f908,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X14 @ ( sK20 @ X14 ) )
& ~ ( v14 @ ( sK20 @ X14 ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f907]) ).
thf(f909,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 ) )
| ( ( ~ ( v14 @ ( sK20 @ X14 ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f908]) ).
thf(f911,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 @ X12 @ X13 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(not_proxy_clausification,[],[f909]) ).
thf(f913,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f744]) ).
thf(f914,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 @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
& ( v15 @ Y0 ) )
@ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f913]) ).
thf(f915,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 @ X13 @ ( sK21 @ X13 ) )
& ( v15 @ ( sK21 @ X13 ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f914]) ).
thf(f916,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(and_proxy_clausification,[],[f915]) ).
thf(f924,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 @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f739]) ).
thf(f925,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
& ( v16 @ Y0 ) )
@ ( sK23 @ X12 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(sigma_proxy_clausification,[],[f924]) ).
thf(f926,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( mrel @ X12 @ ( sK23 @ X12 ) )
& ( v16 @ ( sK23 @ X12 ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f925]) ).
thf(f927,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 @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f926]) ).
thf(f961,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f709]) ).
thf(f962,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f709]) ).
thf(f963,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ( v22 @ Y0 ) )
@ ( sK31 @ X6 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f962]) ).
thf(f964,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( mrel @ X6 @ ( sK31 @ X6 ) )
& ( v22 @ ( sK31 @ X6 ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f963]) ).
thf(f965,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f964]) ).
thf(f967,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
& ~ ( v22 @ Y0 ) )
@ ( sK32 @ X6 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(sigma_proxy_clausification,[],[f961]) ).
thf(f968,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X6 @ ( sK32 @ X6 ) )
& ~ ( v22 @ ( sK32 @ X6 ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f967]) ).
thf(f969,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ~ ( v22 @ ( sK32 @ X6 ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f968]) ).
thf(f971,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f969]) ).
thf(f972,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f704]) ).
thf(f978,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
& ~ ( v23 @ Y0 ) )
@ ( sK34 @ X5 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(sigma_proxy_clausification,[],[f972]) ).
thf(f979,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( mrel @ X5 @ ( sK34 @ X5 ) )
& ~ ( v23 @ ( sK34 @ X5 ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f978]) ).
thf(f980,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ~ ( v23 @ ( sK34 @ X5 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f979]) ).
thf(f982,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f980]) ).
thf(f984,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f699]) ).
thf(f985,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
& ( v24 @ Y0 ) )
@ ( sK35 @ X4 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f984]) ).
thf(f986,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X4 @ ( sK35 @ X4 ) )
& ( v24 @ ( sK35 @ X4 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f985]) ).
thf(f987,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f986]) ).
thf(f1989,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) )
| ( v23 @ Y5 ) ) ) ) ) )
| ( v25 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f1990,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) )
| ( v23 @ Y5 ) ) ) ) ) )
| ( v25 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1989]) ).
thf(f1991,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) )
| ( v25 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1990]) ).
thf(f1992,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) )
| ( v25 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1991]) ).
thf(f1993,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) )
| ( v23 @ Y4 ) ) ) ) ) )
| ( v25 @ Y2 ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1992]) ).
thf(f1994,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) )
| ( v25 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1993]) ).
thf(f1995,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) )
| ( v25 @ Y1 ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1994]) ).
thf(f1996,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) )
| ( v23 @ Y3 ) ) ) ) ) )
| ( v25 @ Y1 ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1995]) ).
thf(f1997,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) )
| ( v25 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1996]) ).
thf(f1998,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) )
| ( v25 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1997]) ).
thf(f1999,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) )
| ( v23 @ Y2 ) ) ) ) ) )
| ( v25 @ Y0 ) ) )
@ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1998]) ).
thf(f2000,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ X3 @ X4 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) )
| ( v25 @ X4 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1999]) ).
thf(f2001,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) )
| ( v25 @ X4 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2000]) ).
thf(f2002,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) )
| ( v23 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f2001]) ).
thf(f2003,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) )
| ( v23 @ Y1 ) ) ) ) )
@ X5 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2002]) ).
thf(f2004,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) )
| ( v23 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2003]) ).
thf(f2005,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) )
| ( v23 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2004]) ).
thf(f2006,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) )
| ( v23 @ Y0 ) ) )
@ X6 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2005]) ).
thf(f2007,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) )
| ( v23 @ X6 ) ) )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f2006]) ).
thf(f2008,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 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) )
| ( v23 @ X6 ) )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f2007]) ).
thf(f2009,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f2008]) ).
thf(f2010,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2009]) ).
thf(f2011,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X6 @ X7 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v23 @ X6 )
= $true ) ),
inference(beta-eta_normalization,[],[f2010]) ).
thf(f2012,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2011]) ).
thf(f2013,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v23 @ X6 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v22 @ X7 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f2012]) ).
thf(f2014,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( ( ~ ( v22 @ X7 ) )
= $true )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2013]) ).
thf(f2015,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true ) ),
inference(not_proxy_clausification,[],[f2014]) ).
thf(f2016,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2015]) ).
thf(f2017,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f2016]) ).
thf(f2018,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2017]) ).
thf(f2019,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2018]) ).
thf(f2020,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2019]) ).
thf(f2021,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2020]) ).
thf(f2022,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 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2021]) ).
thf(f2023,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f2022]) ).
thf(f2024,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2023]) ).
thf(f2025,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 @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2024]) ).
thf(f2026,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f2025]) ).
thf(f2027,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] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2026]) ).
thf(f2028,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f2027]) ).
thf(f2029,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2028]) ).
thf(f2030,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 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2029]) ).
thf(f2031,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] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(beta-eta_normalization,[],[f2030]) ).
thf(f2032,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] :
( ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ 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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(imp_proxy_clausification,[],[f2031]) ).
thf(f2033,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 @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2032]) ).
thf(f2034,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] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2033]) ).
thf(f2035,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] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f2034]) ).
thf(f2036,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 @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2035]) ).
thf(f2037,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 @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f2036]) ).
thf(f2038,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2037]) ).
thf(f2039,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] :
( ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $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 )
=> ~ ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f2038]) ).
thf(f2040,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 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2039]) ).
thf(f2041,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2040]) ).
thf(f2042,plain,
! [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] :
( ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X17 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(pi_proxy_clausification,[],[f2041]) ).
thf(f2043,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f2042]) ).
thf(f2044,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2043]) ).
thf(f2045,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,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v9 @ Y2 ) ) ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2044]) ).
thf(f2046,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X18: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f2045]) ).
thf(f2047,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,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2046]) ).
thf(f2048,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v9 @ Y1 ) ) ) )
@ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2047]) ).
thf(f2049,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X1: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2048]) ).
thf(f2050,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2049]) ).
thf(f2051,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X18: mworld,X7: mworld,X16: mworld,X4: mworld,X6: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v9 @ Y0 ) )
@ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2050]) ).
thf(f2052,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X1: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X19 @ X20 )
=> ~ ( v9 @ X20 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f2051]) ).
thf(f2053,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: 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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ~ ( v9 @ X20 ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2052]) ).
thf(f2054,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(not_proxy_clausification,[],[f2053]) ).
thf(f2210,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f2211,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2210]) ).
thf(f2212,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f2211]) ).
thf(f2213,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2212]) ).
thf(f2214,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f2213]) ).
thf(f2215,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f2214]) ).
thf(f2216,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2215]) ).
thf(f2217,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 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2216]) ).
thf(f2218,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2217]) ).
thf(f2219,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) )
@ X3 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2218]) ).
thf(f2220,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2219]) ).
thf(f2221,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2220]) ).
thf(f2222,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2221]) ).
thf(f2223,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2222]) ).
thf(f2224,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v28 @ 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2223]) ).
thf(f2225,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( 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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) )
@ X5 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2224]) ).
thf(f2226,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2225]) ).
thf(f2227,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ ( v24 @ X5 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2226]) ).
thf(f2228,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ~ ( v24 @ X5 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f2227]) ).
thf(f2229,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f2228]) ).
thf(f2230,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) )
@ X6 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2229]) ).
thf(f2231,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2230]) ).
thf(f2232,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2231]) ).
thf(f2233,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2232]) ).
thf(f2234,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X6 @ X7 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| ( v22 @ X7 ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2233]) ).
thf(f2235,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| ( v22 @ X7 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2234]) ).
thf(f2236,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f2235]) ).
thf(f2237,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $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 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2236]) ).
thf(f2238,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2237]) ).
thf(f2239,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2238]) ).
thf(f2240,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) )
@ X9 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2239]) ).
thf(f2241,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 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2240]) ).
thf(f2242,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 @ X4 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2241]) ).
thf(f2243,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v22 @ X7 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) )
@ X10 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2242]) ).
thf(f2244,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2243]) ).
thf(f2245,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2244]) ).
thf(f2246,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( v18 @ Y0 ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2245]) ).
thf(f2247,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X10 @ X11 )
=> ( v18 @ X11 ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2246]) ).
thf(f2248,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2247]) ).
thf(f2391,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) )
| ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f2392,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) )
| ( v13 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f2391]) ).
thf(f2393,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f2392]) ).
thf(f2394,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 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2393]) ).
thf(f2395,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) )
| ( v13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y2 ) ) ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2394]) ).
thf(f2396,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2395]) ).
thf(f2397,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2396]) ).
thf(f2398,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) )
| ( v13 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y1 ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2397]) ).
thf(f2399,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y0 ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2398]) ).
thf(f2400,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2399]) ).
thf(f2401,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) )
| ( v13 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ Y0 ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2400]) ).
thf(f2402,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ X4 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2401]) ).
thf(f2403,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v25 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2402]) ).
thf(f2404,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( ~ ( v25 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f2403]) ).
thf(f2405,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( ( ~ ( v25 @ X4 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2404]) ).
thf(f2406,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) )
| ( v13 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f2405]) ).
thf(f2407,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $false )
| ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2406]) ).
thf(f2408,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $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 )
=> ( ( !! @ 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 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2407]) ).
thf(f2409,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) )
| ( v13 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2408]) ).
thf(f2410,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2409]) ).
thf(f2411,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f2410]) ).
thf(f2412,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) )
| ( v13 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2411]) ).
thf(f2413,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2412]) ).
thf(f2414,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2413]) ).
thf(f2415,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) )
| ( v13 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2414]) ).
thf(f2416,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2415]) ).
thf(f2417,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2416]) ).
thf(f2418,plain,
! [X2: mworld,X3: 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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) )
| ( v13 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2417]) ).
thf(f2419,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 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $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 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2418]) ).
thf(f2420,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2419]) ).
thf(f2421,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) )
| ( v13 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f2420]) ).
thf(f2422,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
= ( 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 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f2421]) ).
thf(f2423,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f2422]) ).
thf(f2424,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) )
| ( v13 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2423]) ).
thf(f2425,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $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 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2424]) ).
thf(f2426,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 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2425]) ).
thf(f2427,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) )
| ( v13 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2426]) ).
thf(f2428,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2427]) ).
thf(f2429,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 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f2428]) ).
thf(f2430,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) )
| ( v13 @ Y3 ) ) ) ) ) ) ) ) )
@ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2429]) ).
thf(f2431,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 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2430]) ).
thf(f2432,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] :
( ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f2431]) ).
thf(f2433,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 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) )
| ( v13 @ Y2 ) ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2432]) ).
thf(f2434,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 @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ( v13 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2433]) ).
thf(f2435,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 @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ( v13 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f2434]) ).
thf(f2436,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 @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $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 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) )
| ( v13 @ Y1 ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2435]) ).
thf(f2437,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ( v13 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f2436]) ).
thf(f2438,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 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ( v13 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2437]) ).
thf(f2439,plain,
! [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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) )
| ( v13 @ Y0 ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2438]) ).
thf(f2440,plain,
! [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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ( v13 @ X16 ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f2439]) ).
thf(f2441,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 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
| ( v13 @ X16 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2440]) ).
thf(f2442,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] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f2441]) ).
thf(f2443,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 @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) )
@ X17 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2442]) ).
thf(f2444,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f2443]) ).
thf(f2445,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 @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
| ( ( v25 @ X4 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2444]) ).
thf(f2446,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2445]) ).
thf(f2447,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(beta-eta_normalization,[],[f2446]) ).
thf(f2448,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X18: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(imp_proxy_clausification,[],[f2447]) ).
thf(f2449,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X18: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2448]) ).
thf(f2450,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X16: mworld,X4: mworld,X9: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ( v10 @ X19 ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f2449]) ).
thf(f2451,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X16: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) )
| ( v10 @ X19 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f2450]) ).
thf(f2452,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(or_proxy_clausification,[],[f2451]) ).
thf(f2453,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) )
@ X20 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2452]) ).
thf(f2454,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X8: mworld,X9: 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 @ X17 @ X18 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2453]) ).
thf(f2455,plain,
! [X2: mworld,X3: 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,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2454]) ).
thf(f2456,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) )
@ X21 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2455]) ).
thf(f2457,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X1: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(beta-eta_normalization,[],[f2456]) ).
thf(f2458,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,X6: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f2457]) ).
thf(f2459,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X18: mworld,X16: mworld,X4: mworld,X14: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) )
@ X22 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2458]) ).
thf(f2460,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X8: mworld,X4: mworld,X6: mworld,X14: mworld,X7: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( v25 @ X4 )
= $false )
| ( ( ( mrel @ X21 @ X22 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2459]) ).
thf(f2461,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X9: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
= $true )
| ( ( v10 @ X19 )
= $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2460]) ).
thf(f2462,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,X14: mworld,X19: mworld,X18: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X23 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(pi_proxy_clausification,[],[f2461]) ).
thf(f2463,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( ( mrel @ X22 @ X23 )
=> ~ ( v6 @ X23 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f2462]) ).
thf(f2464,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,X9: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ~ ( v6 @ X23 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2463]) ).
thf(f2465,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X19: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(not_proxy_clausification,[],[f2464]) ).
thf(f2466,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f2467,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2466]) ).
thf(f2468,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f2467]) ).
thf(f2469,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2468]) ).
thf(f2470,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f2469]) ).
thf(f2471,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2470]) ).
thf(f2472,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2471]) ).
thf(f2473,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) )
@ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2472]) ).
thf(f2474,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ X3 ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2473]) ).
thf(f2475,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( 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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ X3 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2474]) ).
thf(f2476,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( v26 @ X3 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f2475]) ).
thf(f2477,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ 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 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v26 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f2476]) ).
thf(f2478,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2477]) ).
thf(f2479,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2478]) ).
thf(f2480,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v26 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2479]) ).
thf(f2481,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f2480]) ).
thf(f2482,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2481]) ).
thf(f2483,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2482]) ).
thf(f2484,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2483]) ).
thf(f2485,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2484]) ).
thf(f2486,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f2485]) ).
thf(f2487,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f2486]) ).
thf(f2488,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2487]) ).
thf(f2489,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2488]) ).
thf(f2490,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) )
@ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2489]) ).
thf(f2491,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f2490]) ).
thf(f2492,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2491]) ).
thf(f2493,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 @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) )
@ X9 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2492]) ).
thf(f2494,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2493]) ).
thf(f2495,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2494]) ).
thf(f2496,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) )
@ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2495]) ).
thf(f2497,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2496]) ).
thf(f2498,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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f2497]) ).
thf(f2499,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 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) )
@ X11 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2498]) ).
thf(f2500,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v18 @ X11 ) ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2499]) ).
thf(f2501,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) )
| ~ ( v18 @ X11 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f2500]) ).
thf(f2502,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ~ ( v18 @ X11 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(or_proxy_clausification,[],[f2501]) ).
thf(f2503,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f2502]) ).
thf(f2504,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2503]) ).
thf(f2505,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2504]) ).
thf(f2506,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f2505]) ).
thf(f2507,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
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) )
@ X13 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f2506]) ).
thf(f2508,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2507]) ).
thf(f2509,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 @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2508]) ).
thf(f2510,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 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ Y0 ) ) )
@ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2509]) ).
thf(f2511,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X14 ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2510]) ).
thf(f2512,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2511]) ).
thf(f2513,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ~ ( v15 @ X14 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(or_proxy_clausification,[],[f2512]) ).
thf(f2514,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(not_proxy_clausification,[],[f2513]) ).
thf(f2515,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2514]) ).
thf(f2516,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2515]) ).
thf(f2517,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
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2516]) ).
thf(f2518,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 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(pi_proxy_clausification,[],[f2517]) ).
thf(f2519,plain,
! [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 @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(beta-eta_normalization,[],[f2518]) ).
thf(f2520,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
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f2519]) ).
thf(f2521,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(pi_proxy_clausification,[],[f2520]) ).
thf(f2522,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f2521]) ).
thf(f2523,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(imp_proxy_clausification,[],[f2522]) ).
thf(f2524,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,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f2523]) ).
thf(f2525,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,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f2524]) ).
thf(f2526,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X8: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(imp_proxy_clausification,[],[f2525]) ).
thf(f2527,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X1: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2526]) ).
thf(f2528,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X8: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f2527]) ).
thf(f2529,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X18: mworld,X9: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v15 @ X14 ) ) ),
inference(imp_proxy_clausification,[],[f2528]) ).
thf(f2530,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X19: mworld,X6: mworld,X14: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) ) ) ) ) ) )
@ X20 )
= $true )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f2529]) ).
thf(f2531,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2530]) ).
thf(f2532,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,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2531]) ).
thf(f2533,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) ) ) ) )
@ X21 )
= $true )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f2532]) ).
thf(f2534,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X19: mworld,X14: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f2533]) ).
thf(f2535,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X9: mworld,X4: mworld,X18: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f2534]) ).
thf(f2536,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,X6: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) ) )
@ X22 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f2535]) ).
thf(f2537,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X21 @ X22 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f2536]) ).
thf(f2538,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X7: mworld,X8: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2537]) ).
thf(f2539,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,X6: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X23 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(pi_proxy_clausification,[],[f2538]) ).
thf(f2540,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X6: mworld,X18: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( ( mrel @ X22 @ X23 )
=> ~ ( v6 @ X23 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f2539]) ).
thf(f2541,plain,
! [X2: mworld,X21: 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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ~ ( v6 @ X23 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2540]) ).
thf(f2542,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X1: mworld,X7: mworld,X4: mworld,X16: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(not_proxy_clausification,[],[f2541]) ).
thf(f3050,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f3051,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f3050]) ).
thf(f3052,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f3051]) ).
thf(f3053,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3052]) ).
thf(f3054,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f3053]) ).
thf(f3055,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3054]) ).
thf(f3056,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( v28 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f3055]) ).
thf(f3057,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3056]) ).
thf(f3058,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3057]) ).
thf(f3059,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3058]) ).
thf(f3060,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3059]) ).
thf(f3061,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3060]) ).
thf(f3062,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v28 @ X1 )
= $true )
| ( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3061]) ).
thf(f3063,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3062]) ).
thf(f3064,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3063]) ).
thf(f3065,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v28 @ X1 )
= $true )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3064]) ).
thf(f3066,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v28 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3065]) ).
thf(f3067,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3066]) ).
thf(f3068,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v28 @ X1 )
= $true )
| ( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3067]) ).
thf(f3069,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3068]) ).
thf(f3070,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 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3069]) ).
thf(f3071,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3070]) ).
thf(f3072,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3071]) ).
thf(f3073,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3072]) ).
thf(f3074,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f3073]) ).
thf(f3075,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3074]) ).
thf(f3076,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3075]) ).
thf(f3077,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 @ X2 @ X3 ) )
| ( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f3076]) ).
thf(f3078,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v28 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3077]) ).
thf(f3079,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v28 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3078]) ).
thf(f3080,plain,
! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f3079]) ).
thf(f3081,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 @ X8 @ X9 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3080]) ).
thf(f3082,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 @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) )
@ X11 )
= $true )
| ( ( v28 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3081]) ).
thf(f3083,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 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $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 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3082]) ).
thf(f3084,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3083]) ).
thf(f3085,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v28 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3084]) ).
thf(f3086,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3085]) ).
thf(f3087,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ 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 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f3086]) ).
thf(f3088,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 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) )
@ X13 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3087]) ).
thf(f3089,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3088]) ).
thf(f3090,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3089]) ).
thf(f3091,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f3090]) ).
thf(f3092,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 @ X5 @ X6 ) )
| ( ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ ( v15 @ X14 ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f3091]) ).
thf(f3093,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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3092]) ).
thf(f3094,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 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( ( ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(or_proxy_clausification,[],[f3093]) ).
thf(f3095,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 )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ~ ( v15 @ X14 ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f3094]) ).
thf(f3096,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f3095]) ).
thf(f3097,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( ( mrel @ X14 @ X15 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ X15 ) ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3096]) ).
thf(f3098,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
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ X15 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f3097]) ).
thf(f3099,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(or_proxy_clausification,[],[f3098]) ).
thf(f3100,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
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v14 @ X15 ) ) ),
inference(pi_proxy_clausification,[],[f3099]) ).
thf(f3101,plain,
! [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 @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f3100]) ).
thf(f3102,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] :
( ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3101]) ).
thf(f3103,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] :
( ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X17 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(pi_proxy_clausification,[],[f3102]) ).
thf(f3104,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 @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(beta-eta_normalization,[],[f3103]) ).
thf(f3105,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 @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f3104]) ).
thf(f3106,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 @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) )
@ X18 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(pi_proxy_clausification,[],[f3105]) ).
thf(f3107,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3106]) ).
thf(f3108,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3107]) ).
thf(f3109,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X19: mworld,X4: mworld,X14: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) )
@ X19 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3108]) ).
thf(f3110,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(beta-eta_normalization,[],[f3109]) ).
thf(f3111,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X18: mworld,X16: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(imp_proxy_clausification,[],[f3110]) ).
thf(f3112,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,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( v9 @ Y0 ) )
@ X20 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(pi_proxy_clausification,[],[f3111]) ).
thf(f3113,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X16: mworld,X4: mworld,X19: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( ( mrel @ X19 @ X20 )
=> ( v9 @ X20 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(beta-eta_normalization,[],[f3112]) ).
thf(f3114,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,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(imp_proxy_clausification,[],[f3113]) ).
thf(f3893,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f3894,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 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f3893]) ).
thf(f3895,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f3894]) ).
thf(f3896,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 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ ( v28 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3895]) ).
thf(f3897,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 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f3896]) ).
thf(f3898,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v28 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3897]) ).
thf(f3899,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 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(not_proxy_clausification,[],[f3898]) ).
thf(f3900,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3899]) ).
thf(f3901,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3900]) ).
thf(f3902,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 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3901]) ).
thf(f3903,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3902]) ).
thf(f3904,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3903]) ).
thf(f3905,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(or_proxy_clausification,[],[f3904]) ).
thf(f3906,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3905]) ).
thf(f3907,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v26 @ X3 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3906]) ).
thf(f3908,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3907]) ).
thf(f3909,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3908]) ).
thf(f3910,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3909]) ).
thf(f3911,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 @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3910]) ).
thf(f3912,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3911]) ).
thf(f3913,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( ( 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f3912]) ).
thf(f3914,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f3913]) ).
thf(f3915,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( ^ [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 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3914]) ).
thf(f3916,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 @ X2 @ X3 ) )
| ( ( ( 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3915]) ).
thf(f3917,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $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 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3916]) ).
thf(f3918,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( ^ [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 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v26 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3917]) ).
thf(f3919,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f3918]) ).
thf(f3920,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $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 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f3919]) ).
thf(f3921,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( ^ [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 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v26 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f3920]) ).
thf(f3922,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(beta-eta_normalization,[],[f3921]) ).
thf(f3923,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(imp_proxy_clausification,[],[f3922]) ).
thf(f3924,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 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( ^ [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 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3923]) ).
thf(f3925,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(beta-eta_normalization,[],[f3924]) ).
thf(f3926,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 @ X8 @ X9 ) )
| ( ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f3925]) ).
thf(f3927,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 @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $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 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) )
@ X11 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f3926]) ).
thf(f3928,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 @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f3927]) ).
thf(f3929,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 ) )
| ( ( !! @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3928]) ).
thf(f3930,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 ) )
| ( ( v26 @ X3 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) )
@ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f3929]) ).
thf(f3931,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( ( ( mrel @ 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 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f3930]) ).
thf(f3932,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) ) ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v26 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f3931]) ).
thf(f3933,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 ) )
| ( ( ^ [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 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) )
@ X13 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f3932]) ).
thf(f3934,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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ ( v16 @ X13 ) ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f3933]) ).
thf(f3935,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] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ ( v16 @ X13 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f3934]) ).
thf(f3936,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] :
( ( ( v26 @ X3 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( ~ ( v16 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(or_proxy_clausification,[],[f3935]) ).
thf(f3937,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 @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) )
@ X14 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ~ ( v16 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f3936]) ).
thf(f3938,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 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) )
@ X14 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f3937]) ).
thf(f3939,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(beta-eta_normalization,[],[f3938]) ).
thf(f3940,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 @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f3939]) ).
thf(f3941,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 @ X10 @ X11 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) )
@ X15 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f3940]) ).
thf(f3942,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3941]) ).
thf(f3943,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f3942]) ).
thf(f3944,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ~ ( v13 @ Y0 ) )
@ X16 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(pi_proxy_clausification,[],[f3943]) ).
thf(f3945,plain,
! [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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( ( mrel @ X15 @ X16 )
=> ~ ( v13 @ X16 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(beta-eta_normalization,[],[f3944]) ).
thf(f3946,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( ~ ( v13 @ X16 ) ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(imp_proxy_clausification,[],[f3945]) ).
thf(f3947,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] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f3946]) ).
thf(f4386,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f987,f245]) ).
thf(f4387,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4386]) ).
thf(f4388,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4387,f245]) ).
thf(f4389,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4388]) ).
thf(f4390,plain,
! [X2: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $true
= ( v24 @ ( sK35 @ X4 ) ) ) ),
inference(forward_demodulation,[],[f4389,f245]) ).
thf(f4391,plain,
! [X2: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4390]) ).
thf(f4392,plain,
! [X4: mworld] :
( ( $true
= ( v24 @ ( sK35 @ X4 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4391,f245]) ).
thf(f4393,plain,
! [X4: mworld] :
( $true
= ( v24 @ ( sK35 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4392]) ).
thf(f4394,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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v18 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $true ) ),
inference(forward_demodulation,[],[f2248,f245]) ).
thf(f4395,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4394]) ).
thf(f4396,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $true )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4395,f245]) ).
thf(f4397,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 @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4396]) ).
thf(f4398,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
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $true )
| ( $true
= ( v18 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4397,f245]) ).
thf(f4399,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 @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4398]) ).
thf(f4400,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f4399,f245]) ).
thf(f4401,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4400]) ).
thf(f4402,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $true ) ),
inference(forward_demodulation,[],[f4401,f245]) ).
thf(f4403,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4402]) ).
thf(f4404,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4403,f245]) ).
thf(f4405,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4404]) ).
thf(f4406,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( ( v22 @ X7 )
= $true )
| ( $false = $true )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4405,f245]) ).
thf(f4407,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( v18 @ X11 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4406]) ).
thf(f4408,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $false = $true )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4407,f245]) ).
thf(f4409,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4408]) ).
thf(f4410,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v28 @ X1 ) )
| ( $true
= ( v18 @ X11 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v24 @ X5 ) ) ),
inference(forward_demodulation,[],[f4409,f245]) ).
thf(f4411,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f4410]) ).
thf(f4412,plain,
! [X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $true
= ( v18 @ X11 ) )
| ( $false = $true )
| ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4411,f245]) ).
thf(f4413,plain,
! [X10: mworld,X11: mworld,X1: mworld,X9: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $true )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v24 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4412]) ).
thf(f4414,plain,
! [X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false = $true )
| ( $true
= ( v18 @ X11 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(forward_demodulation,[],[f4413,f245]) ).
thf(f4415,plain,
! [X11: mworld,X1: mworld,X7: mworld,X5: mworld] :
( ( $false
= ( v24 @ X5 ) )
| ( $true
= ( v18 @ X11 ) )
| ( ( v22 @ X7 )
= $true )
| ( $false
= ( v28 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4414]) ).
thf(f4417,definition,
( spl41_1
<=> ! [X5: mworld] :
( $false
= ( v24 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_1])],[avatar_definition]) ).
thf(f4418,plain,
( ! [X5: mworld] :
( $false
= ( v24 @ X5 ) )
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f4417]) ).
thf(f4420,definition,
( spl41_2
<=> ! [X7: mworld] :
( ( v22 @ X7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_2])],[avatar_definition]) ).
thf(f4421,plain,
( ! [X7: mworld] :
( ( v22 @ X7 )
= $true )
| ~ spl41_2 ),
inference(avatar_component_clause,[],[f4420]) ).
thf(f4423,definition,
( spl41_3
<=> ! [X1: mworld] :
( $false
= ( v28 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_3])],[avatar_definition]) ).
thf(f4424,plain,
( ! [X1: mworld] :
( $false
= ( v28 @ X1 ) )
| ~ spl41_3 ),
inference(avatar_component_clause,[],[f4423]) ).
thf(f4426,definition,
( spl41_4
<=> ! [X11: mworld] :
( $true
= ( v18 @ X11 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_4])],[avatar_definition]) ).
thf(f4427,plain,
( ! [X11: mworld] :
( $true
= ( v18 @ X11 ) )
| ~ spl41_4 ),
inference(avatar_component_clause,[],[f4426]) ).
thf(f4428,plain,
( spl41_1
| spl41_2
| spl41_3
| spl41_4 ),
inference(avatar_split_clause,[],[f4415,f4426,f4423,f4420,f4417]) ).
thf(f4488,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f982,f245]) ).
thf(f4489,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4488]) ).
thf(f4490,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4489,f245]) ).
thf(f4491,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4490]) ).
thf(f4492,plain,
! [X2: mworld,X3: mworld,X1: mworld,X5: mworld] :
( ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4491,f245]) ).
thf(f4493,plain,
! [X2: mworld,X3: mworld,X1: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[],[f4492]) ).
thf(f4494,plain,
! [X2: mworld,X3: mworld,X5: mworld] :
( ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4493,f245]) ).
thf(f4495,plain,
! [X2: mworld,X3: mworld,X5: mworld] :
( ( $false
= ( v23 @ ( sK34 @ X5 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4494]) ).
thf(f4496,plain,
! [X5: mworld] :
( ( $false = $true )
| ( $false
= ( v23 @ ( sK34 @ X5 ) ) ) ),
inference(forward_demodulation,[],[f4495,f245]) ).
thf(f4497,plain,
! [X5: mworld] :
( $false
= ( v23 @ ( sK34 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4496]) ).
thf(f4500,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f971,f245]) ).
thf(f4501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f4500]) ).
thf(f4502,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4501,f245]) ).
thf(f4503,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4502]) ).
thf(f4504,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4503,f245]) ).
thf(f4505,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4504]) ).
thf(f4506,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false ) ),
inference(forward_demodulation,[],[f4505,f245]) ).
thf(f4507,plain,
! [X3: mworld,X1: mworld,X6: mworld,X4: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f4506]) ).
thf(f4508,plain,
! [X1: mworld,X6: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false ) ),
inference(forward_demodulation,[],[f4507,f245]) ).
thf(f4509,plain,
! [X1: mworld,X6: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ ( sK32 @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f4508]) ).
thf(f4510,plain,
( ! [X1: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_2 ),
inference(forward_demodulation,[],[f4509,f4421]) ).
thf(f4511,plain,
( ! [X1: mworld] :
( $false
= ( mrel @ mactual @ X1 ) )
| ~ spl41_2 ),
inference(trivial_inequality_removal,[],[f4510]) ).
thf(f4512,plain,
( ( $false = $true )
| ~ spl41_2 ),
inference(forward_demodulation,[],[f4511,f245]) ).
thf(f4513,plain,
( $false
| ~ spl41_2 ),
inference(trivial_inequality_removal,[],[f4512]) ).
thf(f4514,plain,
~ spl41_2,
inference(avatar_contradiction_clause,[],[f4513]) ).
thf(f4517,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f965,f245]) ).
thf(f4518,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(trivial_inequality_removal,[],[f4517]) ).
thf(f4519,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4518,f245]) ).
thf(f4520,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4519]) ).
thf(f4521,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4520,f245]) ).
thf(f4522,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4521]) ).
thf(f4523,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld] :
( ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4522,f245]) ).
thf(f4524,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld] :
( ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4523]) ).
thf(f4525,plain,
! [X2: mworld,X1: mworld,X6: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4524,f245]) ).
thf(f4526,plain,
! [X2: mworld,X1: mworld,X6: mworld] :
( ( $true
= ( v22 @ ( sK31 @ X6 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4525]) ).
thf(f4527,plain,
! [X6: mworld] :
( ( $false = $true )
| ( $true
= ( v22 @ ( sK31 @ X6 ) ) ) ),
inference(forward_demodulation,[],[f4526,f245]) ).
thf(f4528,plain,
! [X6: mworld] :
( $true
= ( v22 @ ( sK31 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4527]) ).
thf(f4564,definition,
( spl41_9
<=> ! [X15: mworld] :
( $true
= ( v14 @ X15 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_9])],[avatar_definition]) ).
thf(f4565,plain,
( ! [X15: mworld] :
( $true
= ( v14 @ X15 ) )
| ~ spl41_9 ),
inference(avatar_component_clause,[],[f4564]) ).
thf(f4567,definition,
( spl41_10
<=> ! [X3: mworld] :
( ( v26 @ X3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_10])],[avatar_definition]) ).
thf(f4568,plain,
( ! [X3: mworld] :
( ( v26 @ X3 )
= $true )
| ~ spl41_10 ),
inference(avatar_component_clause,[],[f4567]) ).
thf(f4631,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
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f3947,f245]) ).
thf(f4632,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v13 @ X16 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4631]) ).
thf(f4633,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 @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4632,f245]) ).
thf(f4634,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f4633]) ).
thf(f4635,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 @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4634,f245]) ).
thf(f4636,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 @ X14 @ X15 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v13 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f4635]) ).
thf(f4637,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
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f4636,f245]) ).
thf(f4638,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 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v13 @ X16 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4637]) ).
thf(f4639,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4638,f245]) ).
thf(f4640,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v26 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4639]) ).
thf(f4641,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4640,f245]) ).
thf(f4642,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4641]) ).
thf(f4643,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v13 @ X16 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(forward_demodulation,[],[f4642,f245]) ).
thf(f4644,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4643]) ).
thf(f4645,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f4644,f245]) ).
thf(f4646,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f4645]) ).
thf(f4647,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(forward_demodulation,[],[f4646,f245]) ).
thf(f4648,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( v26 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4647]) ).
thf(f4649,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f4648,f245]) ).
thf(f4650,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f4649]) ).
thf(f4651,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f4650,f245]) ).
thf(f4652,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v26 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f4651]) ).
thf(f4653,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f4652,f245]) ).
thf(f4654,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4653]) ).
thf(f4655,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v28 @ X1 ) )
| ( $false = $true )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f4654,f245]) ).
thf(f4656,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X16: mworld,X7: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4655]) ).
thf(f4657,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X16: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ X13 )
= $false )
| ( ( v26 @ X3 )
= $true ) ),
inference(forward_demodulation,[],[f4656,f245]) ).
thf(f4658,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X9: mworld,X16: mworld,X12: mworld,X13: mworld] :
( ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v13 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f4657]) ).
thf(f4659,plain,
! [X3: mworld,X11: mworld,X1: mworld,X16: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false ) ),
inference(forward_demodulation,[],[f4658,f245]) ).
thf(f4660,plain,
! [X3: mworld,X11: mworld,X1: mworld,X16: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v26 @ X3 )
= $true )
| ( $false
= ( v28 @ X1 ) )
| ( $false
= ( v13 @ X16 ) )
| ( ( v16 @ X13 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4659]) ).
thf(f4661,plain,
! [X3: mworld,X1: mworld,X16: mworld,X13: mworld] :
( ( $false
= ( v13 @ X16 ) )
| ( $false = $true )
| ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v28 @ X1 ) ) ),
inference(forward_demodulation,[],[f4660,f245]) ).
thf(f4662,plain,
! [X3: mworld,X1: mworld,X16: mworld,X13: mworld] :
( ( ( v26 @ X3 )
= $true )
| ( ( v16 @ X13 )
= $false )
| ( $false
= ( v13 @ X16 ) )
| ( $false
= ( v28 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4661]) ).
thf(f4664,definition,
( spl41_12
<=> ! [X16: mworld] :
( $false
= ( v13 @ X16 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_12])],[avatar_definition]) ).
thf(f4665,plain,
( ! [X16: mworld] :
( $false
= ( v13 @ X16 ) )
| ~ spl41_12 ),
inference(avatar_component_clause,[],[f4664]) ).
thf(f4667,definition,
( spl41_13
<=> ! [X13: mworld] :
( ( v16 @ X13 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl41_13])],[avatar_definition]) ).
thf(f4668,plain,
( ! [X13: mworld] :
( ( v16 @ X13 )
= $false )
| ~ spl41_13 ),
inference(avatar_component_clause,[],[f4667]) ).
thf(f4669,plain,
( spl41_3
| spl41_12
| spl41_10
| spl41_13 ),
inference(avatar_split_clause,[],[f4662,f4667,f4567,f4664,f4423]) ).
thf(f4672,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f927,f245]) ).
thf(f4673,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 @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4672]) ).
thf(f4674,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 @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4673,f245]) ).
thf(f4675,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 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f4674]) ).
thf(f4676,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4675,f245]) ).
thf(f4677,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X4: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4676]) ).
thf(f4678,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(forward_demodulation,[],[f4677,f245]) ).
thf(f4679,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f4678]) ).
thf(f4680,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f4679,f245]) ).
thf(f4681,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4680]) ).
thf(f4682,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f4681,f245]) ).
thf(f4683,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4682]) ).
thf(f4684,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f4683,f245]) ).
thf(f4685,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4684]) ).
thf(f4686,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f4685,f245]) ).
thf(f4687,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4686]) ).
thf(f4688,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f4687,f245]) ).
thf(f4689,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X12: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4688]) ).
thf(f4690,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X12: mworld] :
( ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f4689,f245]) ).
thf(f4691,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X12: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f4690]) ).
thf(f4692,plain,
! [X2: mworld,X1: mworld,X12: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(forward_demodulation,[],[f4691,f245]) ).
thf(f4693,plain,
! [X2: mworld,X1: mworld,X12: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v16 @ ( sK23 @ X12 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4692]) ).
thf(f4694,plain,
! [X12: mworld] :
( ( ( v16 @ ( sK23 @ X12 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4693,f245]) ).
thf(f4695,plain,
! [X12: mworld] :
( ( v16 @ ( sK23 @ X12 ) )
= $true ),
inference(trivial_inequality_removal,[],[f4694]) ).
thf(f4762,definition,
( spl41_15
<=> ! [X16: mworld] :
( $true
= ( v13 @ X16 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_15])],[avatar_definition]) ).
thf(f4763,plain,
( ! [X16: mworld] :
( $true
= ( v13 @ X16 ) )
| ~ spl41_15 ),
inference(avatar_component_clause,[],[f4762]) ).
thf(f4798,plain,
( ( $false = $true )
| ~ spl41_1 ),
inference(constrained_superposition,[],[f4393,f4418]) ).
thf(f4802,plain,
( $false
| ~ spl41_1 ),
inference(trivial_inequality_removal,[],[f4798]) ).
thf(f4803,plain,
~ spl41_1,
inference(avatar_contradiction_clause,[],[f4802]) ).
thf(f4804,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f916,f245]) ).
thf(f4805,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4804]) ).
thf(f4806,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 = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f4805,f245]) ).
thf(f4807,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 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4806]) ).
thf(f4808,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 @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f4807,f245]) ).
thf(f4809,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4808]) ).
thf(f4810,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 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f4809,f245]) ).
thf(f4811,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 @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4810]) ).
thf(f4812,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4811,f245]) ).
thf(f4813,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4812]) ).
thf(f4814,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f4813,f245]) ).
thf(f4815,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4814]) ).
thf(f4816,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(forward_demodulation,[],[f4815,f245]) ).
thf(f4817,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4816]) ).
thf(f4818,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(forward_demodulation,[],[f4817,f245]) ).
thf(f4819,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X9: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4818]) ).
thf(f4820,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f4819,f245]) ).
thf(f4821,plain,
! [X2: mworld,X3: mworld,X1: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f4820]) ).
thf(f4822,plain,
! [X2: mworld,X3: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4821,f245]) ).
thf(f4823,plain,
! [X2: mworld,X3: mworld,X8: mworld,X9: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f4822]) ).
thf(f4824,plain,
! [X2: mworld,X3: mworld,X12: mworld,X13: mworld] :
( ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4823,f245]) ).
thf(f4825,plain,
! [X2: mworld,X3: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4824]) ).
thf(f4826,plain,
! [X2: mworld,X3: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(forward_demodulation,[],[f4825,f245]) ).
thf(f4827,plain,
! [X2: mworld,X3: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v15 @ ( sK21 @ X13 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f4826]) ).
thf(f4828,plain,
! [X13: mworld] :
( ( ( v15 @ ( sK21 @ X13 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4827,f245]) ).
thf(f4829,plain,
! [X13: mworld] :
( ( v15 @ ( sK21 @ X13 ) )
= $true ),
inference(trivial_inequality_removal,[],[f4828]) ).
thf(f4906,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 @ X13 @ X14 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f911,f245]) ).
thf(f4907,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f4906]) ).
thf(f4908,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(forward_demodulation,[],[f4907,f245]) ).
thf(f4909,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 @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f4908]) ).
thf(f4910,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f4909,f245]) ).
thf(f4911,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 @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4910]) ).
thf(f4912,plain,
! [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 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f4911,f245]) ).
thf(f4913,plain,
! [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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f4912]) ).
thf(f4914,plain,
! [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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f4913,f245]) ).
thf(f4915,plain,
! [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 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4914]) ).
thf(f4916,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false ) ),
inference(forward_demodulation,[],[f4915,f245]) ).
thf(f4917,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v14 @ ( sK20 @ X14 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f4916]) ).
thf(f4918,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4917,f4565]) ).
thf(f4919,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4918]) ).
thf(f4920,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4919,f245]) ).
thf(f4921,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4920]) ).
thf(f4922,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4921,f245]) ).
thf(f4923,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4922]) ).
thf(f4924,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4923,f245]) ).
thf(f4925,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4924]) ).
thf(f4926,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4925,f245]) ).
thf(f4927,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4926]) ).
thf(f4928,plain,
( ! [X3: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4927,f245]) ).
thf(f4929,plain,
( ! [X3: mworld,X14: mworld,X4: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4928]) ).
thf(f4930,plain,
( ! [X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4929,f245]) ).
thf(f4931,plain,
( ! [X14: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4930]) ).
thf(f4932,plain,
( ! [X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true ) )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4931,f245]) ).
thf(f4933,plain,
( ! [X12: mworld,X13: mworld] :
( $false
= ( mrel @ X12 @ X13 ) )
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4932]) ).
thf(f4934,plain,
( ( $false = $true )
| ~ spl41_9 ),
inference(forward_demodulation,[],[f4933,f245]) ).
thf(f4935,plain,
( $false
| ~ spl41_9 ),
inference(trivial_inequality_removal,[],[f4934]) ).
thf(f4936,plain,
~ spl41_9,
inference(avatar_contradiction_clause,[],[f4935]) ).
thf(f5027,definition,
( spl41_18
<=> ! [X14: mworld] :
( $false
= ( v15 @ X14 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_18])],[avatar_definition]) ).
thf(f5028,plain,
( ! [X14: mworld] :
( $false
= ( v15 @ X14 ) )
| ~ spl41_18 ),
inference(avatar_component_clause,[],[f5027]) ).
thf(f5030,definition,
( spl41_19
<=> ! [X20: mworld] :
( ( v9 @ X20 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_19])],[avatar_definition]) ).
thf(f5031,plain,
( ! [X20: mworld] :
( ( v9 @ X20 )
= $true )
| ~ spl41_19 ),
inference(avatar_component_clause,[],[f5030]) ).
thf(f5035,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 @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ ( sK17 @ X15 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(forward_demodulation,[],[f894,f245]) ).
thf(f5036,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
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v13 @ ( sK17 @ X15 ) ) ) ),
inference(trivial_inequality_removal,[],[f5035]) ).
thf(f5037,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 @ X6 @ X7 )
= $false )
| ( $true
= ( v13 @ ( sK17 @ X15 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f5036,f245]) ).
thf(f5038,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $true
= ( v13 @ ( sK17 @ X15 ) ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5037]) ).
thf(f5039,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 @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5038,f4665]) ).
thf(f5040,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 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5039]) ).
thf(f5041,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 @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5040,f245]) ).
thf(f5042,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 @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5041]) ).
thf(f5043,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 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5042,f245]) ).
thf(f5044,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 @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5043]) ).
thf(f5045,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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5044,f245]) ).
thf(f5046,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 @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5045]) ).
thf(f5047,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5046,f245]) ).
thf(f5048,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5047]) ).
thf(f5049,plain,
( ! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5048,f245]) ).
thf(f5050,plain,
( ! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5049]) ).
thf(f5051,plain,
( ! [X10: 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 @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5050,f245]) ).
thf(f5052,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5051]) ).
thf(f5053,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5052,f245]) ).
thf(f5054,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X5: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5053]) ).
thf(f5055,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5054,f245]) ).
thf(f5056,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5055]) ).
thf(f5057,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5056,f245]) ).
thf(f5058,plain,
( ! [X10: mworld,X8: mworld,X6: mworld,X9: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5057]) ).
thf(f5059,plain,
( ! [X10: mworld,X6: mworld,X9: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5058,f245]) ).
thf(f5060,plain,
( ! [X10: mworld,X6: mworld,X9: mworld,X14: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5059]) ).
thf(f5061,plain,
( ! [X10: mworld,X6: mworld,X9: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5060,f245]) ).
thf(f5062,plain,
( ! [X10: mworld,X6: mworld,X9: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5061]) ).
thf(f5063,plain,
( ! [X6: mworld,X5: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true ) )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5062,f245]) ).
thf(f5064,plain,
( ! [X6: mworld,X5: mworld] :
( $false
= ( mrel @ X5 @ X6 ) )
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5063]) ).
thf(f5065,plain,
( ( $false = $true )
| ~ spl41_12 ),
inference(forward_demodulation,[],[f5064,f245]) ).
thf(f5066,plain,
( $false
| ~ spl41_12 ),
inference(trivial_inequality_removal,[],[f5065]) ).
thf(f5067,plain,
~ spl41_12,
inference(avatar_contradiction_clause,[],[f5066]) ).
thf(f5133,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
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f900,f245]) ).
thf(f5134,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 @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5133]) ).
thf(f5135,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 @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5134,f245]) ).
thf(f5136,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 @ X3 @ X4 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5135]) ).
thf(f5137,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
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5136,f245]) ).
thf(f5138,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 @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5137]) ).
thf(f5139,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 @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f5138,f245]) ).
thf(f5140,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 @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5139]) ).
thf(f5141,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 = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5140,f245]) ).
thf(f5142,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 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5141]) ).
thf(f5143,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,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f5142,f245]) ).
thf(f5144,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,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5143]) ).
thf(f5145,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5144,f245]) ).
thf(f5146,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5145]) ).
thf(f5147,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f5146,f245]) ).
thf(f5148,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5147]) ).
thf(f5149,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5148,f245]) ).
thf(f5150,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5149]) ).
thf(f5151,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5150,f245]) ).
thf(f5152,plain,
! [X2: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5151]) ).
thf(f5153,plain,
! [X10: mworld,X11: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5152,f245]) ).
thf(f5154,plain,
! [X10: mworld,X11: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5153]) ).
thf(f5155,plain,
! [X10: mworld,X11: mworld,X6: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false ) ),
inference(forward_demodulation,[],[f5154,f245]) ).
thf(f5156,plain,
! [X10: mworld,X11: mworld,X6: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5155]) ).
thf(f5157,plain,
! [X6: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5156,f245]) ).
thf(f5158,plain,
! [X6: mworld,X14: mworld,X15: mworld,X5: mworld,X13: mworld] :
( ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5157]) ).
thf(f5159,plain,
! [X6: mworld,X15: mworld,X5: mworld] :
( ( $false = $true )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5158,f245]) ).
thf(f5160,plain,
! [X6: mworld,X15: mworld,X5: mworld] :
( ( ( v13 @ ( sK18 @ X15 ) )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5159]) ).
thf(f5161,plain,
! [X15: mworld] :
( ( $false = $true )
| ( ( v13 @ ( sK18 @ X15 ) )
= $false ) ),
inference(forward_demodulation,[],[f5160,f245]) ).
thf(f5162,plain,
! [X15: mworld] :
( ( v13 @ ( sK18 @ X15 ) )
= $false ),
inference(trivial_inequality_removal,[],[f5161]) ).
thf(f5165,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: 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 @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f2054,f245]) ).
thf(f5166,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,X18: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5165]) ).
thf(f5167,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X9: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5166,f245]) ).
thf(f5168,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X16: mworld,X7: mworld,X4: mworld,X19: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5167]) ).
thf(f5169,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X7: mworld,X4: mworld,X14: mworld,X18: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5168,f245]) ).
thf(f5170,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5169]) ).
thf(f5171,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X7: mworld,X18: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5170,f245]) ).
thf(f5172,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X8: mworld,X9: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5171]) ).
thf(f5173,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,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5172,f245]) ).
thf(f5174,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X18: mworld,X14: mworld,X4: mworld,X19: mworld,X7: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5173]) ).
thf(f5175,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X4: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f5174,f245]) ).
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,X18: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5175]) ).
thf(f5177,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X9: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5176,f245]) ).
thf(f5178,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: 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 @ X18 @ X19 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5177]) ).
thf(f5179,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,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5178,f245]) ).
thf(f5180,plain,
! [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,X20: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(trivial_inequality_removal,[],[f5179]) ).
thf(f5181,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,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5180,f245]) ).
thf(f5182,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,X16: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5181]) ).
thf(f5183,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5182,f245]) ).
thf(f5184,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X6: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(trivial_inequality_removal,[],[f5183]) ).
thf(f5185,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5184,f245]) ).
thf(f5186,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,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5185]) ).
thf(f5187,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,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5186,f245]) ).
thf(f5188,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,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5187]) ).
thf(f5189,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5188,f245]) ).
thf(f5190,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5189]) ).
thf(f5191,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f5190,f245]) ).
thf(f5192,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5191]) ).
thf(f5193,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5192,f245]) ).
thf(f5194,plain,
! [X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X12: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5193]) ).
thf(f5195,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X15: mworld,X12: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false = $true )
| ( ( v25 @ X4 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5194,f245]) ).
thf(f5196,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X15: mworld,X12: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5195]) ).
thf(f5197,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5196,f245]) ).
thf(f5198,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5197]) ).
thf(f5199,plain,
! [X10: mworld,X11: mworld,X6: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false = $true )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5198,f245]) ).
thf(f5200,plain,
! [X10: mworld,X11: mworld,X6: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( ( v25 @ X4 )
= $true )
| ( $false
= ( v9 @ X20 ) ) ),
inference(trivial_inequality_removal,[],[f5199]) ).
thf(f5201,plain,
! [X11: mworld,X6: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( $false = $true )
| ( ( v25 @ X4 )
= $true )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f5200,f245]) ).
thf(f5202,plain,
! [X11: mworld,X6: mworld,X7: mworld,X4: mworld,X12: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v25 @ X4 )
= $true )
| ( ( v23 @ X6 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5201]) ).
thf(f5203,plain,
! [X6: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( ( v23 @ X6 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( ( v25 @ X4 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5202,f245]) ).
thf(f5204,plain,
! [X6: mworld,X7: mworld,X4: mworld,X20: mworld] :
( ( $false
= ( v9 @ X20 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $true )
| ( ( v23 @ X6 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5203]) ).
thf(f5206,definition,
( spl41_22
<=> ! [X6: mworld] :
( ( v23 @ X6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_22])],[avatar_definition]) ).
thf(f5207,plain,
( ! [X6: mworld] :
( ( v23 @ X6 )
= $true )
| ~ spl41_22 ),
inference(avatar_component_clause,[],[f5206]) ).
thf(f5209,definition,
( spl41_23
<=> ! [X7: mworld] :
( ( v22 @ X7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl41_23])],[avatar_definition]) ).
thf(f5210,plain,
( ! [X7: mworld] :
( ( v22 @ X7 )
= $false )
| ~ spl41_23 ),
inference(avatar_component_clause,[],[f5209]) ).
thf(f5212,definition,
( spl41_24
<=> ! [X4: mworld] :
( ( v25 @ X4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_24])],[avatar_definition]) ).
thf(f5213,plain,
( ! [X4: mworld] :
( ( v25 @ X4 )
= $true )
| ~ spl41_24 ),
inference(avatar_component_clause,[],[f5212]) ).
thf(f5215,definition,
( spl41_25
<=> ! [X20: mworld] :
( $false
= ( v9 @ X20 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_25])],[avatar_definition]) ).
thf(f5216,plain,
( ! [X20: mworld] :
( $false
= ( v9 @ X20 ) )
| ~ spl41_25 ),
inference(avatar_component_clause,[],[f5215]) ).
thf(f5217,plain,
( spl41_22
| spl41_23
| spl41_24
| spl41_25 ),
inference(avatar_split_clause,[],[f5204,f5215,f5212,f5209,f5206]) ).
thf(f5219,plain,
( ( $false = $true )
| ~ spl41_22 ),
inference(constrained_superposition,[],[f4497,f5207]) ).
thf(f5222,plain,
( $false
| ~ spl41_22 ),
inference(trivial_inequality_removal,[],[f5219]) ).
thf(f5223,plain,
~ spl41_22,
inference(avatar_contradiction_clause,[],[f5222]) ).
thf(f5224,plain,
( ( $false = $true )
| ~ spl41_23 ),
inference(constrained_superposition,[],[f5210,f4528]) ).
thf(f5230,plain,
( $false
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f5224]) ).
thf(f5231,plain,
~ spl41_23,
inference(avatar_contradiction_clause,[],[f5230]) ).
thf(f5400,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X6: mworld,X18: mworld,X4: mworld,X14: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f845,f245]) ).
thf(f5401,plain,
! [X2: mworld,X21: 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,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5400]) ).
thf(f5402,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X6: mworld,X18: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f5401,f245]) ).
thf(f5403,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X18: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f5402]) ).
thf(f5404,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X6: mworld,X7: mworld,X16: mworld,X14: mworld,X19: mworld,X9: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5403,f245]) ).
thf(f5405,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X7: mworld,X9: mworld,X14: mworld,X6: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5404]) ).
thf(f5406,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5405,f245]) ).
thf(f5407,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X1: mworld,X14: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5406]) ).
thf(f5408,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X7: mworld,X14: mworld,X9: mworld,X6: mworld,X4: mworld,X16: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5407,f245]) ).
thf(f5409,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,X8: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5408]) ).
thf(f5410,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X19: mworld,X1: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true ) ),
inference(forward_demodulation,[],[f5409,f245]) ).
thf(f5411,plain,
! [X21: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X8: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5410]) ).
thf(f5412,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X1: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5411,f245]) ).
thf(f5413,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5412]) ).
thf(f5414,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X1: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5413,f245]) ).
thf(f5415,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X7: mworld,X1: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5414]) ).
thf(f5416,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X16: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5415,f245]) ).
thf(f5417,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X19: mworld,X16: mworld,X9: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f5416]) ).
thf(f5418,plain,
! [X21: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X4: mworld,X8: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5417,f245]) ).
thf(f5419,plain,
! [X21: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X19: mworld,X9: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5418]) ).
thf(f5420,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X16: mworld,X14: mworld,X9: mworld,X1: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f5419,f245]) ).
thf(f5421,plain,
! [X21: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X1: mworld,X4: mworld,X6: mworld,X16: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5420]) ).
thf(f5422,plain,
! [X21: 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,X22: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f5421,f245]) ).
thf(f5423,plain,
! [X21: 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,X22: mworld,X5: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(trivial_inequality_removal,[],[f5422]) ).
thf(f5424,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5423,f245]) ).
thf(f5425,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f5424]) ).
thf(f5426,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5425,f245]) ).
thf(f5427,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f5426]) ).
thf(f5428,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(forward_demodulation,[],[f5427,f245]) ).
thf(f5429,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5428]) ).
thf(f5430,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true ) ),
inference(forward_demodulation,[],[f5429,f245]) ).
thf(f5431,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5430]) ).
thf(f5432,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5431,f245]) ).
thf(f5433,plain,
! [X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5432]) ).
thf(f5434,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5433,f245]) ).
thf(f5435,plain,
! [X10: mworld,X11: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X15: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5434]) ).
thf(f5436,plain,
! [X10: mworld,X11: mworld,X6: mworld,X14: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5435,f245]) ).
thf(f5437,plain,
! [X10: mworld,X11: mworld,X6: mworld,X14: mworld,X15: mworld,X22: mworld,X5: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5436]) ).
thf(f5438,plain,
! [X10: mworld,X11: mworld,X6: mworld,X22: mworld,X5: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5437,f245]) ).
thf(f5439,plain,
! [X10: mworld,X11: mworld,X6: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5438]) ).
thf(f5440,plain,
! [X6: mworld,X22: mworld,X5: mworld] :
( ( $false = $true )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5439,f245]) ).
thf(f5441,plain,
! [X6: mworld,X5: mworld,X22: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v6 @ ( sK7 @ X22 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f5440]) ).
thf(f5442,plain,
! [X22: mworld] :
( ( ( v6 @ ( sK7 @ X22 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5441,f245]) ).
thf(f5443,plain,
! [X22: mworld] :
( ( v6 @ ( sK7 @ X22 ) )
= $true ),
inference(trivial_inequality_removal,[],[f5442]) ).
thf(f5541,plain,
( ( $false = $true )
| ~ spl41_15 ),
inference(constrained_superposition,[],[f4763,f5162]) ).
thf(f5545,plain,
( $false
| ~ spl41_15 ),
inference(trivial_inequality_removal,[],[f5541]) ).
thf(f5546,plain,
~ spl41_15,
inference(avatar_contradiction_clause,[],[f5545]) ).
thf(f5644,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X8: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f840,f245]) ).
thf(f5645,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X16: mworld,X4: mworld,X6: mworld,X14: mworld,X18: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5644]) ).
thf(f5646,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X1: mworld,X4: mworld,X14: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(forward_demodulation,[],[f5645,f245]) ).
thf(f5647,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X16: mworld,X8: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5646]) ).
thf(f5648,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,X6: mworld,X7: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X12: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5647,f245]) ).
thf(f5649,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X19: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X12: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5648]) ).
thf(f5650,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,X8: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(forward_demodulation,[],[f5649,f245]) ).
thf(f5651,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X19: mworld,X6: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5650]) ).
thf(f5652,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X12: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5651,f245]) ).
thf(f5653,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X19: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5652]) ).
thf(f5654,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X6: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5653,f245]) ).
thf(f5655,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(trivial_inequality_removal,[],[f5654]) ).
thf(f5656,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X19: mworld,X1: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X12: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5655,f245]) ).
thf(f5657,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X4: mworld,X1: mworld,X16: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5656]) ).
thf(f5658,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X19: mworld,X7: mworld,X1: mworld,X4: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(forward_demodulation,[],[f5657,f245]) ).
thf(f5659,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5658]) ).
thf(f5660,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X1: mworld,X4: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5659,f245]) ).
thf(f5661,plain,
! [X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X1: mworld,X4: mworld,X19: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(trivial_inequality_removal,[],[f5660]) ).
thf(f5662,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(forward_demodulation,[],[f5661,f245]) ).
thf(f5663,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(trivial_inequality_removal,[],[f5662]) ).
thf(f5664,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X6: mworld,X4: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5663,f245]) ).
thf(f5665,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X9: mworld,X7: mworld,X4: mworld,X14: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5664]) ).
thf(f5666,plain,
! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X18: mworld,X4: mworld,X14: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5665,f245]) ).
thf(f5667,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X1: mworld,X4: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5666]) ).
thf(f5668,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5667,f245]) ).
thf(f5669,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5668]) ).
thf(f5670,plain,
! [X3: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5669,f245]) ).
thf(f5671,plain,
! [X3: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) ),
inference(trivial_inequality_removal,[],[f5670]) ).
thf(f5672,plain,
! [X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5671,f245]) ).
thf(f5673,plain,
! [X3: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5672]) ).
thf(f5674,plain,
! [X3: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5673,f245]) ).
thf(f5675,plain,
! [X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) ),
inference(trivial_inequality_removal,[],[f5674]) ).
thf(f5676,plain,
! [X3: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5675,f245]) ).
thf(f5677,plain,
! [X3: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5676]) ).
thf(f5678,plain,
! [X3: mworld,X18: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5677,f245]) ).
thf(f5679,plain,
! [X3: mworld,X18: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5678]) ).
thf(f5680,plain,
! [X3: mworld,X18: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) ) ),
inference(forward_demodulation,[],[f5679,f245]) ).
thf(f5681,plain,
! [X3: mworld,X18: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5680]) ).
thf(f5682,plain,
! [X3: mworld,X18: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(forward_demodulation,[],[f5681,f245]) ).
thf(f5683,plain,
! [X3: mworld,X18: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X23: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5682]) ).
thf(f5684,plain,
! [X3: mworld,X18: mworld,X4: mworld,X17: mworld,X23: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f5683,f245]) ).
thf(f5685,plain,
! [X3: mworld,X18: mworld,X4: mworld,X17: mworld,X23: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) ) ),
inference(trivial_inequality_removal,[],[f5684]) ).
thf(f5686,plain,
! [X3: mworld,X4: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f5685,f245]) ).
thf(f5687,plain,
! [X3: mworld,X4: mworld,X23: mworld] :
( ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[],[f5686]) ).
thf(f5688,plain,
! [X23: mworld] :
( ( $false
= ( v5 @ ( sK6 @ X23 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5687,f245]) ).
thf(f5689,plain,
! [X23: mworld] :
( $false
= ( v5 @ ( sK6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5688]) ).
thf(f5759,plain,
( ( $false = $true )
| ~ spl41_18 ),
inference(constrained_superposition,[],[f5028,f4829]) ).
thf(f5764,plain,
( $false
| ~ spl41_18 ),
inference(trivial_inequality_removal,[],[f5759]) ).
thf(f5765,plain,
~ spl41_18,
inference(avatar_contradiction_clause,[],[f5764]) ).
thf(f5771,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X18: mworld,X6: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(forward_demodulation,[],[f2465,f245]) ).
thf(f5772,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X6: mworld,X7: mworld,X18: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5771]) ).
thf(f5773,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,X6: mworld,X1: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5772,f245]) ).
thf(f5774,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X18: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f5773]) ).
thf(f5775,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( ( v25 @ X4 )
= $false )
| ( $false = $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5774,f245]) ).
thf(f5776,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,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X5: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5775]) ).
thf(f5777,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X8: mworld,X19: mworld,X7: mworld,X9: mworld,X4: mworld,X16: mworld,X6: mworld,X14: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5776,f245]) ).
thf(f5778,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X6: mworld,X1: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5777]) ).
thf(f5779,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X9: mworld,X16: mworld,X4: mworld,X6: mworld,X14: mworld,X7: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false = $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) ),
inference(forward_demodulation,[],[f5778,f245]) ).
thf(f5780,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,X9: mworld,X8: mworld,X14: mworld,X17: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5779]) ).
thf(f5781,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X9: mworld,X8: mworld,X17: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X12: mworld,X20: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5780,f245]) ).
thf(f5782,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X1: mworld,X17: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5781]) ).
thf(f5783,plain,
! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X4: mworld,X14: mworld,X18: mworld,X16: mworld,X17: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f5782,f245]) ).
thf(f5784,plain,
! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X8: mworld,X19: mworld,X18: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X6: mworld,X9: mworld,X17: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f5783]) ).
thf(f5785,plain,
! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X9: mworld,X17: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f5784,f245]) ).
thf(f5786,plain,
! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X6: mworld,X7: mworld,X17: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v25 @ X4 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X20 @ X21 ) ) ),
inference(trivial_inequality_removal,[],[f5785]) ).
thf(f5787,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X6: mworld,X4: mworld,X1: mworld,X17: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false = $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5786,f245]) ).
thf(f5788,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X16: mworld,X4: mworld,X1: mworld,X17: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true ) ),
inference(trivial_inequality_removal,[],[f5787]) ).
thf(f5789,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X1: mworld,X4: mworld,X6: mworld,X16: mworld,X17: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(forward_demodulation,[],[f5788,f245]) ).
thf(f5790,plain,
! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5789]) ).
thf(f5791,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X16: mworld,X7: mworld,X4: mworld,X6: mworld,X9: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) ),
inference(forward_demodulation,[],[f5790,f245]) ).
thf(f5792,plain,
! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X4: mworld,X9: mworld,X18: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X13: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5791]) ).
thf(f5793,plain,
! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X8: mworld,X9: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) ),
inference(forward_demodulation,[],[f5792,f245]) ).
thf(f5794,plain,
! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X8: mworld,X9: mworld,X4: mworld,X7: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(trivial_inequality_removal,[],[f5793]) ).
thf(f5795,plain,
! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X8: mworld,X9: mworld,X4: mworld,X16: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v25 @ X4 )
= $false )
| ( $true
= ( v13 @ X16 ) ) ),
inference(forward_demodulation,[],[f5794,f245]) ).
thf(f5796,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X9: mworld,X4: mworld,X7: mworld,X1: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5795]) ).
thf(f5797,plain,
! [X2: mworld,X21: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( ( v25 @ X4 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) ),
inference(forward_demodulation,[],[f5796,f245]) ).
thf(f5798,plain,
! [X2: mworld,X21: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X4: mworld,X8: mworld,X9: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v25 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5797]) ).
thf(f5799,plain,
! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X7: mworld,X4: mworld,X18: mworld,X16: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5798,f245]) ).
thf(f5800,plain,
! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X4: mworld,X1: mworld,X16: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v25 @ X4 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v13 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5799]) ).
thf(f5801,plain,
( ! [X2: mworld,X21: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X19: mworld,X1: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5800,f5213]) ).
thf(f5802,plain,
( ! [X2: mworld,X21: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X6: mworld,X18: mworld,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X13: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5801]) ).
thf(f5803,plain,
( ! [X2: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X1: mworld,X9: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5802,f245]) ).
thf(f5804,plain,
( ! [X2: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X16: mworld,X7: mworld,X1: mworld,X9: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5803]) ).
thf(f5805,plain,
( ! [X2: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X16: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5804,f245]) ).
thf(f5806,plain,
( ! [X2: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X6: mworld,X7: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5805]) ).
thf(f5807,plain,
( ! [X8: mworld,X6: mworld,X9: mworld,X7: mworld,X19: mworld,X16: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5806,f245]) ).
thf(f5808,plain,
( ! [X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5807]) ).
thf(f5809,plain,
( ! [X8: mworld,X6: mworld,X9: mworld,X7: mworld,X16: mworld,X19: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( v10 @ X19 )
= $true ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5808,f245]) ).
thf(f5810,plain,
( ! [X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X19: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5809]) ).
thf(f5811,plain,
( ! [X8: mworld,X19: mworld,X9: mworld,X7: mworld,X16: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5810,f245]) ).
thf(f5812,plain,
( ! [X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v13 @ X16 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v10 @ X19 )
= $true ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5811]) ).
thf(f5813,plain,
( ! [X8: mworld,X19: mworld,X7: mworld,X16: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( v10 @ X19 )
= $true ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5812,f245]) ).
thf(f5814,plain,
( ! [X8: mworld,X19: mworld,X7: mworld,X16: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v13 @ X16 ) )
| ( ( v10 @ X19 )
= $true ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5813]) ).
thf(f5815,plain,
( ! [X8: mworld,X19: mworld,X16: mworld,X7: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false = $true ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5814,f245]) ).
thf(f5816,plain,
( ! [X8: mworld,X19: mworld,X7: mworld,X16: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( v10 @ X19 )
= $true )
| ( $true
= ( v13 @ X16 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5815]) ).
thf(f5817,plain,
( ! [X19: mworld,X16: mworld,X23: mworld] :
( ( ( v10 @ X19 )
= $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false = $true )
| ( $true
= ( v13 @ X16 ) ) )
| ~ spl41_24 ),
inference(forward_demodulation,[],[f5816,f245]) ).
thf(f5818,plain,
( ! [X19: mworld,X16: mworld,X23: mworld] :
( ( $true
= ( v13 @ X16 ) )
| ( ( v10 @ X19 )
= $true )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_24 ),
inference(trivial_inequality_removal,[],[f5817]) ).
thf(f5820,definition,
( spl41_30
<=> ! [X23: mworld] :
( $false
= ( v6 @ X23 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_30])],[avatar_definition]) ).
thf(f5821,plain,
( ! [X23: mworld] :
( $false
= ( v6 @ X23 ) )
| ~ spl41_30 ),
inference(avatar_component_clause,[],[f5820]) ).
thf(f5823,definition,
( spl41_31
<=> ! [X19: mworld] :
( ( v10 @ X19 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_31])],[avatar_definition]) ).
thf(f5824,plain,
( ! [X19: mworld] :
( ( v10 @ X19 )
= $true )
| ~ spl41_31 ),
inference(avatar_component_clause,[],[f5823]) ).
thf(f5825,plain,
( spl41_15
| spl41_30
| spl41_31
| ~ spl41_24 ),
inference(avatar_split_clause,[],[f5818,f5212,f5823,f5820,f4762]) ).
thf(f5895,plain,
( ( $false = $true )
| ~ spl41_30 ),
inference(constrained_superposition,[],[f5821,f5443]) ).
thf(f5901,plain,
( $false
| ~ spl41_30 ),
inference(trivial_inequality_removal,[],[f5895]) ).
thf(f5902,plain,
~ spl41_30,
inference(avatar_contradiction_clause,[],[f5901]) ).
thf(f5903,plain,
( ( $false = $true )
| ~ spl41_19
| ~ spl41_25 ),
inference(forward_demodulation,[],[f5031,f5216]) ).
thf(f5904,plain,
( $false
| ~ spl41_19
| ~ spl41_25 ),
inference(trivial_inequality_removal,[],[f5903]) ).
thf(f5905,plain,
( ~ spl41_19
| ~ spl41_25 ),
inference(avatar_contradiction_clause,[],[f5904]) ).
thf(f5911,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X18: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X19: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f2542,f245]) ).
thf(f5912,plain,
! [X2: mworld,X21: 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,X22: mworld,X5: mworld,X23: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(trivial_inequality_removal,[],[f5911]) ).
thf(f5913,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X6: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) ) ),
inference(forward_demodulation,[],[f5912,f245]) ).
thf(f5914,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X16: mworld,X19: mworld,X4: mworld,X6: mworld,X14: mworld,X7: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v18 @ X11 ) ) ),
inference(trivial_inequality_removal,[],[f5913]) ).
thf(f5915,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X9: mworld,X14: mworld,X7: mworld,X1: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(forward_demodulation,[],[f5914,f245]) ).
thf(f5916,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X1: mworld,X14: mworld,X9: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X5: mworld,X13: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) ),
inference(trivial_inequality_removal,[],[f5915]) ).
thf(f5917,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X7: mworld,X6: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false ) ),
inference(forward_demodulation,[],[f5916,f245]) ).
thf(f5918,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,X18: mworld,X19: mworld,X4: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( v15 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f5917]) ).
thf(f5919,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X1: mworld,X16: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v26 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5918,f245]) ).
thf(f5920,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X8: mworld,X16: mworld,X14: mworld,X7: mworld,X9: mworld,X4: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) ),
inference(trivial_inequality_removal,[],[f5919]) ).
thf(f5921,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false = $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5920,f245]) ).
thf(f5922,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X1: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v26 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f5921]) ).
thf(f5923,plain,
! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X6: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) ),
inference(forward_demodulation,[],[f5922,f245]) ).
thf(f5924,plain,
! [X2: mworld,X21: 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,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( v26 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v6 @ X23 ) ) ),
inference(trivial_inequality_removal,[],[f5923]) ).
thf(f5925,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X19: mworld,X1: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5924,f4568]) ).
thf(f5926,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5925]) ).
thf(f5927,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X9: mworld,X6: mworld,X14: mworld,X4: mworld,X8: mworld,X7: mworld,X17: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X12: mworld,X20: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false = $true ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5926,f245]) ).
thf(f5928,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X19: mworld,X17: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld,X20: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v18 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5927]) ).
thf(f5929,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X6: mworld,X9: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false = $true ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5928,f245]) ).
thf(f5930,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X6: mworld,X17: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5929]) ).
thf(f5931,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X14: mworld,X4: mworld,X7: mworld,X1: mworld,X17: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X23: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v18 @ X11 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5930,f245]) ).
thf(f5932,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X19: mworld,X9: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5931]) ).
thf(f5933,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X19: mworld,X17: mworld,X5: mworld,X22: mworld,X12: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v18 @ X11 ) ) )
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5932,f245]) ).
thf(f5934,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X8: mworld,X6: mworld,X7: mworld,X14: mworld,X19: mworld,X9: mworld,X4: mworld,X17: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( $false
= ( v18 @ X11 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5933]) ).
thf(f5935,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X1: mworld,X4: mworld,X6: mworld,X14: mworld,X17: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5934,f4427]) ).
thf(f5936,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X9: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld,X22: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5935]) ).
thf(f5937,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X5: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5936,f245]) ).
thf(f5938,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X10: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X8: mworld,X17: mworld,X22: mworld,X5: mworld,X12: mworld,X13: mworld,X23: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5937]) ).
thf(f5939,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X18: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5938,f245]) ).
thf(f5940,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X1: mworld,X17: mworld,X5: mworld,X12: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5939]) ).
thf(f5941,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X5: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5940,f245]) ).
thf(f5942,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X6: mworld,X17: mworld,X5: mworld,X23: mworld,X13: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5941]) ).
thf(f5943,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X1: mworld,X9: mworld,X7: mworld,X14: mworld,X6: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5942,f245]) ).
thf(f5944,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X7: mworld,X8: mworld,X4: mworld,X14: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5943]) ).
thf(f5945,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false = $true ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5944,f245]) ).
thf(f5946,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X18: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5945]) ).
thf(f5947,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5946,f245]) ).
thf(f5948,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5947]) ).
thf(f5949,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5948,f245]) ).
thf(f5950,plain,
( ! [X2: mworld,X3: mworld,X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5949]) ).
thf(f5951,plain,
( ! [X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false = $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5950,f245]) ).
thf(f5952,plain,
( ! [X10: mworld,X18: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X17: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5951]) ).
thf(f5953,plain,
( ! [X10: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5952,f245]) ).
thf(f5954,plain,
( ! [X10: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X5: mworld,X23: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5953]) ).
thf(f5955,plain,
( ! [X10: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X23: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5954,f245]) ).
thf(f5956,plain,
( ! [X10: mworld,X8: mworld,X9: mworld,X7: mworld,X14: mworld,X23: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5955]) ).
thf(f5957,plain,
( ! [X10: mworld,X9: mworld,X14: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5956,f245]) ).
thf(f5958,plain,
( ! [X10: mworld,X9: mworld,X14: mworld,X23: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5957]) ).
thf(f5959,plain,
( ! [X14: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( v6 @ X23 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(forward_demodulation,[],[f5958,f245]) ).
thf(f5960,plain,
( ! [X14: mworld,X23: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( v6 @ X23 ) ) )
| ~ spl41_4
| ~ spl41_10 ),
inference(trivial_inequality_removal,[],[f5959]) ).
thf(f5961,plain,
( spl41_30
| spl41_18
| ~ spl41_4
| ~ spl41_10 ),
inference(avatar_split_clause,[],[f5960,f4567,f4426,f5027,f5820]) ).
thf(f5997,plain,
( ! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f627,f5824]) ).
thf(f5998,plain,
( ! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f5997]) ).
thf(f5999,plain,
( ! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X23 @ X24 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f5998,f245]) ).
thf(f6000,plain,
( ! [X2: mworld,X21: mworld,X11: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X13: mworld,X20: mworld,X3: mworld,X10: mworld,X1: mworld,X8: mworld,X19: mworld,X7: mworld,X14: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X23: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f5999]) ).
thf(f6001,plain,
( ! [X20: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X1: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld,X15: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6000,f245]) ).
thf(f6002,plain,
( ! [X20: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X9: mworld,X17: mworld,X24: mworld,X5: mworld,X15: mworld,X12: mworld,X22: mworld,X13: mworld,X23: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6001]) ).
thf(f6003,plain,
( ! [X15: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X1: mworld,X4: mworld,X14: mworld,X17: mworld,X24: mworld,X22: mworld,X5: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6002,f245]) ).
thf(f6004,plain,
( ! [X12: mworld,X2: mworld,X21: 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,X24: mworld,X15: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6003]) ).
thf(f6005,plain,
( ! [X13: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X7: mworld,X14: mworld,X4: mworld,X8: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X22: mworld,X23: mworld,X24: mworld,X20: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6004,f245]) ).
thf(f6006,plain,
( ! [X23: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X24: mworld,X5: mworld,X12: mworld,X15: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6005]) ).
thf(f6007,plain,
( ! [X12: mworld,X2: mworld,X21: 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,X24: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6006,f245]) ).
thf(f6008,plain,
( ! [X23: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X8: mworld,X17: mworld,X15: mworld,X24: mworld,X22: mworld,X5: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6007]) ).
thf(f6009,plain,
( ! [X12: mworld,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,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6008,f245]) ).
thf(f6010,plain,
( ! [X13: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6009]) ).
thf(f6011,plain,
( ! [X5: mworld,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,X24: mworld,X22: mworld,X15: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6010,f245]) ).
thf(f6012,plain,
( ! [X20: mworld,X2: mworld,X21: 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,X22: mworld,X12: mworld,X13: mworld,X23: mworld,X24: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6011]) ).
thf(f6013,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X24: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X15: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6012,f245]) ).
thf(f6014,plain,
( ! [X5: mworld,X2: mworld,X21: 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,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6013]) ).
thf(f6015,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X24: mworld,X15: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X22: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6014,f245]) ).
thf(f6016,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X24: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6015]) ).
thf(f6017,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X24: mworld,X15: mworld,X12: mworld,X22: mworld,X13: mworld,X20: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6016,f245]) ).
thf(f6018,plain,
( ! [X13: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X24: mworld,X15: mworld,X5: mworld,X23: mworld,X12: mworld,X20: mworld,X22: mworld] :
( ( $false
= ( mrel @ X23 @ X24 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6017]) ).
thf(f6019,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X24: mworld,X15: mworld,X22: mworld,X23: mworld,X13: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( v9 @ X20 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) ) )
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6018,f245]) ).
thf(f6020,plain,
( ! [X23: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X24: mworld,X5: mworld,X12: mworld,X15: mworld,X13: mworld,X22: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v9 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6019]) ).
thf(f6021,plain,
( ! [X5: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6020,f5031]) ).
thf(f6022,plain,
( ! [X24: mworld,X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X13: mworld,X20: mworld,X5: mworld] :
( ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6021]) ).
thf(f6023,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X24: mworld,X5: mworld,X22: mworld,X23: mworld,X15: mworld,X20: mworld,X12: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false = $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6022,f245]) ).
thf(f6024,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X6: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X24: mworld,X15: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X5: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6023]) ).
thf(f6025,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X15: mworld,X22: mworld,X5: mworld,X23: mworld,X24: mworld,X20: mworld,X12: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6024,f245]) ).
thf(f6026,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X15: mworld,X5: mworld,X22: mworld,X23: mworld,X12: mworld,X20: mworld,X24: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6025]) ).
thf(f6027,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X15: mworld,X22: mworld,X12: mworld,X24: mworld,X23: mworld,X20: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v5 @ X24 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6026,f245]) ).
thf(f6028,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X24: mworld,X22: mworld,X12: mworld,X23: mworld,X15: mworld,X20: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X20 @ X21 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6027]) ).
thf(f6029,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X24: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6028,f245]) ).
thf(f6030,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X24: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6029]) ).
thf(f6031,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X7: mworld,X15: mworld,X22: mworld,X12: mworld,X23: mworld,X24: mworld] :
( ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( ( mrel @ X21 @ X22 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6030,f245]) ).
thf(f6032,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X16: mworld,X4: mworld,X14: mworld,X15: mworld,X22: mworld,X12: mworld,X24: mworld,X23: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6031]) ).
thf(f6033,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X24: mworld,X12: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X21 @ X22 )
= $false )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6032,f245]) ).
thf(f6034,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X11: mworld,X1: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X24: mworld,X12: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( mrel @ X21 @ X22 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6033]) ).
thf(f6035,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6034,f245]) ).
thf(f6036,plain,
( ! [X2: mworld,X21: mworld,X3: mworld,X1: mworld,X16: mworld,X7: mworld,X14: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld] :
( ( ( mrel @ X21 @ X22 )
= $false )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6035]) ).
thf(f6037,plain,
( ! [X2: mworld,X3: mworld,X1: mworld,X7: mworld,X14: mworld,X16: mworld,X24: mworld,X22: mworld,X15: mworld,X23: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false = $true )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X2 @ X3 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6036,f245]) ).
thf(f6038,plain,
( ! [X2: mworld,X3: mworld,X1: mworld,X16: mworld,X14: mworld,X7: mworld,X24: mworld,X15: mworld,X22: mworld,X23: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6037]) ).
thf(f6039,plain,
( ! [X1: mworld,X7: mworld,X16: mworld,X14: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld] :
( ( ( v22 @ X7 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6038,f245]) ).
thf(f6040,plain,
( ! [X1: mworld,X7: mworld,X14: mworld,X16: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6039]) ).
thf(f6041,plain,
( ! [X7: mworld,X16: mworld,X14: mworld,X24: mworld,X22: mworld,X15: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X14 @ X15 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6040,f245]) ).
thf(f6042,plain,
( ! [X7: mworld,X14: mworld,X16: mworld,X24: mworld,X15: mworld,X22: mworld,X23: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X14 @ X15 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X22 @ X23 ) ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6041]) ).
thf(f6043,plain,
( ! [X16: mworld,X7: mworld,X24: mworld,X15: mworld,X22: mworld,X23: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( $false = $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6042,f245]) ).
thf(f6044,plain,
( ! [X16: mworld,X7: mworld,X15: mworld,X22: mworld,X24: mworld,X23: mworld] :
( ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v22 @ X7 )
= $false )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6043]) ).
thf(f6045,plain,
( ! [X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6044,f245]) ).
thf(f6046,plain,
( ! [X7: mworld,X24: mworld,X22: mworld,X23: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( $false
= ( mrel @ X22 @ X23 ) )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6045]) ).
thf(f6047,plain,
( ! [X7: mworld,X24: mworld] :
( ( $false = $true )
| ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(forward_demodulation,[],[f6046,f245]) ).
thf(f6048,plain,
( ! [X7: mworld,X24: mworld] :
( ( ( v5 @ X24 )
= $true )
| ( ( v22 @ X7 )
= $false ) )
| ~ spl41_19
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f6047]) ).
thf(f6050,definition,
( spl41_34
<=> ! [X24: mworld] :
( ( v5 @ X24 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl41_34])],[avatar_definition]) ).
thf(f6051,plain,
( ! [X24: mworld] :
( ( v5 @ X24 )
= $true )
| ~ spl41_34 ),
inference(avatar_component_clause,[],[f6050]) ).
thf(f6052,plain,
( spl41_34
| spl41_23
| ~ spl41_19
| ~ spl41_31 ),
inference(avatar_split_clause,[],[f6048,f5823,f5030,f5209,f6050]) ).
thf(f6054,plain,
( ( $false = $true )
| ~ spl41_34 ),
inference(constrained_superposition,[],[f5689,f6051]) ).
thf(f6057,plain,
( $false
| ~ spl41_34 ),
inference(trivial_inequality_removal,[],[f6054]) ).
thf(f6058,plain,
~ spl41_34,
inference(avatar_contradiction_clause,[],[f6057]) ).
thf(f6061,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X19: mworld,X7: mworld,X14: mworld,X16: mworld,X4: mworld,X8: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( ( v9 @ X20 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) ),
inference(forward_demodulation,[],[f3114,f245]) ).
thf(f6062,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X9: mworld,X4: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X11 @ X12 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( v9 @ X20 )
= $true ) ),
inference(trivial_inequality_removal,[],[f6061]) ).
thf(f6065,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X18: mworld,X7: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(forward_demodulation,[],[f6062,f245]) ).
thf(f6066,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X18: mworld,X7: mworld,X16: mworld,X4: mworld,X6: mworld,X14: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X4 @ X5 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v28 @ X1 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f6065]) ).
thf(f6069,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X8: mworld,X7: mworld,X19: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v28 @ X1 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) ) ),
inference(forward_demodulation,[],[f6066,f245]) ).
thf(f6070,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X9: mworld,X6: mworld,X7: mworld,X16: mworld,X14: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X16 @ X17 ) ) ),
inference(trivial_inequality_removal,[],[f6069]) ).
thf(f6073,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X7: mworld,X4: mworld,X14: mworld,X18: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X9 @ X10 ) ) ),
inference(forward_demodulation,[],[f6070,f245]) ).
thf(f6074,plain,
! [X2: mworld,X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X7: mworld,X9: mworld,X4: mworld,X14: mworld,X16: mworld,X18: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X2 @ X3 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(trivial_inequality_removal,[],[f6073]) ).
thf(f6077,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X16: mworld,X19: mworld,X4: mworld,X1: mworld,X14: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v28 @ X1 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) ),
inference(forward_demodulation,[],[f6074,f245]) ).
thf(f6078,plain,
! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X1: mworld,X4: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v28 @ X1 )
= $true )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f6077]) ).
thf(f6081,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X6: mworld,X7: mworld,X14: mworld,X16: mworld,X1: mworld,X4: mworld,X9: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6078,f4424]) ).
thf(f6082,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X6: mworld,X8: mworld,X7: mworld,X9: mworld,X19: mworld,X14: mworld,X16: mworld,X4: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( ( mrel @ X6 @ X7 )
= $false )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X18 @ X19 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6081]) ).
thf(f6085,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X7: mworld,X1: mworld,X4: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6082,f245]) ).
thf(f6086,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X19: mworld,X9: mworld,X14: mworld,X16: mworld,X7: mworld,X4: mworld,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X12: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X12 @ X13 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6085]) ).
thf(f6089,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X1: mworld,X7: mworld,X9: mworld,X4: mworld,X16: mworld,X14: mworld,X6: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6086,f245]) ).
thf(f6090,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X6: mworld,X19: mworld,X16: mworld,X14: mworld,X9: mworld,X4: mworld,X18: mworld,X7: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X16 @ X17 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X7 @ X8 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6089]) ).
thf(f6093,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,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false = $true ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6090,f245]) ).
thf(f6094,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,X1: mworld,X17: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( v9 @ X20 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X17 @ X18 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6093]) ).
thf(f6097,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X7: mworld,X4: mworld,X18: mworld,X6: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false = $true ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6094,f245]) ).
thf(f6098,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X7: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X18: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X7 @ X8 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6097]) ).
thf(f6101,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X18: mworld,X4: mworld,X6: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v14 @ X15 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6098,f245]) ).
thf(f6102,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X6: mworld,X9: mworld,X19: mworld,X1: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X9 @ X10 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6101]) ).
thf(f6105,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X4: mworld,X16: mworld,X6: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X5 @ X6 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6102,f245]) ).
thf(f6106,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X1: mworld,X18: mworld,X6: mworld,X19: mworld,X8: mworld,X14: mworld,X9: mworld,X16: mworld,X4: mworld,X15: mworld,X5: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X5 @ X6 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6105]) ).
thf(f6109,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X1: mworld,X4: mworld,X14: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v9 @ X20 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X13 @ X14 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6106,f245]) ).
thf(f6110,plain,
( ! [X3: mworld,X10: mworld,X11: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X16: mworld,X14: mworld,X4: mworld,X9: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X10 @ X11 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6109]) ).
thf(f6112,plain,
( ! [X3: mworld,X18: mworld,X8: mworld,X19: mworld,X9: mworld,X1: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v9 @ X20 )
= $true ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6110,f245]) ).
thf(f6113,plain,
( ! [X3: mworld,X18: mworld,X1: mworld,X19: mworld,X8: mworld,X9: mworld,X14: mworld,X16: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X18 @ X19 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6112]) ).
thf(f6114,plain,
( ! [X3: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6113,f245]) ).
thf(f6115,plain,
( ! [X3: mworld,X1: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X8 @ X9 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6114]) ).
thf(f6116,plain,
( ! [X3: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6115,f245]) ).
thf(f6117,plain,
( ! [X3: mworld,X8: mworld,X19: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X19 @ X20 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v9 @ X20 )
= $true ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6116]) ).
thf(f6118,plain,
( ! [X3: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6117,f245]) ).
thf(f6119,plain,
( ! [X3: mworld,X8: mworld,X9: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( mrel @ X8 @ X9 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6118]) ).
thf(f6120,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false = $true )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6119,f245]) ).
thf(f6121,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X13: mworld,X20: mworld] :
( ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X13 @ X14 ) )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6120]) ).
thf(f6122,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X20: mworld] :
( ( ( v9 @ X20 )
= $true )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6121,f245]) ).
thf(f6123,plain,
( ! [X3: mworld,X16: mworld,X14: mworld,X4: mworld,X15: mworld,X20: mworld] :
( ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( ( v9 @ X20 )
= $true ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6122]) ).
thf(f6124,plain,
( ! [X16: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( ( v9 @ X20 )
= $true )
| ( $false = $true )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( $true
= ( v14 @ X15 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6123,f245]) ).
thf(f6125,plain,
( ! [X16: mworld,X14: mworld,X15: mworld,X20: mworld] :
( ( $true
= ( v14 @ X15 ) )
| ( $false
= ( v15 @ X14 ) )
| ( $false
= ( mrel @ X15 @ X16 ) )
| ( ( v9 @ X20 )
= $true ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6124]) ).
thf(f6126,plain,
( ! [X14: mworld,X15: mworld,X20: mworld] :
( ( $false = $true )
| ( ( v9 @ X20 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) ) )
| ~ spl41_3 ),
inference(forward_demodulation,[],[f6125,f245]) ).
thf(f6127,plain,
( ! [X14: mworld,X15: mworld,X20: mworld] :
( ( ( v9 @ X20 )
= $true )
| ( $false
= ( v15 @ X14 ) )
| ( $true
= ( v14 @ X15 ) ) )
| ~ spl41_3 ),
inference(trivial_inequality_removal,[],[f6126]) ).
thf(f6128,plain,
( spl41_9
| spl41_18
| spl41_19
| ~ spl41_3 ),
inference(avatar_split_clause,[],[f6127,f4423,f5030,f5027,f4564]) ).
thf(f6251,plain,
( ( $false = $true )
| ~ spl41_13 ),
inference(constrained_superposition,[],[f4695,f4668]) ).
thf(f6255,plain,
( $false
| ~ spl41_13 ),
inference(trivial_inequality_removal,[],[f6251]) ).
thf(f6256,plain,
~ spl41_13,
inference(avatar_contradiction_clause,[],[f6255]) ).
cnf(s1,plain,
( spl41_1
| spl41_2
| spl41_3
| spl41_4 ),
inference(sat_conversion,[],[f4428]) ).
cnf(s3,plain,
~ spl41_2,
inference(sat_conversion,[],[f4514]) ).
cnf(s7,plain,
( spl41_3
| spl41_10
| spl41_12
| spl41_13 ),
inference(sat_conversion,[],[f4669]) ).
cnf(s11,plain,
~ spl41_1,
inference(sat_conversion,[],[f4803]) ).
cnf(s15,plain,
~ spl41_9,
inference(sat_conversion,[],[f4936]) ).
cnf(s17,plain,
~ spl41_12,
inference(sat_conversion,[],[f5067]) ).
cnf(s19,plain,
( spl41_22
| spl41_23
| spl41_24
| spl41_25 ),
inference(sat_conversion,[],[f5217]) ).
cnf(s21,plain,
~ spl41_22,
inference(sat_conversion,[],[f5223]) ).
cnf(s23,plain,
~ spl41_23,
inference(sat_conversion,[],[f5231]) ).
cnf(s26,plain,
~ spl41_15,
inference(sat_conversion,[],[f5546]) ).
cnf(s32,plain,
~ spl41_18,
inference(sat_conversion,[],[f5765]) ).
cnf(s33,plain,
( spl41_15
| ~ spl41_24
| spl41_30
| spl41_31 ),
inference(sat_conversion,[],[f5825]) ).
cnf(s37,plain,
~ spl41_30,
inference(sat_conversion,[],[f5902]) ).
cnf(s38,plain,
( ~ spl41_19
| ~ spl41_25 ),
inference(sat_conversion,[],[f5905]) ).
cnf(s40,plain,
( ~ spl41_4
| ~ spl41_10
| spl41_18
| spl41_30 ),
inference(sat_conversion,[],[f5961]) ).
cnf(s43,plain,
( ~ spl41_19
| spl41_23
| ~ spl41_31
| spl41_34 ),
inference(sat_conversion,[],[f6052]) ).
cnf(s45,plain,
~ spl41_34,
inference(sat_conversion,[],[f6058]) ).
cnf(s47,plain,
( ~ spl41_3
| spl41_9
| spl41_18
| spl41_19 ),
inference(sat_conversion,[],[f6128]) ).
cnf(s53,plain,
~ spl41_13,
inference(sat_conversion,[],[f6256]) ).
cnf(s54,plain,
( ~ spl41_19
| spl41_23
| ~ spl41_31 ),
inference(rat,[],[s43,s45]) ).
cnf(s57,plain,
( spl41_15
| ~ spl41_24
| spl41_31 ),
inference(rat,[],[s33,s37]) ).
cnf(s59,plain,
( spl41_24
| spl41_25 ),
inference(rat,[],[s19,s23,s21]) ).
cnf(s64,plain,
( spl41_3
| spl41_10 ),
inference(rat,[],[s7,s53,s17]) ).
cnf(s68,plain,
( spl41_3
| spl41_4 ),
inference(rat,[],[s1,s3,s11]) ).
cnf(s69,plain,
spl41_3,
inference(rat,[],[s40,s68,s64,s32,s37]) ).
cnf(s70,plain,
spl41_19,
inference(rat,[],[s47,s15,s32,s69]) ).
cnf(s74,plain,
~ spl41_31,
inference(rat,[],[s54,s23,s70]) ).
cnf(s75,plain,
~ spl41_25,
inference(rat,[],[s38,s70]) ).
cnf(s79,plain,
~ spl41_24,
inference(rat,[],[s57,s26,s74]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s59,s75,s79]) ).
thf(f6257,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO904^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:26:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.24 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
% 0.74/0.37 % (394890)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.37 % (394895)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3558053299:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.37 % (394901)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.37 % (394901)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
% 0.74/0.37 % (394896)lrs+10_16_si=on:nwc=1.5:random_seed=4161895379:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.37 % (394897)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1586547665:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.37 % (394899)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=472351573:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.37 % (394898)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=1691357986: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)
% 0.74/0.37 % (394900)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3235261815:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.37 % (394901)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=1631210183:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.37 % (394897)Instruction limit reached!
% 0.74/0.37 % (394897)------------------------------
% 0.74/0.37 % (394897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (394897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (394897)CaDiCaL version: 2.1.3
% 0.74/0.37 % (394897)Termination reason: Instruction limit
% 0.74/0.37 % (394897)Termination phase: shuffling
% 0.74/0.37 % (394897)Time elapsed: 0.003 s
% 0.74/0.37 % (394897)Peak memory usage: 10 MB
% 0.74/0.37 % (394897)Instructions burned: 7 (million)
% 0.74/0.37 % (394896)Instruction limit reached!
% 0.74/0.37 % (394896)------------------------------
% 0.74/0.37 % (394896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (394896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (394896)CaDiCaL version: 2.1.3
% 0.74/0.37 % (394896)Termination reason: Instruction limit
% 0.74/0.37 % (394896)Termination phase: shuffling
% 0.74/0.37 % (394896)Time elapsed: 0.007 s
% 0.74/0.37 % (394896)Peak memory usage: 10 MB
% 0.74/0.37 % (394896)Instructions burned: 20 (million)
% 0.74/0.37 % (394899)Instruction limit reached!
% 0.74/0.37 % (394899)------------------------------
% 0.74/0.37 % (394899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (394895)Instruction limit reached!
% 0.74/0.37 % (394895)------------------------------
% 0.74/0.37 % (394895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (394899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (394895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (394899)CaDiCaL version: 2.1.3
% 0.74/0.37 % (394899)Termination reason: Instruction limit
% 0.74/0.37 % (394899)Termination phase: shuffling
% 0.74/0.37 % (394899)Time elapsed: 0.008 s
% 0.74/0.37 % (394899)Peak memory usage: 9 MB
% 0.74/0.37 % (394899)Instructions burned: 25 (million)
% 0.74/0.37 % (394895)CaDiCaL version: 2.1.3
% 0.74/0.37 % (394895)Termination reason: Instruction limit
% 0.74/0.37 % (394895)Termination phase: Property scanning
% 0.74/0.37 % (394895)Time elapsed: 0.016 s
% 0.74/0.37 % (394895)Peak memory usage: 10 MB
% 0.74/0.37 % (394895)Instructions burned: 90 (million)
% 0.74/0.37 % (394911)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.37 % (394911)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3830485162:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.39 % (394911)Instruction limit reached!
% 0.74/0.39 % (394911)------------------------------
% 0.74/0.39 % (394911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394911)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394911)Termination reason: Instruction limit
% 0.74/0.39 % (394911)Termination phase: shuffling
% 0.74/0.39 % (394911)Time elapsed: 0.001 s
% 0.74/0.39 % (394911)Peak memory usage: 10 MB
% 0.74/0.39 % (394911)Instructions burned: 7 (million)
% 0.74/0.39 % (394909)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1812587255:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.39 % (394909)Instruction limit reached!
% 0.74/0.39 % (394909)------------------------------
% 0.74/0.39 % (394909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394909)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394909)Termination reason: Instruction limit
% 0.74/0.39 % (394909)Termination phase: shuffling
% 0.74/0.39 % (394909)Time elapsed: 0.003 s
% 0.74/0.39 % (394909)Peak memory usage: 10 MB
% 0.74/0.39 % (394909)Instructions burned: 9 (million)
% 0.74/0.39 % (394910)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3967582810:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.39 % (394900)Instruction limit reached!
% 0.74/0.39 % (394900)------------------------------
% 0.74/0.39 % (394900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394900)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394900)Termination reason: Instruction limit
% 0.74/0.39 % (394900)Termination phase: Function definition elimination
% 0.74/0.39 % (394900)Time elapsed: 0.026 s
% 0.74/0.39 % (394900)Peak memory usage: 10 MB
% 0.74/0.39 % (394900)Instructions burned: 76 (million)
% 0.74/0.39 % (394912)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3738206698:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.39 % (394914)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
% 0.74/0.39 % (394914)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.39 % (394910)Instruction limit reached!
% 0.74/0.39 % (394910)------------------------------
% 0.74/0.39 % (394910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394910)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394910)Termination reason: Instruction limit
% 0.74/0.39 % (394910)Termination phase: shuffling
% 0.74/0.39 % (394910)Time elapsed: 0.003 s
% 0.74/0.39 % (394910)Peak memory usage: 10 MB
% 0.74/0.39 % (394910)Instructions burned: 9 (million)
% 0.74/0.39 % (394914)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1251536829:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.39 % (394912)Instruction limit reached!
% 0.74/0.39 % (394912)------------------------------
% 0.74/0.39 % (394912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394912)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394912)Termination reason: Instruction limit
% 0.74/0.39 % (394912)Termination phase: shuffling
% 0.74/0.39 % (394912)Time elapsed: 0.005 s
% 0.74/0.39 % (394912)Peak memory usage: 10 MB
% 0.74/0.39 % (394912)Instructions burned: 14 (million)
% 0.74/0.39 % (394914)Instruction limit reached!
% 0.74/0.39 % (394914)------------------------------
% 0.74/0.39 % (394914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.39 % (394914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.39 % (394914)CaDiCaL version: 2.1.3
% 0.74/0.39 % (394914)Termination reason: Instruction limit
% 0.74/0.39 % (394914)Termination phase: Function definition elimination
% 0.74/0.39 % (394914)Time elapsed: 0.006 s
% 0.74/0.41 % (394914)Peak memory usage: 10 MB
% 0.74/0.41 % (394914)Instructions burned: 30 (million)
% 0.74/0.41 % (394920)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.41 % (394917)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=3338273175:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.41 % (394918)lrs+10_1_si=on:cs=on:random_seed=2689395822:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.41 % (394923)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3647762019:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.41 % (394920)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=373685665:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.41 % (394918)Instruction limit reached!
% 0.74/0.41 % (394918)------------------------------
% 0.74/0.41 % (394918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (394918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (394918)CaDiCaL version: 2.1.3
% 0.74/0.41 % (394918)Termination reason: Instruction limit
% 0.74/0.41 % (394918)Termination phase: shuffling
% 0.74/0.41 % (394918)Time elapsed: 0.003 s
% 0.74/0.41 % (394918)Peak memory usage: 10 MB
% 0.74/0.41 % (394918)Instructions burned: 10 (million)
% 0.74/0.41 % (394920)Instruction limit reached!
% 0.74/0.41 % (394920)------------------------------
% 0.74/0.41 % (394920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (394920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (394920)CaDiCaL version: 2.1.3
% 0.74/0.41 % (394920)Termination reason: Instruction limit
% 0.74/0.41 % (394920)Termination phase: shuffling
% 0.74/0.41 % (394920)Time elapsed: 0.003 s
% 0.74/0.41 % (394920)Peak memory usage: 10 MB
% 0.74/0.41 % (394920)Instructions burned: 6 (million)
% 0.74/0.41 % (394922)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1771318628:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.41 % (394901)Instruction limit reached!
% 0.74/0.41 % (394901)------------------------------
% 0.74/0.41 % (394901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (394901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (394901)CaDiCaL version: 2.1.3
% 0.74/0.41 % (394901)Termination reason: Instruction limit
% 0.74/0.41 % (394901)Termination phase: Saturation
% 0.74/0.41 % (394901)Time elapsed: 0.060 s
% 0.74/0.41 % (394901)Peak memory usage: 12 MB
% 0.74/0.41 % (394901)Instructions burned: 160 (million)
% 0.74/0.41 % (394923)Refutation not found, incomplete strategy
% 0.74/0.41 % (394923)------------------------------
% 0.74/0.41 % (394923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (394923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (394923)CaDiCaL version: 2.1.3
% 0.74/0.41 % (394923)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.41 % (394923)Time elapsed: 0.014 s
% 0.74/0.41 % (394923)Peak memory usage: 12 MB
% 0.74/0.41 % (394923)Instructions burned: 57 (million)
% 0.74/0.41 % (394923)------------------------------
% 0.74/0.41 % (394923)------------------------------
% 0.74/0.41 % (394928)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=338733454:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.74/0.41 % (394929)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2450780382:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.74/0.41 % (394932)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3374597264:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.41 % (394929)Instruction limit reached!
% 0.74/0.41 % (394929)------------------------------
% 0.74/0.41 % (394929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (394929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (394929)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394929)Termination reason: Instruction limit
% 0.74/0.44 % (394929)Termination phase: shuffling
% 0.74/0.44 % (394929)Time elapsed: 0.005 s
% 0.74/0.44 % (394929)Peak memory usage: 10 MB
% 0.74/0.44 % (394929)Instructions burned: 16 (million)
% 0.74/0.44 % (394932)Instruction limit reached!
% 0.74/0.44 % (394932)------------------------------
% 0.74/0.44 % (394932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (394932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (394932)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394932)Termination reason: Instruction limit
% 0.74/0.44 % (394932)Termination phase: shuffling
% 0.74/0.44 % (394932)Time elapsed: 0.003 s
% 0.74/0.44 % (394932)Peak memory usage: 10 MB
% 0.74/0.44 % (394932)Instructions burned: 18 (million)
% 0.74/0.44 % (394928)Instruction limit reached!
% 0.74/0.44 % (394928)------------------------------
% 0.74/0.44 % (394928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (394928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (394917)Instruction limit reached!
% 0.74/0.44 % (394917)------------------------------
% 0.74/0.44 % (394917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (394917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (394917)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394917)Termination reason: Instruction limit
% 0.74/0.44 % (394917)Termination phase: Property scanning
% 0.74/0.44 % (394917)Time elapsed: 0.033 s
% 0.74/0.44 % (394917)Peak memory usage: 10 MB
% 0.74/0.44 % (394917)Instructions burned: 88 (million)
% 0.74/0.44 % (394928)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394928)Termination reason: Instruction limit
% 0.74/0.44 % (394928)Termination phase: shuffling
% 0.74/0.44 % (394928)Time elapsed: 0.009 s
% 0.74/0.44 % (394928)Peak memory usage: 10 MB
% 0.74/0.44 % (394928)Instructions burned: 29 (million)
% 0.74/0.44 % (394931)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2270116198:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.74/0.44 % (394922)Instruction limit reached!
% 0.74/0.44 % (394922)------------------------------
% 0.74/0.44 % (394922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (394922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (394922)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394922)Termination reason: Instruction limit
% 0.74/0.44 % (394922)Termination phase: shuffling
% 0.74/0.44 % (394922)Time elapsed: 0.025 s
% 0.74/0.44 % (394922)Peak memory usage: 10 MB
% 0.74/0.44 % (394922)Instructions burned: 38 (million)
% 0.74/0.44 % (394937)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2660597256:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.74/0.44 % (394937)Instruction limit reached!
% 0.74/0.44 % (394937)------------------------------
% 0.74/0.44 % (394937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (394937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (394937)CaDiCaL version: 2.1.3
% 0.74/0.44 % (394937)Termination reason: Instruction limit
% 0.74/0.44 % (394937)Termination phase: Function definition elimination
% 0.74/0.44 % (394937)Time elapsed: 0.006 s
% 0.74/0.44 % (394937)Peak memory usage: 10 MB
% 0.74/0.44 % (394937)Instructions burned: 31 (million)
% 0.74/0.44 % (394936)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2271167478: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)
% 0.74/0.44 % (394938)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3020694219:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.74/0.44 % (394939)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4026279241:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.74/0.44 % (394941)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
% 0.74/0.44 % (394941)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.74/0.44 % (394936)Instruction limit reached!
% 0.74/0.44 % (394936)------------------------------
% 1.46/0.47 % (394936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394936)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394936)Termination reason: Instruction limit
% 1.46/0.47 % (394936)Termination phase: shuffling
% 1.46/0.47 % (394936)Time elapsed: 0.004 s
% 1.46/0.47 % (394936)Peak memory usage: 10 MB
% 1.46/0.47 % (394936)Instructions burned: 11 (million)
% 1.46/0.47 % (394931)Refutation not found, incomplete strategy
% 1.46/0.47 % (394931)------------------------------
% 1.46/0.47 % (394931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394931)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394931)Termination reason: Refutation not found, incomplete strategy
% 1.46/0.47 % (394931)Time elapsed: 0.021 s
% 1.46/0.47 % (394931)Peak memory usage: 12 MB
% 1.46/0.47 % (394931)Instructions burned: 61 (million)
% 1.46/0.47 % (394943)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.46/0.47 % (394931)------------------------------
% 1.46/0.47 % (394931)------------------------------
% 1.46/0.47 % (394941)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=2921617067:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.46/0.47 % (394943)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=1266801334:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.46/0.47 % (394938)Instruction limit reached!
% 1.46/0.47 % (394938)------------------------------
% 1.46/0.47 % (394938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394938)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394938)Termination reason: Instruction limit
% 1.46/0.47 % (394938)Termination phase: shuffling
% 1.46/0.47 % (394938)Time elapsed: 0.008 s
% 1.46/0.47 % (394938)Peak memory usage: 10 MB
% 1.46/0.47 % (394938)Instructions burned: 25 (million)
% 1.46/0.47 % (394943)Instruction limit reached!
% 1.46/0.47 % (394943)------------------------------
% 1.46/0.47 % (394943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394943)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394943)Termination reason: Instruction limit
% 1.46/0.47 % (394943)Termination phase: shuffling
% 1.46/0.47 % (394943)Time elapsed: 0.002 s
% 1.46/0.47 % (394943)Peak memory usage: 10 MB
% 1.46/0.47 % (394943)Instructions burned: 13 (million)
% 1.46/0.47 % (394941)Instruction limit reached!
% 1.46/0.47 % (394941)------------------------------
% 1.46/0.47 % (394941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394941)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394941)Termination reason: Instruction limit
% 1.46/0.47 % (394941)Termination phase: Property scanning
% 1.46/0.47 % (394941)Time elapsed: 0.006 s
% 1.46/0.47 % (394941)Peak memory usage: 10 MB
% 1.46/0.47 % (394941)Instructions burned: 15 (million)
% 1.46/0.47 % (394952)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=895088241:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.46/0.47 % (394947)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=1517773530:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.46/0.47 % (394939)Instruction limit reached!
% 1.46/0.47 % (394939)------------------------------
% 1.46/0.47 % (394939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.47 % (394939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.47 % (394939)CaDiCaL version: 2.1.3
% 1.46/0.47 % (394939)Termination reason: Instruction limit
% 1.46/0.47 % (394939)Termination phase: Property scanning
% 1.46/0.47 % (394939)Time elapsed: 0.021 s
% 1.46/0.47 % (394939)Peak memory usage: 10 MB
% 1.46/0.47 % (394939)Instructions burned: 61 (million)
% 1.46/0.47 % (394952)Instruction limit reached!
% 1.46/0.52 % (394952)------------------------------
% 1.46/0.52 % (394952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.52 % (394952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.52 % (394952)CaDiCaL version: 2.1.3
% 1.46/0.52 % (394952)Termination reason: Instruction limit
% 1.46/0.52 % (394952)Termination phase: shuffling
% 1.46/0.52 % (394952)Time elapsed: 0.004 s
% 1.46/0.52 % (394952)Peak memory usage: 10 MB
% 1.46/0.52 % (394952)Instructions burned: 22 (million)
% 1.46/0.52 % (394949)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1630202345:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.46/0.52 % (394949)Instruction limit reached!
% 1.46/0.52 % (394949)------------------------------
% 1.46/0.52 % (394949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.52 % (394949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.52 % (394949)CaDiCaL version: 2.1.3
% 1.46/0.52 % (394949)Termination reason: Instruction limit
% 1.46/0.52 % (394949)Termination phase: shuffling
% 1.46/0.52 % (394949)Time elapsed: 0.003 s
% 1.46/0.52 % (394949)Peak memory usage: 10 MB
% 1.46/0.52 % (394951)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3478745972:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.46/0.52 % (394949)Instructions burned: 9 (million)
% 1.46/0.52 % (394953)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3743053545:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.46/0.52 % (394947)Instruction limit reached!
% 1.46/0.52 % (394947)------------------------------
% 1.46/0.52 % (394947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.52 % (394947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.52 % (394947)CaDiCaL version: 2.1.3
% 1.46/0.52 % (394947)Termination reason: Instruction limit
% 1.46/0.52 % (394947)Termination phase: Property scanning
% 1.46/0.52 % (394947)Time elapsed: 0.012 s
% 1.46/0.52 % (394947)Peak memory usage: 10 MB
% 1.46/0.52 % (394947)Instructions burned: 31 (million)
% 1.46/0.52 % (394957)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3057132307:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.46/0.52 % (394951)Instruction limit reached!
% 1.46/0.52 % (394951)------------------------------
% 1.46/0.52 % (394951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.52 % (394951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.52 % (394951)CaDiCaL version: 2.1.3
% 1.46/0.52 % (394951)Termination reason: Instruction limit
% 1.46/0.52 % (394951)Termination phase: Property scanning
% 1.46/0.52 % (394951)Time elapsed: 0.009 s
% 1.46/0.52 % (394951)Peak memory usage: 10 MB
% 1.46/0.52 % (394951)Instructions burned: 23 (million)
% 1.46/0.52 % (394956)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=855762429:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.46/0.52 % (394960)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1824607716:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.46/0.52 % (394963)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.46/0.52 % (394957)Refutation not found, incomplete strategy
% 1.46/0.52 % (394957)------------------------------
% 1.46/0.52 % (394957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.46/0.52 % (394957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.46/0.52 % (394957)CaDiCaL version: 2.1.3
% 1.46/0.52 % (394957)Termination reason: Refutation not found, incomplete strategy
% 1.46/0.52 % (394957)Time elapsed: 0.015 s
% 1.46/0.52 % (394957)Peak memory usage: 13 MB
% 1.46/0.52 % (394957)Instructions burned: 77 (million)
% 1.46/0.52 % (394957)------------------------------
% 1.46/0.52 % (394957)------------------------------
% 1.46/0.52 % (394963)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=209448729:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.46/0.52 % (394964)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=466965073:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 2.20/0.60 % (394963)Instruction limit reached!
% 2.20/0.60 % (394963)------------------------------
% 2.20/0.60 % (394963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394963)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394963)Termination reason: Instruction limit
% 2.20/0.60 % (394963)Termination phase: Property scanning
% 2.20/0.60 % (394963)Time elapsed: 0.004 s
% 2.20/0.60 % (394963)Peak memory usage: 10 MB
% 2.20/0.60 % (394963)Instructions burned: 9 (million)
% 2.20/0.60 % (394967)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=2087965157:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/169Mi)
% 2.20/0.60 % (394960)Instruction limit reached!
% 2.20/0.60 % (394960)------------------------------
% 2.20/0.60 % (394960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394960)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394960)Termination reason: Instruction limit
% 2.20/0.60 % (394960)Termination phase: Property scanning
% 2.20/0.60 % (394960)Time elapsed: 0.014 s
% 2.20/0.60 % (394960)Peak memory usage: 10 MB
% 2.20/0.60 % (394960)Instructions burned: 43 (million)
% 2.20/0.60 % (394967)Refutation not found, incomplete strategy
% 2.20/0.60 % (394967)------------------------------
% 2.20/0.60 % (394967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394967)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394967)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.60 % (394967)Time elapsed: 0.011 s
% 2.20/0.60 % (394967)Peak memory usage: 12 MB
% 2.20/0.60 % (394967)Instructions burned: 57 (million)
% 2.20/0.60 % (394970)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.20/0.60 % (394967)------------------------------
% 2.20/0.60 % (394967)------------------------------
% 2.20/0.60 % (394970)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4177482858:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2998 on theBenchmark for (2998ds/6Mi)
% 2.20/0.60 % (394964)Refutation not found, incomplete strategy
% 2.20/0.60 % (394964)------------------------------
% 2.20/0.60 % (394964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394964)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394964)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.60 % (394964)Time elapsed: 0.020 s
% 2.20/0.60 % (394964)Peak memory usage: 12 MB
% 2.20/0.60 % (394964)Instructions burned: 56 (million)
% 2.20/0.60 % (394964)------------------------------
% 2.20/0.60 % (394964)------------------------------
% 2.20/0.60 % (394972)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=731698784:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.20/0.60 % (394970)Instruction limit reached!
% 2.20/0.60 % (394970)------------------------------
% 2.20/0.60 % (394970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394970)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394970)Termination reason: Instruction limit
% 2.20/0.60 % (394970)Termination phase: Property scanning
% 2.20/0.60 % (394970)Time elapsed: 0.004 s
% 2.20/0.60 % (394970)Peak memory usage: 10 MB
% 2.20/0.60 % (394970)Instructions burned: 11 (million)
% 2.20/0.60 % (394974)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=865367252:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.20/0.60 % (394972)Instruction limit reached!
% 2.20/0.60 % (394972)------------------------------
% 2.20/0.60 % (394972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.60 % (394972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.60 % (394972)CaDiCaL version: 2.1.3
% 2.20/0.60 % (394972)Termination reason: Instruction limit
% 2.58/0.65 % (394972)Termination phase: shuffling
% 2.58/0.65 % (394972)Time elapsed: 0.008 s
% 2.58/0.65 % (394972)Peak memory usage: 10 MB
% 2.58/0.65 % (394972)Instructions burned: 24 (million)
% 2.58/0.65 % (394974)Instruction limit reached!
% 2.58/0.65 % (394974)------------------------------
% 2.58/0.65 % (394974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.65 % (394974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.65 % (394974)CaDiCaL version: 2.1.3
% 2.58/0.65 % (394974)Termination reason: Instruction limit
% 2.58/0.65 % (394974)Termination phase: Property scanning
% 2.58/0.65 % (394974)Time elapsed: 0.004 s
% 2.58/0.65 % (394974)Peak memory usage: 10 MB
% 2.58/0.65 % (394974)Instructions burned: 22 (million)
% 2.58/0.65 % (394956)Instruction limit reached!
% 2.58/0.65 % (394956)------------------------------
% 2.58/0.65 % (394956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.65 % (394956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.65 % (394956)CaDiCaL version: 2.1.3
% 2.58/0.65 % (394956)Termination reason: Instruction limit
% 2.58/0.65 % (394956)Termination phase: Property scanning
% 2.58/0.65 % (394956)Time elapsed: 0.051 s
% 2.58/0.65 % (394956)Peak memory usage: 11 MB
% 2.58/0.65 % (394956)Instructions burned: 143 (million)
% 2.58/0.65 % (394976)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=3467990126:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.58/0.65 % (394977)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=1438721773:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.58/0.65 % (394979)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=1741402425:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.58/0.65 % (394980)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1732729904:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.58/0.65 % (394981)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3447076377:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2997 on theBenchmark for (2997ds/21Mi)
% 2.58/0.65 % (394979)Instruction limit reached!
% 2.58/0.65 % (394979)------------------------------
% 2.58/0.65 % (394979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.65 % (394979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.65 % (394979)CaDiCaL version: 2.1.3
% 2.58/0.65 % (394979)Termination reason: Instruction limit
% 2.58/0.65 % (394979)Termination phase: shuffling
% 2.58/0.65 % (394979)Time elapsed: 0.015 s
% 2.58/0.65 % (394979)Peak memory usage: 10 MB
% 2.58/0.65 % (394979)Instructions burned: 45 (million)
% 2.58/0.65 % (394981)Instruction limit reached!
% 2.58/0.65 % (394981)------------------------------
% 2.58/0.65 % (394981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.65 % (394981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.65 % (394981)CaDiCaL version: 2.1.3
% 2.58/0.65 % (394981)Termination reason: Instruction limit
% 2.58/0.65 % (394981)Termination phase: shuffling
% 2.58/0.65 % (394981)Time elapsed: 0.007 s
% 2.58/0.65 % (394981)Peak memory usage: 10 MB
% 2.58/0.65 % (394981)Instructions burned: 23 (million)
% 2.58/0.65 % (394980)Refutation not found, incomplete strategy
% 2.58/0.65 % (394980)------------------------------
% 2.58/0.65 % (394980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.65 % (394980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.65 % (394980)CaDiCaL version: 2.1.3
% 2.58/0.65 % (394980)Termination reason: Refutation not found, incomplete strategy
% 2.58/0.65 % (394980)Time elapsed: 0.022 s
% 2.58/0.65 % (394980)Peak memory usage: 13 MB
% 2.58/0.65 % (394980)Instructions burned: 109 (million)
% 2.58/0.65 % (394980)------------------------------
% 2.58/0.65 % (394980)------------------------------
% 2.58/0.65 % (394987)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.58/0.69 % (394987)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=894381293:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/200Mi)
% 2.58/0.69 % (394988)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1880638463:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/13Mi)
% 2.58/0.69 % (394989)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=346010173:i=66:s2at=3:nm=2:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/66Mi)
% 2.58/0.69 % (394988)Instruction limit reached!
% 2.58/0.69 % (394988)------------------------------
% 2.58/0.69 % (394988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.69 % (394988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.69 % (394988)CaDiCaL version: 2.1.3
% 2.58/0.69 % (394988)Termination reason: Instruction limit
% 2.58/0.69 % (394988)Termination phase: shuffling
% 2.58/0.69 % (394988)Time elapsed: 0.005 s
% 2.58/0.69 % (394988)Peak memory usage: 10 MB
% 2.58/0.69 % (394988)Instructions burned: 16 (million)
% 2.58/0.69 % (394989)Instruction limit reached!
% 2.58/0.69 % (394989)------------------------------
% 2.58/0.69 % (394989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.69 % (394989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.69 % (394989)CaDiCaL version: 2.1.3
% 2.58/0.69 % (394989)Termination reason: Instruction limit
% 2.58/0.69 % (394989)Termination phase: Property scanning
% 2.58/0.69 % (394989)Time elapsed: 0.013 s
% 2.58/0.69 % (394989)Peak memory usage: 11 MB
% 2.58/0.69 % (394989)Instructions burned: 68 (million)
% 2.58/0.69 % (394994)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2315143023:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 2.58/0.69 % (394993)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1281724051:i=51:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/51Mi)
% 2.58/0.69 % (394994)Instruction limit reached!
% 2.58/0.69 % (394994)------------------------------
% 2.58/0.69 % (394994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.69 % (394994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.69 % (394994)CaDiCaL version: 2.1.3
% 2.58/0.69 % (394994)Termination reason: Instruction limit
% 2.58/0.69 % (394994)Termination phase: Function definition elimination
% 2.58/0.69 % (394994)Time elapsed: 0.006 s
% 2.58/0.69 % (394994)Peak memory usage: 10 MB
% 2.58/0.69 % (394994)Instructions burned: 33 (million)
% 2.58/0.69 % (394997)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1914238628:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 2.58/0.69 % (394993)Instruction limit reached!
% 2.58/0.69 % (394993)------------------------------
% 2.58/0.69 % (394993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.69 % (394993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.69 % (394993)CaDiCaL version: 2.1.3
% 2.58/0.69 % (394993)Termination reason: Instruction limit
% 2.58/0.69 % (394993)Termination phase: Preprocessing 3
% 2.58/0.69 % (394993)Time elapsed: 0.019 s
% 2.58/0.69 % (394993)Peak memory usage: 10 MB
% 2.58/0.69 % (394993)Instructions burned: 52 (million)
% 2.58/0.69 % (394999)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=1521676189:cond=on:i=34:hud=10:nm=10:rtra=on_2996 on theBenchmark for (2996ds/34Mi)
% 2.58/0.69 % (394987)Instruction limit reached!
% 2.58/0.69 % (394987)------------------------------
% 2.58/0.69 % (394987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.58/0.69 % (394987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.69 % (394987)CaDiCaL version: 2.1.3
% 2.58/0.69 % (394987)Termination reason: Instruction limit
% 2.58/0.69 % (394987)Termination phase: Saturation
% 2.58/0.69 % (394987)Time elapsed: 0.074 s
% 2.58/0.69 % (394987)Peak memory usage: 12 MB
% 2.58/0.69 % (394987)Instructions burned: 201 (million)
% 2.58/0.69 % (394898)Instruction limit reached!
% 2.58/0.69 % (394898)------------------------------
% 2.58/0.69 % (394898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (394898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (394898)CaDiCaL version: 2.1.3
% 3.07/0.76 % (394898)Termination reason: Instruction limit
% 3.07/0.76 % (394898)Termination phase: Saturation
% 3.07/0.76 % (394898)Time elapsed: 0.313 s
% 3.07/0.76 % (394898)Peak memory usage: 16 MB
% 3.07/0.76 % (394898)Instructions burned: 635 (million)
% 3.07/0.76 % (394976)Instruction limit reached!
% 3.07/0.76 % (394976)------------------------------
% 3.07/0.76 % (394976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (394976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (394976)CaDiCaL version: 2.1.3
% 3.07/0.76 % (394976)Termination reason: Instruction limit
% 3.07/0.76 % (394976)Termination phase: Saturation
% 3.07/0.76 % (394976)Time elapsed: 0.119 s
% 3.07/0.76 % (394976)Peak memory usage: 13 MB
% 3.07/0.76 % (394976)Instructions burned: 317 (million)
% 3.07/0.76 % (394997)Instruction limit reached!
% 3.07/0.76 % (394997)------------------------------
% 3.07/0.76 % (394997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (394997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (394997)CaDiCaL version: 2.1.3
% 3.07/0.76 % (394997)Termination reason: Instruction limit
% 3.07/0.76 % (394997)Termination phase: Saturation
% 3.07/0.76 % (394997)Time elapsed: 0.032 s
% 3.07/0.76 % (394997)Peak memory usage: 12 MB
% 3.07/0.76 % (394997)Instructions burned: 141 (million)
% 3.07/0.76 % (394999)Instruction limit reached!
% 3.07/0.76 % (394999)------------------------------
% 3.07/0.76 % (394999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (394999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (394999)CaDiCaL version: 2.1.3
% 3.07/0.76 % (394999)Termination reason: Instruction limit
% 3.07/0.76 % (394999)Termination phase: Function definition elimination
% 3.07/0.76 % (394999)Time elapsed: 0.014 s
% 3.07/0.76 % (394999)Peak memory usage: 10 MB
% 3.07/0.76 % (394999)Instructions burned: 35 (million)
% 3.07/0.76 % (395004)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=830011768:cond=on:i=96:bd=all:rtra=on_2996 on theBenchmark for (2996ds/96Mi)
% 3.07/0.76 % (395002)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.07/0.76 % (395001)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1772178664:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2996 on theBenchmark for (2996ds/67Mi)
% 3.07/0.76 % (395002)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1229810479:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2996 on theBenchmark for (2996ds/180Mi)
% 3.07/0.76 % (395003)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3191201770:st=2:i=246:sd=3:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/246Mi)
% 3.07/0.76 % (395005)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2020208750:i=427:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/427Mi)
% 3.07/0.76 % (395004)Instruction limit reached!
% 3.07/0.76 % (395004)------------------------------
% 3.07/0.76 % (395004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (395004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (395004)CaDiCaL version: 2.1.3
% 3.07/0.76 % (395004)Termination reason: Instruction limit
% 3.07/0.76 % (395004)Termination phase: Property scanning
% 3.07/0.76 % (395004)Time elapsed: 0.018 s
% 3.07/0.76 % (395004)Peak memory usage: 11 MB
% 3.07/0.76 % (395004)Instructions burned: 97 (million)
% 3.07/0.76 % (395001)Instruction limit reached!
% 3.07/0.76 % (395001)------------------------------
% 3.07/0.76 % (395001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (395001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.76 % (395001)CaDiCaL version: 2.1.3
% 3.07/0.76 % (395001)Termination reason: Instruction limit
% 3.07/0.76 % (395001)Termination phase: Function definition elimination
% 3.07/0.76 % (395001)Time elapsed: 0.023 s
% 3.07/0.76 % (395001)Peak memory usage: 10 MB
% 3.07/0.76 % (395001)Instructions burned: 70 (million)
% 3.07/0.76 % (395003)Refutation not found, incomplete strategy
% 3.07/0.76 % (395003)------------------------------
% 3.07/0.76 % (395003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.76 % (395003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395003)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395003)Termination reason: Refutation not found, incomplete strategy
% 3.46/0.88 % (395003)Time elapsed: 0.020 s
% 3.46/0.88 % (395003)Peak memory usage: 12 MB
% 3.46/0.88 % (395003)Instructions burned: 58 (million)
% 3.46/0.88 % (395003)------------------------------
% 3.46/0.88 % (395003)------------------------------
% 3.46/0.88 % (395011)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=897082959:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/874Mi)
% 3.46/0.88 % (395005)Refutation not found, incomplete strategy
% 3.46/0.88 % (395005)------------------------------
% 3.46/0.88 % (395005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.88 % (395005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395005)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395005)Termination reason: Refutation not found, incomplete strategy
% 3.46/0.88 % (395005)Time elapsed: 0.019 s
% 3.46/0.88 % (395005)Peak memory usage: 12 MB
% 3.46/0.88 % (395005)Instructions burned: 56 (million)
% 3.46/0.88 % (395005)------------------------------
% 3.46/0.88 % (395005)------------------------------
% 3.46/0.88 % (395011)Refutation not found, incomplete strategy
% 3.46/0.88 % (395011)------------------------------
% 3.46/0.88 % (395011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.88 % (395011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395011)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395011)Termination reason: Refutation not found, incomplete strategy
% 3.46/0.88 % (395011)Time elapsed: 0.011 s
% 3.46/0.88 % (395011)Peak memory usage: 12 MB
% 3.46/0.88 % (395011)Instructions burned: 61 (million)
% 3.46/0.88 % (395011)------------------------------
% 3.46/0.88 % (395011)------------------------------
% 3.46/0.88 % (395012)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=709243367:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/515Mi)
% 3.46/0.88 % (395014)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=4027805477:st=1.5:i=130:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/130Mi)
% 3.46/0.88 % (395016)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2461790786:s2a=on:i=571:nm=16:rtra=on_2995 on theBenchmark for (2995ds/571Mi)
% 3.46/0.88 % (395015)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2544948781:i=44:ep=R:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/44Mi)
% 3.46/0.88 % (395014)Refutation not found, incomplete strategy
% 3.46/0.88 % (395014)------------------------------
% 3.46/0.88 % (395014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.88 % (395014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395014)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395014)Termination reason: Refutation not found, incomplete strategy
% 3.46/0.88 % (395014)Time elapsed: 0.010 s
% 3.46/0.88 % (395014)Peak memory usage: 12 MB
% 3.46/0.88 % (395014)Instructions burned: 24 (million)
% 3.46/0.88 % (395014)------------------------------
% 3.46/0.88 % (395014)------------------------------
% 3.46/0.88 % (395015)Instruction limit reached!
% 3.46/0.88 % (395015)------------------------------
% 3.46/0.88 % (395015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.88 % (395015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395015)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395015)Termination reason: Instruction limit
% 3.46/0.88 % (395015)Termination phase: Property scanning
% 3.46/0.88 % (395015)Time elapsed: 0.017 s
% 3.46/0.88 % (395015)Peak memory usage: 10 MB
% 3.46/0.88 % (395015)Instructions burned: 46 (million)
% 3.46/0.88 % (395002)Instruction limit reached!
% 3.46/0.88 % (395002)------------------------------
% 3.46/0.88 % (395002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.88 % (395002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.88 % (395002)CaDiCaL version: 2.1.3
% 3.46/0.88 % (395002)Termination reason: Instruction limit
% 3.46/0.88 % (395002)Termination phase: Saturation
% 3.46/0.88 % (395002)Time elapsed: 0.068 s
% 3.46/0.88 % (395002)Peak memory usage: 12 MB
% 3.46/0.88 % (395002)Instructions burned: 182 (million)
% 3.46/0.88 % (395016)Refutation not found, incomplete strategy
% 3.46/0.88 % (395016)------------------------------
% 3.46/0.88 % (395016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/0.94 % (395016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/0.94 % (395016)CaDiCaL version: 2.1.3
% 3.95/0.94 % (395016)Termination reason: Refutation not found, incomplete strategy
% 3.95/0.94 % (395016)Time elapsed: 0.023 s
% 3.95/0.94 % (395016)Peak memory usage: 13 MB
% 3.95/0.94 % (395016)Instructions burned: 112 (million)
% 3.95/0.94 % (395016)------------------------------
% 3.95/0.94 % (395016)------------------------------
% 3.95/0.94 % (395021)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3663924264:i=450:rtra=on:ixr=off:ntd=on_2995 on theBenchmark for (2995ds/450Mi)
% 3.95/0.94 % (395024)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=2567990245: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_2995 on theBenchmark for (2995ds/105Mi)
% 3.95/0.94 % (395022)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1177492410:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/95Mi)
% 3.95/0.94 % (395023)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=2110411967:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2995 on theBenchmark for (2995ds/65Mi)
% 3.95/0.94 % (395024)Instruction limit reached!
% 3.95/0.94 % (395024)------------------------------
% 3.95/0.94 % (395024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/0.94 % (395024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/0.94 % (395024)CaDiCaL version: 2.1.3
% 3.95/0.94 % (395024)Termination reason: Instruction limit
% 3.95/0.94 % (395024)Termination phase: Property scanning
% 3.95/0.94 % (395024)Time elapsed: 0.021 s
% 3.95/0.94 % (395024)Peak memory usage: 10 MB
% 3.95/0.94 % (395024)Instructions burned: 109 (million)
% 3.95/0.94 % (395023)Instruction limit reached!
% 3.95/0.94 % (395023)------------------------------
% 3.95/0.94 % (395023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/0.94 % (395023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/0.94 % (395023)CaDiCaL version: 2.1.3
% 3.95/0.94 % (395023)Termination reason: Instruction limit
% 3.95/0.94 % (395023)Termination phase: Property scanning
% 3.95/0.94 % (395023)Time elapsed: 0.025 s
% 3.95/0.94 % (395023)Peak memory usage: 11 MB
% 3.95/0.94 % (395023)Instructions burned: 67 (million)
% 3.95/0.94 % (395029)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=365414669:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2995 on theBenchmark for (2995ds/5755Mi)
% 3.95/0.94 % (395022)Instruction limit reached!
% 3.95/0.94 % (395022)------------------------------
% 3.95/0.94 % (395022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/0.94 % (395022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/0.94 % (395022)CaDiCaL version: 2.1.3
% 3.95/0.94 % (395022)Termination reason: Instruction limit
% 3.95/0.94 % (395022)Termination phase: Property scanning
% 3.95/0.94 % (395022)Time elapsed: 0.034 s
% 3.95/0.94 % (395022)Peak memory usage: 10 MB
% 3.95/0.94 % (395022)Instructions burned: 98 (million)
% 3.95/0.94 % (395029)Refutation not found, incomplete strategy
% 3.95/0.94 % (395029)------------------------------
% 3.95/0.94 % (395029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/0.94 % (395029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/0.94 % (395029)CaDiCaL version: 2.1.3
% 3.95/0.94 % (395029)Termination reason: Refutation not found, incomplete strategy
% 3.95/0.94 % (395029)Time elapsed: 0.011 s
% 3.95/0.94 % (395029)Peak memory usage: 13 MB
% 3.95/0.94 % (395029)Instructions burned: 59 (million)
% 3.95/0.94 % (395029)------------------------------
% 3.95/0.94 % (395029)------------------------------
% 3.95/0.94 % (395030)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1460461238:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/375Mi)
% 3.95/0.94 % (395032)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1741731970:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2995 on theBenchmark for (2995ds/495Mi)
% 3.95/1.04 % (395033)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=552582420:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 3.95/1.04 % (395033)Instruction limit reached!
% 3.95/1.04 % (395033)------------------------------
% 3.95/1.04 % (395033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395033)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395033)Termination reason: Instruction limit
% 3.95/1.04 % (395033)Termination phase: Function definition elimination
% 3.95/1.04 % (395033)Time elapsed: 0.013 s
% 3.95/1.04 % (395033)Peak memory usage: 10 MB
% 3.95/1.04 % (395033)Instructions burned: 37 (million)
% 3.95/1.04 % (395037)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1425136007:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2994 on theBenchmark for (2994ds/91Mi)
% 3.95/1.04 % (395037)Instruction limit reached!
% 3.95/1.04 % (395037)------------------------------
% 3.95/1.04 % (395037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395037)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395037)Termination reason: Instruction limit
% 3.95/1.04 % (395037)Termination phase: Property scanning
% 3.95/1.04 % (395037)Time elapsed: 0.033 s
% 3.95/1.04 % (395037)Peak memory usage: 11 MB
% 3.95/1.04 % (395037)Instructions burned: 93 (million)
% 3.95/1.04 % (395039)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=366637717:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2994 on theBenchmark for (2994ds/66Mi)
% 3.95/1.04 % (395012)Instruction limit reached!
% 3.95/1.04 % (395012)------------------------------
% 3.95/1.04 % (395012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395012)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395012)Termination reason: Instruction limit
% 3.95/1.04 % (395012)Termination phase: Saturation
% 3.95/1.04 % (395012)Time elapsed: 0.194 s
% 3.95/1.04 % (395012)Peak memory usage: 14 MB
% 3.95/1.04 % (395012)Instructions burned: 517 (million)
% 3.95/1.04 % (395021)Instruction limit reached!
% 3.95/1.04 % (395021)------------------------------
% 3.95/1.04 % (395021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395021)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395021)Termination reason: Instruction limit
% 3.95/1.04 % (395021)Termination phase: Saturation
% 3.95/1.04 % (395021)Time elapsed: 0.170 s
% 3.95/1.04 % (395021)Peak memory usage: 13 MB
% 3.95/1.04 % (395021)Instructions burned: 452 (million)
% 3.95/1.04 % (395041)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1101513399:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2993 on theBenchmark for (2993ds/22Mi)
% 3.95/1.04 % (395039)Refutation not found, incomplete strategy
% 3.95/1.04 % (395039)------------------------------
% 3.95/1.04 % (395039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395039)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395039)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.04 % (395039)Time elapsed: 0.019 s
% 3.95/1.04 % (395039)Peak memory usage: 12 MB
% 3.95/1.04 % (395039)Instructions burned: 55 (million)
% 3.95/1.04 % (395039)------------------------------
% 3.95/1.04 % (395039)------------------------------
% 3.95/1.04 % (395041)Instruction limit reached!
% 3.95/1.04 % (395041)------------------------------
% 3.95/1.04 % (395041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.04 % (395041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.04 % (395041)CaDiCaL version: 2.1.3
% 3.95/1.04 % (395041)Termination reason: Instruction limit
% 3.95/1.04 % (395041)Termination phase: shuffling
% 3.95/1.04 % (395041)Time elapsed: 0.004 s
% 3.95/1.04 % (395041)Peak memory usage: 10 MB
% 3.95/1.04 % (395041)Instructions burned: 24 (million)
% 3.95/1.04 % (395045)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 5.58/1.10 % (395045)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2548811444:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2993 on theBenchmark for (2993ds/137Mi)
% 5.58/1.10 % (395042)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=47211072:i=338:bd=all:ins=4:rtra=on_2993 on theBenchmark for (2993ds/338Mi)
% 5.58/1.10 % (395044)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3647196392:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2993 on theBenchmark for (2993ds/28Mi)
% 5.58/1.10 % (395030)Instruction limit reached!
% 5.58/1.10 % (395030)------------------------------
% 5.58/1.10 % (395030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.10 % (395030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.10 % (395030)CaDiCaL version: 2.1.3
% 5.58/1.10 % (395030)Termination reason: Instruction limit
% 5.58/1.10 % (395030)Termination phase: Saturation
% 5.58/1.10 % (395030)Time elapsed: 0.143 s
% 5.58/1.10 % (395030)Peak memory usage: 13 MB
% 5.58/1.10 % (395030)Instructions burned: 377 (million)
% 5.58/1.10 % (394977)Instruction limit reached!
% 5.58/1.10 % (394977)------------------------------
% 5.58/1.10 % (394977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.10 % (394977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.10 % (394977)CaDiCaL version: 2.1.3
% 5.58/1.10 % (394977)Termination reason: Instruction limit
% 5.58/1.10 % (394977)Termination phase: Saturation
% 5.58/1.10 % (394977)Time elapsed: 0.410 s
% 5.58/1.10 % (394977)Peak memory usage: 18 MB
% 5.58/1.10 % (394977)Instructions burned: 854 (million)
% 5.58/1.10 % (395044)Instruction limit reached!
% 5.58/1.10 % (395044)------------------------------
% 5.58/1.10 % (395044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.10 % (395044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.10 % (395044)CaDiCaL version: 2.1.3
% 5.58/1.10 % (395044)Termination reason: Instruction limit
% 5.58/1.10 % (395044)Termination phase: shuffling
% 5.58/1.10 % (395044)Time elapsed: 0.009 s
% 5.58/1.10 % (395044)Peak memory usage: 10 MB
% 5.58/1.10 % (395044)Instructions burned: 28 (million)
% 5.58/1.10 % (395045)Instruction limit reached!
% 5.58/1.10 % (395045)------------------------------
% 5.58/1.10 % (395045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.10 % (395045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.10 % (395045)CaDiCaL version: 2.1.3
% 5.58/1.10 % (395045)Termination reason: Instruction limit
% 5.58/1.10 % (395045)Termination phase: Saturation
% 5.58/1.10 % (395045)Time elapsed: 0.028 s
% 5.58/1.10 % (395045)Peak memory usage: 12 MB
% 5.58/1.10 % (395045)Instructions burned: 140 (million)
% 5.58/1.10 % (395049)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=2552864283:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2993 on theBenchmark for (2993ds/340Mi)
% 5.58/1.10 % (395051)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 5.58/1.10 % (395050)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2139570394:i=227:sd=1:bd=all:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/227Mi)
% 5.58/1.10 % (395051)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3453294584:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/373Mi)
% 5.58/1.10 % (395052)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1756710488:i=116:ep=RSTC:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/116Mi)
% 5.58/1.10 % (395050)Refutation not found, incomplete strategy
% 5.58/1.10 % (395050)------------------------------
% 5.58/1.10 % (395050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.58/1.10 % (395050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.58/1.10 % (395050)CaDiCaL version: 2.1.3
% 5.58/1.10 % (395050)Termination reason: Refutation not found, incomplete strategy
% 5.58/1.10 % (395050)Time elapsed: 0.019 s
% 5.58/1.10 % (395050)Peak memory usage: 12 MB
% 5.58/1.10 % (395050)Instructions burned: 56 (million)
% 6.22/1.16 % (395050)------------------------------
% 6.22/1.16 % (395050)------------------------------
% 6.22/1.16 % (395052)Instruction limit reached!
% 6.22/1.16 % (395052)------------------------------
% 6.22/1.16 % (395052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.16 % (395052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.16 % (395052)CaDiCaL version: 2.1.3
% 6.22/1.16 % (395052)Termination reason: Instruction limit
% 6.22/1.16 % (395052)Termination phase: Property scanning
% 6.22/1.16 % (395052)Time elapsed: 0.022 s
% 6.22/1.16 % (395052)Peak memory usage: 10 MB
% 6.22/1.16 % (395052)Instructions burned: 119 (million)
% 6.22/1.16 % (395032)Instruction limit reached!
% 6.22/1.16 % (395032)------------------------------
% 6.22/1.16 % (395032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.16 % (395032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.16 % (395032)CaDiCaL version: 2.1.3
% 6.22/1.16 % (395032)Termination reason: Instruction limit
% 6.22/1.16 % (395032)Termination phase: Saturation
% 6.22/1.16 % (395032)Time elapsed: 0.187 s
% 6.22/1.16 % (395032)Peak memory usage: 13 MB
% 6.22/1.16 % (395032)Instructions burned: 497 (million)
% 6.22/1.16 % (395058)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=4201681415:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2993 on theBenchmark for (2993ds/270Mi)
% 6.22/1.16 % (395057)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=796750104:i=575:rtra=on_2993 on theBenchmark for (2993ds/575Mi)
% 6.22/1.16 % (395059)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=18918583: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_2992 on theBenchmark for (2992ds/9840Mi)
% 6.22/1.16 % (395058)Instruction limit reached!
% 6.22/1.16 % (395058)------------------------------
% 6.22/1.16 % (395058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.16 % (395058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.16 % (395058)CaDiCaL version: 2.1.3
% 6.22/1.16 % (395058)Termination reason: Instruction limit
% 6.22/1.16 % (395058)Termination phase: Saturation
% 6.22/1.16 % (395058)Time elapsed: 0.054 s
% 6.22/1.16 % (395058)Peak memory usage: 12 MB
% 6.22/1.16 % (395058)Instructions burned: 273 (million)
% 6.22/1.16 % (395042)Instruction limit reached!
% 6.22/1.16 % (395042)------------------------------
% 6.22/1.16 % (395042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.16 % (395042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.16 % (395042)CaDiCaL version: 2.1.3
% 6.22/1.16 % (395042)Termination reason: Instruction limit
% 6.22/1.16 % (395042)Termination phase: Saturation
% 6.22/1.16 % (395042)Time elapsed: 0.127 s
% 6.22/1.16 % (395042)Peak memory usage: 13 MB
% 6.22/1.16 % (395042)Instructions burned: 338 (million)
% 6.22/1.16 % (395063)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=1441050797:i=421:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/421Mi)
% 6.22/1.16 % (395064)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
% 6.22/1.16 % (395063)Refutation not found, incomplete strategy
% 6.22/1.16 % (395063)------------------------------
% 6.22/1.16 % (395063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.16 % (395063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.16 % (395063)CaDiCaL version: 2.1.3
% 6.22/1.16 % (395063)Termination reason: Refutation not found, incomplete strategy
% 6.22/1.16 % (395063)Time elapsed: 0.010 s
% 6.22/1.16 % (395063)Peak memory usage: 12 MB
% 6.22/1.16 % (395063)Instructions burned: 56 (million)
% 6.22/1.16 % (395063)------------------------------
% 6.22/1.16 % (395063)------------------------------
% 6.22/1.16 % (395064)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=1731246724:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/270Mi)
% 6.22/1.16 % (395067)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3645709202:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/31Mi)
% 6.31/1.28 % (395049)Instruction limit reached!
% 6.31/1.28 % (395049)------------------------------
% 6.31/1.28 % (395049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.28 % (395049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.28 % (395049)CaDiCaL version: 2.1.3
% 6.31/1.28 % (395049)Termination reason: Instruction limit
% 6.31/1.28 % (395049)Termination phase: Saturation
% 6.31/1.28 % (395049)Time elapsed: 0.128 s
% 6.31/1.28 % (395049)Peak memory usage: 12 MB
% 6.31/1.28 % (395049)Instructions burned: 342 (million)
% 6.31/1.28 % (395067)Instruction limit reached!
% 6.31/1.28 % (395067)------------------------------
% 6.31/1.28 % (395067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.28 % (395067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.28 % (395067)CaDiCaL version: 2.1.3
% 6.31/1.28 % (395067)Termination reason: Instruction limit
% 6.31/1.28 % (395067)Termination phase: Function definition elimination
% 6.31/1.28 % (395067)Time elapsed: 0.006 s
% 6.31/1.28 % (395067)Peak memory usage: 10 MB
% 6.31/1.28 % (395067)Instructions burned: 32 (million)
% 6.31/1.28 % (395070)dis+10_2_sil=128000:si=on:random_seed=1056315678:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2991 on theBenchmark for (2991ds/339Mi)
% 6.31/1.28 % (395069)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 6.31/1.28 % (395069)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
% 6.31/1.28 % (395051)Instruction limit reached!
% 6.31/1.28 % (395051)------------------------------
% 6.31/1.28 % (395051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.28 % (395051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.28 % (395051)CaDiCaL version: 2.1.3
% 6.31/1.28 % (395051)Termination reason: Instruction limit
% 6.31/1.28 % (395051)Termination phase: Saturation
% 6.31/1.28 % (395051)Time elapsed: 0.140 s
% 6.31/1.28 % (395051)Peak memory usage: 13 MB
% 6.31/1.28 % (395051)Instructions burned: 375 (million)
% 6.31/1.28 % (395069)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=1485131373:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2991 on theBenchmark for (2991ds/1440Mi)
% 6.31/1.28 % (395070)Refutation not found, incomplete strategy
% 6.31/1.28 % (395070)------------------------------
% 6.31/1.28 % (395070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.28 % (395070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.28 % (395070)CaDiCaL version: 2.1.3
% 6.31/1.28 % (395070)Termination reason: Refutation not found, incomplete strategy
% 6.31/1.28 % (395070)Time elapsed: 0.010 s
% 6.31/1.28 % (395070)Peak memory usage: 12 MB
% 6.31/1.28 % (395070)Instructions burned: 59 (million)
% 6.31/1.28 % (395070)------------------------------
% 6.31/1.28 % (395070)------------------------------
% 6.31/1.28 % (395074)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=3595810201:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2991 on theBenchmark for (2991ds/122Mi)
% 6.31/1.28 % (395072)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2646392624:i=111:add=on:fgj=on:rtra=on:fdi=1024_2991 on theBenchmark for (2991ds/111Mi)
% 6.31/1.28 % (395074)Refutation not found, incomplete strategy
% 6.31/1.28 % (395074)------------------------------
% 6.31/1.28 % (395074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.28 % (395074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.28 % (395074)CaDiCaL version: 2.1.3
% 6.31/1.28 % (395074)Termination reason: Refutation not found, incomplete strategy
% 6.31/1.28 % (395074)Time elapsed: 0.010 s
% 6.31/1.28 % (395074)Peak memory usage: 12 MB
% 6.31/1.28 % (395074)Instructions burned: 57 (million)
% 6.31/1.28 % (395074)------------------------------
% 6.31/1.28 % (395074)------------------------------
% 6.31/1.28 % (395077)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=3327828095:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/136Mi)
% 6.82/1.37 % (395072)Instruction limit reached!
% 6.82/1.37 % (395072)------------------------------
% 6.82/1.37 % (395072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (395072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (395072)CaDiCaL version: 2.1.3
% 6.82/1.37 % (395072)Termination reason: Instruction limit
% 6.82/1.37 % (395072)Termination phase: Property scanning
% 6.82/1.37 % (395072)Time elapsed: 0.040 s
% 6.82/1.37 % (395072)Peak memory usage: 10 MB
% 6.82/1.37 % (395072)Instructions burned: 114 (million)
% 6.82/1.37 % (395077)Instruction limit reached!
% 6.82/1.37 % (395077)------------------------------
% 6.82/1.37 % (395077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (395077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (395077)CaDiCaL version: 2.1.3
% 6.82/1.37 % (395077)Termination reason: Instruction limit
% 6.82/1.37 % (395077)Termination phase: Property scanning
% 6.82/1.37 % (395077)Time elapsed: 0.025 s
% 6.82/1.37 % (395077)Peak memory usage: 10 MB
% 6.82/1.37 % (395077)Instructions burned: 138 (million)
% 6.82/1.37 % (395064)Instruction limit reached!
% 6.82/1.37 % (395064)------------------------------
% 6.82/1.37 % (395064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (395064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (395064)CaDiCaL version: 2.1.3
% 6.82/1.37 % (395064)Termination reason: Instruction limit
% 6.82/1.37 % (395064)Termination phase: Saturation
% 6.82/1.37 % (395064)Time elapsed: 0.100 s
% 6.82/1.37 % (395064)Peak memory usage: 12 MB
% 6.82/1.37 % (395064)Instructions burned: 270 (million)
% 6.82/1.37 % (395080)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=1435087607:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/1254Mi)
% 6.82/1.37 % (395057)Refutation not found, incomplete strategy
% 6.82/1.37 % (395057)------------------------------
% 6.82/1.37 % (395057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (395057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (395057)CaDiCaL version: 2.1.3
% 6.82/1.37 % (395057)Termination reason: Refutation not found, incomplete strategy
% 6.82/1.37 % (395057)Time elapsed: 0.181 s
% 6.82/1.37 % (395057)Peak memory usage: 15 MB
% 6.82/1.37 % (395057)Instructions burned: 482 (million)
% 6.82/1.37 % (395079)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=346467426:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2991 on theBenchmark for (2991ds/232Mi)
% 6.82/1.37 % (395057)------------------------------
% 6.82/1.37 % (395057)------------------------------
% 6.82/1.37 % (395081)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 6.82/1.37 % (395081)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=2999247625:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2991 on theBenchmark for (2991ds/281Mi)
% 6.82/1.37 % (394953)Instruction limit reached!
% 6.82/1.37 % (394953)------------------------------
% 6.82/1.37 % (394953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (394953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (394953)CaDiCaL version: 2.1.3
% 6.82/1.37 % (394953)Termination reason: Instruction limit
% 6.82/1.37 % (394953)Termination phase: Saturation
% 6.82/1.37 % (394953)Time elapsed: 0.735 s
% 6.82/1.37 % (394953)Peak memory usage: 17 MB
% 6.82/1.37 % (394953)Instructions burned: 1241 (million)
% 6.82/1.37 % (395084)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4103854980:i=619:add=on:rtra=on_2991 on theBenchmark for (2991ds/619Mi)
% 6.82/1.37 % (395079)Refutation not found, incomplete strategy
% 6.82/1.37 % (395079)------------------------------
% 6.82/1.37 % (395079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.82/1.37 % (395079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.37 % (395079)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395079)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.53 % (395079)Time elapsed: 0.020 s
% 7.56/1.53 % (395079)Peak memory usage: 12 MB
% 7.56/1.53 % (395079)Instructions burned: 57 (million)
% 7.56/1.53 % (395079)------------------------------
% 7.56/1.53 % (395079)------------------------------
% 7.56/1.53 % (395086)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=1722557549:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/865Mi)
% 7.56/1.53 % (395088)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2612842789:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/212Mi)
% 7.56/1.53 % (395080)Refutation not found, incomplete strategy
% 7.56/1.53 % (395080)------------------------------
% 7.56/1.53 % (395080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.56/1.53 % (395080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/1.53 % (395080)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395080)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.53 % (395080)Time elapsed: 0.090 s
% 7.56/1.53 % (395080)Peak memory usage: 15 MB
% 7.56/1.53 % (395080)Instructions burned: 451 (million)
% 7.56/1.53 % (395080)------------------------------
% 7.56/1.53 % (395080)------------------------------
% 7.56/1.53 % (395091)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=4067205332:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/130Mi)
% 7.56/1.53 % (395091)Refutation not found, incomplete strategy
% 7.56/1.53 % (395091)------------------------------
% 7.56/1.53 % (395091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.56/1.53 % (395091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/1.53 % (395091)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395091)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.53 % (395091)Time elapsed: 0.010 s
% 7.56/1.53 % (395091)Peak memory usage: 12 MB
% 7.56/1.53 % (395091)Instructions burned: 58 (million)
% 7.56/1.53 % (395091)------------------------------
% 7.56/1.53 % (395091)------------------------------
% 7.56/1.53 % (395081)Instruction limit reached!
% 7.56/1.53 % (395081)------------------------------
% 7.56/1.53 % (395081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.56/1.53 % (395081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/1.53 % (395081)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395081)Termination reason: Instruction limit
% 7.56/1.53 % (395081)Termination phase: Saturation
% 7.56/1.53 % (395081)Time elapsed: 0.106 s
% 7.56/1.53 % (395081)Peak memory usage: 12 MB
% 7.56/1.53 % (395081)Instructions burned: 281 (million)
% 7.56/1.53 % (395093)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2229799396:st=1.5:i=346:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/346Mi)
% 7.56/1.53 % (395093)Refutation not found, incomplete strategy
% 7.56/1.53 % (395093)------------------------------
% 7.56/1.53 % (395093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.56/1.53 % (395093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/1.53 % (395093)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395093)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.53 % (395093)Time elapsed: 0.005 s
% 7.56/1.53 % (395093)Peak memory usage: 12 MB
% 7.56/1.53 % (395093)Instructions burned: 24 (million)
% 7.56/1.53 % (395093)------------------------------
% 7.56/1.53 % (395093)------------------------------
% 7.56/1.53 % (395094)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=758646235:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2989 on theBenchmark for (2989ds/152Mi)
% 7.56/1.53 % (395088)Instruction limit reached!
% 7.56/1.53 % (395088)------------------------------
% 7.56/1.53 % (395088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.56/1.53 % (395088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.56/1.53 % (395088)CaDiCaL version: 2.1.3
% 7.56/1.53 % (395088)Termination reason: Instruction limit
% 7.56/1.53 % (395088)Termination phase: Saturation
% 7.56/1.53 % (395088)Time elapsed: 0.097 s
% 7.56/1.53 % (395088)Peak memory usage: 12 MB
% 7.56/1.53 % (395088)Instructions burned: 212 (million)
% 7.56/1.53 % (395096)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=277557255:i=75:ep=R:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/75Mi)
% 8.40/1.68 % (395096)Instruction limit reached!
% 8.40/1.68 % (395096)------------------------------
% 8.40/1.68 % (395096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395096)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395096)Termination reason: Instruction limit
% 8.40/1.68 % (395096)Termination phase: Property scanning
% 8.40/1.68 % (395096)Time elapsed: 0.015 s
% 8.40/1.68 % (395096)Peak memory usage: 10 MB
% 8.40/1.68 % (395096)Instructions burned: 77 (million)
% 8.40/1.68 % (395098)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=637669008:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/387Mi)
% 8.40/1.68 % (395100)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=708375113:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2989 on theBenchmark for (2989ds/148Mi)
% 8.40/1.68 % (395098)Refutation not found, incomplete strategy
% 8.40/1.68 % (395098)------------------------------
% 8.40/1.68 % (395098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395098)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395098)Termination reason: Refutation not found, incomplete strategy
% 8.40/1.68 % (395098)Time elapsed: 0.010 s
% 8.40/1.68 % (395098)Peak memory usage: 12 MB
% 8.40/1.68 % (395098)Instructions burned: 24 (million)
% 8.40/1.68 % (395098)------------------------------
% 8.40/1.68 % (395098)------------------------------
% 8.40/1.68 % (395103)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3452521613:i=161:piset=and:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/161Mi)
% 8.40/1.68 % (395084)Refutation not found, incomplete strategy
% 8.40/1.68 % (395084)------------------------------
% 8.40/1.68 % (395084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395084)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395084)Termination reason: Refutation not found, incomplete strategy
% 8.40/1.68 % (395084)Time elapsed: 0.169 s
% 8.40/1.68 % (395084)Peak memory usage: 15 MB
% 8.40/1.68 % (395084)Instructions burned: 445 (million)
% 8.40/1.68 % (395084)------------------------------
% 8.40/1.68 % (395084)------------------------------
% 8.40/1.68 % (395094)Instruction limit reached!
% 8.40/1.68 % (395094)------------------------------
% 8.40/1.68 % (395094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395094)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395094)Termination reason: Instruction limit
% 8.40/1.68 % (395094)Termination phase: Saturation
% 8.40/1.68 % (395094)Time elapsed: 0.055 s
% 8.40/1.68 % (395094)Peak memory usage: 11 MB
% 8.40/1.68 % (395094)Instructions burned: 154 (million)
% 8.40/1.68 % (395100)Instruction limit reached!
% 8.40/1.68 % (395100)------------------------------
% 8.40/1.68 % (395100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395100)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395100)Termination reason: Instruction limit
% 8.40/1.68 % (395100)Termination phase: Saturation
% 8.40/1.68 % (395100)Time elapsed: 0.038 s
% 8.40/1.68 % (395100)Peak memory usage: 13 MB
% 8.40/1.68 % (395100)Instructions burned: 151 (million)
% 8.40/1.68 % (395105)lrs+10_1_sil=128000:si=on:random_seed=2504235714:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/888Mi)
% 8.40/1.68 % (395106)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=2691429921:i=136:add=on:ins=4:rtra=on:sup=off_2989 on theBenchmark for (2989ds/136Mi)
% 8.40/1.68 % (395107)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=1238818430:i=88:s2at=3:nm=2:rtra=on:rawr=on_2989 on theBenchmark for (2989ds/88Mi)
% 8.40/1.68 % (395107)Instruction limit reached!
% 8.40/1.68 % (395107)------------------------------
% 8.40/1.68 % (395107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395107)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395107)Termination reason: Instruction limit
% 8.40/1.68 % (395107)Termination phase: Property scanning
% 8.40/1.68 % (395107)Time elapsed: 0.018 s
% 8.40/1.68 % (395107)Peak memory usage: 11 MB
% 8.40/1.68 % (395107)Instructions burned: 93 (million)
% 8.40/1.68 % (395111)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2312179320:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2988 on theBenchmark for (2988ds/93Mi)
% 8.40/1.68 % (395103)Instruction limit reached!
% 8.40/1.68 % (395103)------------------------------
% 8.40/1.68 % (395103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395103)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395103)Termination reason: Instruction limit
% 8.40/1.68 % (395103)Termination phase: Saturation
% 8.40/1.68 % (395103)Time elapsed: 0.059 s
% 8.40/1.68 % (395103)Peak memory usage: 12 MB
% 8.40/1.68 % (395103)Instructions burned: 163 (million)
% 8.40/1.68 % (395106)Instruction limit reached!
% 8.40/1.68 % (395106)------------------------------
% 8.40/1.68 % (395106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395106)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395106)Termination reason: Instruction limit
% 8.40/1.68 % (395106)Termination phase: Property scanning
% 8.40/1.68 % (395106)Time elapsed: 0.049 s
% 8.40/1.68 % (395106)Peak memory usage: 11 MB
% 8.40/1.68 % (395106)Instructions burned: 137 (million)
% 8.40/1.68 % (395111)Instruction limit reached!
% 8.40/1.68 % (395111)------------------------------
% 8.40/1.68 % (395111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395111)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395111)Termination reason: Instruction limit
% 8.40/1.68 % (395111)Termination phase: Property scanning
% 8.40/1.68 % (395111)Time elapsed: 0.019 s
% 8.40/1.68 % (395111)Peak memory usage: 11 MB
% 8.40/1.68 % (395111)Instructions burned: 97 (million)
% 8.40/1.68 % (395113)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2937510456:i=2186:rtra=on:ixr=off_2988 on theBenchmark for (2988ds/2186Mi)
% 8.40/1.68 % (395115)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2905035685:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2988 on theBenchmark for (2988ds/805Mi)
% 8.40/1.68 % (395114)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3343440331:s2a=on:i=240:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/240Mi)
% 8.40/1.68 % (395069) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-394890-395069"...
% 8.40/1.68 % (395114)Instruction limit reached!
% 8.40/1.68 % (395114)------------------------------
% 8.40/1.68 % (395114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395114)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395114)Termination reason: Instruction limit
% 8.40/1.68 % (395114)Termination phase: Saturation
% 8.40/1.68 % (395114)Time elapsed: 0.089 s
% 8.40/1.68 % (395114)Peak memory usage: 12 MB
% 8.40/1.68 % (395114)Instructions burned: 242 (million)
% 8.40/1.68 % (395086)Instruction limit reached!
% 8.40/1.68 % (395086)------------------------------
% 8.40/1.68 % (395086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395086)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395086)Termination reason: Instruction limit
% 8.40/1.68 % (395086)Termination phase: Saturation
% 8.40/1.68 % (395086)Time elapsed: 0.351 s
% 8.40/1.68 % (395086)Peak memory usage: 17 MB
% 8.40/1.68 % (395086)Instructions burned: 866 (million)
% 8.40/1.68 % (395119)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 8.40/1.68 % (395119)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=702233571:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2987 on theBenchmark for (2987ds/391Mi)
% 8.40/1.68 % (395119)Refutation not found, incomplete strategy
% 8.40/1.68 % (395119)------------------------------
% 8.40/1.68 % (395119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395119)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395119)Termination reason: Refutation not found, incomplete strategy
% 8.40/1.68 % (395119)Time elapsed: 0.011 s
% 8.40/1.68 % (395119)Peak memory usage: 12 MB
% 8.40/1.68 % (395119)Instructions burned: 28 (million)
% 8.40/1.68 % (395119)------------------------------
% 8.40/1.68 % (395119)------------------------------
% 8.40/1.68 % (395120)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2754122538:i=355:av=off:fsr=off:rtra=on:ixr=off_2987 on theBenchmark for (2987ds/355Mi)
% 8.40/1.68 % (395122)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=146518311:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/314Mi)
% 8.40/1.68 % (395115)Instruction limit reached!
% 8.40/1.68 % (395115)------------------------------
% 8.40/1.68 % (395115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395115)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395115)Termination reason: Instruction limit
% 8.40/1.68 % (395115)Termination phase: Saturation
% 8.40/1.68 % (395115)Time elapsed: 0.159 s
% 8.40/1.68 % (395115)Peak memory usage: 14 MB
% 8.40/1.68 % (395115)Instructions burned: 807 (million)
% 8.40/1.68 % (395122)Refutation not found, incomplete strategy
% 8.40/1.68 % (395122)------------------------------
% 8.40/1.68 % (395122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395122)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395122)Termination reason: Refutation not found, incomplete strategy
% 8.40/1.68 % (395122)Time elapsed: 0.021 s
% 8.40/1.68 % (395122)Peak memory usage: 12 MB
% 8.40/1.68 % (395122)Instructions burned: 59 (million)
% 8.40/1.68 % (395122)------------------------------
% 8.40/1.68 % (395122)------------------------------
% 8.40/1.68 % (395125)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=761076843:s2a=on:i=251:fsr=off:rtra=on_2986 on theBenchmark for (2986ds/251Mi)
% 8.40/1.68 % (395127)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=2931861293: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_2986 on theBenchmark for (2986ds/2470Mi)
% 8.40/1.68 % (395125)Instruction limit reached!
% 8.40/1.68 % (395125)------------------------------
% 8.40/1.68 % (395125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395125)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395125)Termination reason: Instruction limit
% 8.40/1.68 % (395125)Termination phase: Saturation
% 8.40/1.68 % (395125)Time elapsed: 0.049 s
% 8.40/1.68 % (395125)Peak memory usage: 12 MB
% 8.40/1.68 % (395125)Instructions burned: 251 (million)
% 8.40/1.68 % (395129)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=3146986499:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2986 on theBenchmark for (2986ds/673Mi)
% 8.40/1.68 % (395120)Instruction limit reached!
% 8.40/1.68 % (395120)------------------------------
% 8.40/1.68 % (395120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.40/1.68 % (395120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/1.68 % (395120)CaDiCaL version: 2.1.3
% 8.40/1.68 % (395120)Termination reason: Instruction limit
% 8.40/1.68 % (395120)Termination phase: Saturation
% 8.40/1.68 % (395069)...printing done.
% 8.40/1.68 % (395120)Time elapsed: 0.132 s
% 8.40/1.68 % (395120)Peak memory usage: 12 MB
% 8.40/1.68 % (395120)Instructions burned: 355 (million)
% 8.40/1.68 % (395069)Refutation found. Thanks to Tanya!
% 8.40/1.68 % SZS status ContradictoryAxioms for theBenchmark
% 8.40/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 10.14/1.71 % (395069)------------------------------
% 10.14/1.71 % (395069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.14/1.71 % (395069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.14/1.71 % (395069)CaDiCaL version: 2.1.3
% 10.14/1.71 % (395069)Termination reason: Refutation
% 10.14/1.71 % (395069)Time elapsed: 0.609 s
% 10.14/1.71 % (395069)Peak memory usage: 17 MB
% 10.14/1.71 % (395069)Instructions burned: 1543 (million)
% 10.14/1.71 % (394890)Success in time 1.453 s
% 10.14/1.71 % Vampire exiting
%------------------------------------------------------------------------------